causal hypothesis characteristics

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Causal Approaches to Scientific Explanation

This entry discusses some accounts of causal explanation developed after approximately 1990. For a discussion of earlier accounts of explanation including the deductive-nomological (DN) model, Wesley Salmon’s statistical relevance and causal mechanical models, and unificationist models, see the general entry on scientific explanation . Recent accounts of non-causal explanation will be discussed in a separate entry. In addition, a substantial amount of recent discussion of causation and causal explanation has been conducted within the framework of causal models. To avoid overlap with the entry on causal models we do not discuss this literature here.

Our focus in this entry is on the following three accounts – Section 1 those that focus on mechanisms and mechanistic explanations, Section 2 the kairetic account of explanation, and Section 3 interventionist accounts of causal explanation. All of these have as their target explanations of why or perhaps how some phenomenon occurs (in contrast to, say, explanations of what something is, which is generally taken to be non-causal) and they attempt to capture causal explanations that aim at such explananda. Section 4 then takes up some recent proposals having to do with how causal explanations may differ in explanatory depth or goodness. Section 5 discusses some issues having to do with what is distinctive about causal (as opposed to non-causal) explanations.

We also make the following preliminary observation. An account of causal explanation in science may leave open the possibility that there are other sorts of explanations of a non-causal variety (it is just that the account does not claim to capture these, at least without substantial modifications) or it may, more ambitiously, claim that all explanations of the why/how variety are, at least in some extended sense, causal. The kairetic model makes this latter claim, as do many advocates of mechanistic models. By contrast, interventionist models, need not deny that there are non-causal explanations, although the version described below does not attempt to cover such explanations. Finally, we are very conscious that, for reasons of space, we omitted many recent discussions of causal explanation from this entry. We provide brief references to a number of these at the end of this article (Section 6).

1. Mechanisms and Mechanistic Explanations

2. the kairetic account of explanation, 3. interventionist theories, 4. explanatory depth, 5. non-causal and mathematical explanation, 6. additional issues, other internet resources, related entries.

Many accounts of causation and explanation assign a central importance to the notion of mechanism. While discussions of mechanism are present in the early modern period, with the work of Descartes and others, a distinct and very influential research program emerged with the “new mechanist” approaches of the late twentieth and early twenty-first century. This section focuses on work in this tradition.

Wesley Salmon’s causal mechanical (CM) model of explanation (Salmon 1984) was an influential late twentieth century precursor to the work on mechanisms that followed. The CM model is described in the SEP entry on scientific explanation and readers are referred to this for details. For present purposes we just note the following. First, Salmon’s model is proposed as an alternative to the deductive-nomological (DN) model and the “new mechanist” work that follows also rejects the DN model, although in some cases for reasons somewhat different from Salmon’s. Like the CM model and in contrast to the DN model, the new mechanist tradition downplays the role of laws in explanation, in part because (it is thought) there are relatively few laws in the life sciences, which are the primary domain of application of recent work on mechanisms. Second, although Salmon provides an account of causal relationships that are in an obvious sense “mechanical”, he focuses virtually entirely on physical examples (like billiard ball collisions) rather than examples from the life sciences. Third Salmon presents his model as an “ontic” account of explanation, according to which explanations are things or structures in the world and contrasts this with what he regarded as “epistemic” accounts of explanation (including in his view, the DN model) which instead conceive of explanations as representations of what is in the world (Salmon 1984). This “ontic” orientation has been important in the work of some of the new mechanists, such as Craver (2007a), but less so for others. Finally, Salmon’s model introduces a distinction between the “etiological” aspects of explanation which have to do with tracing the causal history of some event E and the “constitutive” aspects which have to do with “the internal causal mechanisms that account for E ’s nature” (Salmon 1984: 275). This focus on the role of “constitution” is retained by a number of the new mechanists.

We may think of the “new mechanism” research program properly speaking as initiated by writers like Bechtel and Richardson (1993 [2010]), Glennan (1996, 1997), and Machamer, Darden, and Craver (2000). Although these writers provide accounts that differ in detail, [ 1 ] they share common elements: mechanisms are understood as causal systems, exhibiting a characteristic organization, with multiple causal factors that work together in a coordinated manner to produce some effect of interest. Providing a mechanistic explanation involves explaining an outcome by appealing to the causal mechanism that produces it. The components of a mechanism stand in causal relationships but most accounts conceptualize the relationship between these components and the mechanism itself as a part-whole or “constitutive relationship” – e.g., a human cell is constituted by various molecules, compounds and organelles, the human visual system is constituted by various visual processing areas (including V1–V5) and an automobile engine may be constituted by pistons, cylinders, camshaft and carburetor, among other components. Such part/whole relations are generally conceptualized as non-causal – that is, constitution is seen as a non-causal relationship. Thus, on these accounts, mechanisms are composed of or constituted by lower-level causal parts that interact together to produce the higher-level behavior of the (whole) mechanism understood as some effect of interest. This part-whole picture gives mechanistic explanation a partially reductive character, in the sense that higher-level outcomes characterizing the whole mechanism are explained by the lower-level causes that produce them. In many accounts this is depicted in nested, hierarchical diagrams describing these relations between levels of mechanisms (Craver 2007a).

Although philosophical discussion has often focused on the role of constitutive relations in mechanisms and how best to understand these, it is, as noted above, also common to think of mechanism as consisting of factors or components that stand in causal (“etiological”) relations to one another with accompanying characteristic spatial, temporal or geometrical organization. This feature of mechanism and mechanistic explanation is emphasized by Illari and Williamson (2010, 2012) and Woodward (2002, 2013). In particular, elucidating a mechanism is often understood as involving the identification of “mediating” factors that are “between” the input to the mechanism and its eventual output – “between” both in the sense of causally between and in the sense that the operation of these mediating factors often can be thought of as spatially and temporally between the input to the mechanism and its output. (The causal structure and the spatiotemporal structure thus “mirror” or run parallel to each other.) Often this information about intermediates can be thought of as describing the “steps” by which the mechanism operates over time. For example, mechanistic explanations of the action potential will cite the (anatomical) structure of the neural cell membrane, the relative location and structure of ion channels (in this membrane), ion types on either side of this membrane, and the various temporal steps in the opening and closing of ion channels that generate the action potential. A step-by-step description of this mechanism cites all of these parts and their interactions from the beginning of the causal process to the end. In this respect a description of a mechanism will provide more detail than, say, directed acyclic graphs which describe causal relations among variables but do not provide spatio-temporal or geometrical information.

A hotly debated issue in the literature on mechanisms concerns the amount of detail descriptions of mechanisms or mechanistic explanations need to contain. While some mechanists suggest that mechanisms (or their descriptions) can be abstract or lacking in detail (Levy & Bechtel 2012), it is more commonly claimed that mechanistic explanations must contain significant detail – perhaps as much “relevant” detail as possible or at least that this should be so for an “ideally complete description” of a mechanism (see Craver 2006 and the discussion in Section 4 ). Thus, a mere description of an input-output causal relation, even if correct, lacks sufficient detail to count as a description of a mechanism. For example, a randomized control trial can support the claim that drug X causes recovery Y , but this alone doesn’t elucidate the “mechanism of action” of the drug. Craver (2007a: 113–4) goes further, suggesting that even models that provide substantial information about anatomical structures and causal intermediaries are deficient qua mechanistic explanations if they omit detail thought to be relevant. For example, the original Hodgkin-Huxley (HH) model of the action potential identified a role for the opening and closing of membrane channels but did not specify the molecular mechanisms involved in the opening and closing of those channels. Craver (2006, 2007a, 2008) takes this to show that the HH model is explanatorily deficient – it is a “mechanism sketch” rather than a fully satisfactory mechanistic explanation. (This is echoed by Glennan who states that the monocausal model of disease – a one cause-one effect relationship – is “the sketchiest of mechanism sketches” [Glennan 2017: 226].) This “the more relevant detail the better” view has in turn been criticized by those who think that one can sometimes improve the quality of an explanation or at least make it no worse by omitting detail. For such criticism see, e.g., Batterman and Rice (2014), Levy (2014), Chirimuuta (2014), Ross (2015, 2020), etc. and for a response see by Craver and Kaplan (2020). [ 2 ]

The new mechanists differ among themselves in their views of causation and their attitudes toward general theories of causation found in the philosophical literature. Since a mechanism involves components standing in causal relations, one might think that a satisfactory treatment of mechanisms should include an account of what is meant by “causal relations”. Some mechanists have attempted to provide such an account. For example, Craver (2007a) appeals to elements of Woodward’s interventionist account of causation in this connection and for other purposes – e.g., to provide an account of constitutive relevance (Craver 2007b). By contrast, Glennan (1996, 2017) argues that the notion of mechanism is more fundamental than that of causation and that the former can be used to elucidate the latter – roughly, X causes Y when there is a mechanism connecting X to Y . Of course, for Glennan’s project this requires that mechanism is elucidated in a way that doesn’t appeal to the notion causation. Yet another view, inspired by Anscombe (1971) and advocated by Machamer, Darden, and Craver (MDC) (2000), Machamer (2004) and others, eschews any appeal to general theories of causation and instead describes the causal features of mechanism in terms of specific causal verbs. For example, according to MDC, mechanisms involve entities that engage in “activities”, with examples of the latter including “attraction”, “repulsion”, “pushing” and so on (MDC 2000: 5). It is contended that no more general account according to which these are instances of some common genus (causation) is likely to be illuminating. A detailed evaluation of this claim is beyond the scope of this entry, but we do wish to note that relatively general theories of causation that go beyond the cataloging of particular causal activities now flourish not just in philosophy but in disciplines like computer science and statistics (Pearl 2000 [2009]; Morgan & Winship, 2014) where they are often thought to provide scientific and mathematical illumination.

Another issue raised by mechanistic accounts concerns their scope. As we have seen these accounts were originally devised to capture a form of explanation thought to be widespread in the life sciences. This aspiration raises several questions. First, are all explanations in the life sciences “mechanistic” in the sense captured by some model of mechanistic explanation? Many new mechanists have answered this question in the affirmative but there has been considerable pushback to this claim, with other philosophers claiming that there are explanations in the life sciences that appeal to topological or network features (Lange 2013; Huneman 2010; Rathkopf 2018; Kostić 2020; Ross 2021b), to dynamical systems models (Ross 2015) and to other features deemed “non-mechanical” as with computational models in neuroscience (Chirimuuta 2014, 2018). This debate raises the question of how broadly it is appropriate to extend the notion of “mechanism” (Silberstein & Chemero 2013).

While the examples above are generally claimed to be non-causal and non-mechanistic, a further question is whether there are also types of causal explanation that are non-mechanistic. Answering this question depends, in part, on how “mechanism” is defined and what types of causal structures count as “mechanisms”. If mechanisms have the particular features mentioned above – part-whole relationships, some significant detail, and mechanical interactions – it would seem clear that some causal explanations are non-mechanistic in the sense that they cite causal systems and information with different features. For example, causal systems including pathways, networks, and cascades have been advanced as important types of causal structures that do not meet standard mechanism characteristics (Ross 2018, 2021a, forthcoming). Other examples include complex causal processes that lack machine-like and fixed causal parts (Dupré 2013). This work often questions whether “mechanism” fruitfully captures the diversity of causal structures and causal explanations that are present in scientific contexts.

There is an understandable tendency among mechanists to attempt to extend the scope of their accounts as far as possible but presumably the point of the original project was that mechanistic explanations have some distinctive features. Extending the models too far may lead to loss of sight of these. The problem is compounded by the fact that “mechanism” is used in many areas of science as general term of valorization or approval, as is arguably the case for talk of the “mechanism” of natural selection or of “externalizing tendencies” as a “mechanism” leading to substance abuse. The question is whether these candidates for mechanisms have enough in common with, say, the mechanism by which the action potential is produced to warrant the treatment of both by some common model. Of course, this problem also arises when one considers the extent to which talk of mechanisms is appropriate outside of the life sciences. Chemists talk of mechanisms of reaction, physicists of the Higgs mechanism, and economists of mechanism design, but again this raises the question of whether an account of mechanistic explanation should aspire to cover all of these.

This account is developed by Michael Strevens in his Depth (2008) and in a number of papers (2004, 2013, 2018). Strevens describes his theory as a “two factor” account (Strevens 2008: 4). The first factor – Strevens’ starting point – is the notion of causation or dependence (Strevens calls it “causal influence”) that figures in fundamental physics. Strevens is ecumenical about what this involves. He holds that a number of different philosophical treatments of causal influence – conserved quantity, counterfactual or interventionist – will fit his purposes. This notion of causal influence is then used as input to an account of causal explanation – Strevens’ second factor. A causal explanation of an individual event e (Strevens’ starting point) assembles all and only those causal influences that make a difference to (are explanatorily relevant to) e. A key idea here is the notion of causal entailment (Strevens 2008: 74). [ 3 ] A set of premises that causally entail that e occurs deductively entail this claim and do this in a way that “mirrors” the causal influences (ascertained from the first stage) leading to e . This notion of mirroring is largely left at an intuitive level but as an illustration a derivation of an effect from premises describing the cause mirrors the causal influences leading to the effect while the reverse derivation from effect to cause does not. However, more than mirroring is required for causal explanation: The premises in a causal entailment of the sort just described are subjected to a process (a kind of “abstraction”) in which premises that are not necessary for the entailment of e are removed or replaced with weaker alternatives that are still sufficient to entail e – the result of this being to identify factors which are genuinely difference-makers or explanatorily relevant to e . The result is what Strevens calls a “stand-alone” explanation for e (Strevens 2008: 70). (Explanatory relevance or difference-making is thus understood in terms of what, so to speak, is minimally required for causal entailment, constrained by a cohesiveness requirement described below, rather than, as in some other models of explanation, in terms of counterfactuals or statistical relevance.) As an illustration, if the event e is the shattering of a window the causal influences on e , identified from fundamental physics, will be extremely detailed and will consist of influences that affect fine grained features of e ’s occurrence, having to do, e.g., with exactly how the window shatters. But to the extent that the explanandum is just whether e occurs most of those details will be irrelevant in the sense that they will affect only the details of how the shattering occurs and not whether it occurs at all. Dropping these details will result in a derivation that still causally entails e. The causal explanation of e is what remains after all such details have been dropped and only what is necessary for the causal entailment of e is retained.

As Strevens is fully aware, this account faces the following apparent difficulty. There are a number of different causal scenarios that realize causes of bottle shatterings – the impact of rocks but also, say, sonic booms (cf. Hall 2012). In Strevens’ view, we should not countenance causal explanations that disjoin causal models that describe such highly different realizers, even though weakening derivations via the inclusion of such disjunctions may preserve causal entailment. Strevens’ solution appeals to the notion of cohesion ; when different processes serve as “realizers” for the causes of e , these must be “cohesive” in the sense that they are “causally contiguous” from the point of view of the underlying physics. Roughly, contiguous causal processes are those that are nearby or neighbors to one another in a space provided by fundamental physics. [ 4 ] Sonic booms and rock impacts do not satisfy this cohesiveness requirement and hence models involving them as disjunctive premises are excluded. Fundamental physics is thus the arbitrator of whether upper-level properties with different realizers are sufficiently similar to satisfy the cohesion requirement. Or at least this is so for deep “stand alone” explanations in contrast to those explanations that are “framework” dependent (see below).

As Strevens sees it, a virtue of his account is that it separates difficult (“metaphysical”) questions about the nature of the causal relationships (at least as these are found in physics which is Strevens’ starting point) from issues about causal explanation, which are the main focus of the kairetic account. It also follows that most of the causal claims that we consider in common sense and in science (outside of fundamental physics) are in fact claims about causal explanation and explanatory relevance as determined by the kairetic abstraction procedure rather than claims about causation per se. In effect when one claims that “aspirin causes headache relief” one is making a rather complicated causal explanatory claim about the upshot of the application of the abstraction procedure to the causal claims that, properly speaking, are provided by physics. This contrasts with an account in which causal claims outside of physics are largely univocal with causal claims (assuming that there are such) within physics.

We noted above that Strevens imposes a cohesiveness requirement on his abstraction procedure. This seems to have the consequence that upper-level causal generalizations that have realizers that are rather disparate from the point of view of the underlying physics are defective qua explainers, even though there are many examples of such generalizations that (rightly or wrongly) are regarded as explanatory. Strevens addresses this difficulty by introducing the notion of a framework – roughly a set of presuppositions for an explanation. When scientists “framework” some aspect of a causal story, they put that aspect aside (it is presupposed rather an explicit part of the explanation) and focus on getting the story right for the part that remains. A common example is to framework details of implementation, in effect black-boxing the low-level causal explanation of why certain parts of a system behave in the way they do. The resulting explanation simply presupposes that these parts do what they do, without attempting to explain why. Consequently, the black boxes in such explanations are not subject to the cohesion requirement, because they are not the locus of explanatory attention . Thus although explanations appealing to premises with disparate realizers are defective when considered by themselves as stand-alone explanations, we may regard such explanations as dependent on a framework with the framework incorporating information about a presupposed mechanism that satisfies the coherence constraint. [ 5 ] When this is the case, the explanation will be acceptable qua frameworked explanation. Nonetheless in such cases the explanation should in principle be deepened by making explicit the information presupposed in the framework.

Strevens describes his account as “descriptive” rather than “normative” in aspiration. Presumably, however, it is not intended as a description of the bases on which lay people or scientists come to accept causal explanations outside of fundamental physics – people don’t actually go through the abstraction from fundamental physics process that Strevens describes when they arrive at or reason about upper-level causal explanations. Instead, as we understand his account, it is intended to characterize something like what must be the case from the point of view of fundamental physics for upper-level causal judgments to be explanatory – the explanatory upper-level claims must fit with physics in the right way as specified in Strevens’ abstraction procedure and the accompanying cohesiveness constraint. [ 6 ] Perhaps then the account is intended to be descriptive in the sense that the upper-level causal explanations people regard as satisfactory do in fact satisfy the constraints he describes. In addition, the account is intended to be descriptive in the sense that it contends that as a matter of empirical fact people regard their explanations as committed to various claims about the underlying physics even if these claims are presently unknown – e.g., to claims about the cohesiveness of these realizers. [ 7 ] At the same time the kairetic account is also normative in the sense that it judges that explanations that fail to satisfy the constraints of the abstraction procedure are in some way unsatisfactory – thus people are correct to have the commitments described above.

Depth also contains an interesting treatment of the role of idealizations in explanation. It is often thought that idealizations involve the presence of “falsehoods”, or “distortions”. Strevens claims that these “false” features involve claims that do not have to do with difference-makers, in the sense captured by the abstraction procedure. Thus, according to the kairetic model, it does not matter if idealizations involve falsehoods or if they omit certain information since the falsehoods or omitted information do not concern difference-makers – their presence thus does not detract from the resulting explanation. Moreover, we can think of idealizations as conveying useful information about which factors are not difference-makers.

The kairetic account covers a great deal more that we lack the space to discuss including treatments of what Strevens calls “entanglement”, equilibrium explanations, statistical explanation and much else.

As is always the case with ambitious theories in philosophy, there have been a number of criticisms of the kairetic model. Here we mention just two. First, the kairetic model assumes that all legitimate explanation is causal or at least that all explanation must in some way reference or connect with causal information. (A good deal of the discussion in Depth is concerned to show that explanations that might seem to be non-causal can nonetheless be regarded as working by conveying causal information.) This claim that all explanation is causal is by no means an implausible idea – until recently it was widely assumed in the literature on explanation (Skow 2014). Nonetheless this idea has recently been challenged by a number of philosophers (Baker 2005; Batterman 2000, 2002, 2010a; Lange 2013, 2016; Lyon 2012; Pincock 2007). Relatedly, the kairetic account assumes that fundamental physics is “causal” – physics describes causal relations, and indeed lots of causal relations, enough to generate a large range of upper-level causal explanations when the abstraction procedure is applied. Some hold instead that the dependence relations described in physics are either not causal at all (causation being a notion that applies only to upper-level or macroscopic relationships) or else that these dependence relations lack certain important features (such as asymmetry) that are apparently present in causal explanatory claims outside of physics (Ney 2009, 2016). These claims about the absence of causation in physics are controversial but if correct, it follows that physics does not provide the input that Strevens’ account needs. [ 8 ]

A second set of issues concern the kairetic abstraction process. Here there are several worries. First, the constraints on this process have struck some as vague since they involve judgments of cohesiveness of realizers from the point of view of underlying physics. Does physics or any other science really provide a principled, objective basis for such judgments? Second, it seems, as suggested above, that upper-level causal explanations often generalize over realizers that are very disparate from the point of view of the underlying physics. Potochnik (2011, 2017) focuses on the example, also discussed by Strevens, of the Lotka-Volterra (LV) equations which are applied to a large variety of different organisms that stand in predator/prey relations. Strevens uses his ideas about frameworks to argue that use of the LV equations is in some sense justifiable, but it also appears to be a consequence of his account (and Strevens seems to agree) that explanations appealing to the LV equations are not very deep, considered as standalone explanations. But, at least as a descriptive matter, Potochnik claims, this does not seem to correspond to the judgments or practices of the scientists using these equations, who seem happy to use the LV equations despite the fact that they fail to satisfy the causal contiguity requirement. Potochnik thus challenges this portion of the descriptive adequacy of Strevens’ account. Of course, one might respond that these scientists ought to judge in accord with Strevens’ account, but as noted above, this involves taking the account to have normative implications and not as merely descriptive.

A more general form of this issue arises in connection with “universal” behavior (Batterman 2002). There are a number of cases in which physical and biological systems that are very different from one another in terms of their low-level realizers exhibit similar or identical upper-level behavior (Batterman 2002; Batterman & Rice 2014; Ross 2015). As a well-known example, substances as diverse as ferromagnets and various liquid/gas systems exhibit similar behavior around their critical points (Batterman 2000, 2002). Renormalization techniques are often thought to explain this commonality in behavior, but they do so precisely by showing that the physical details of these systems do not matter for (are irrelevant to) the aspects of their upper-level behavior of interest. The features of these systems that are relevant to their behavior have to do with their dimensionality and symmetry properties among others and this is revealed by the renormalization group analysis (RGA) (Batterman 2010b). One interesting question is whether we can think of that analysis as an instance of Strevens’ kairetic procedure. On the one hand the RGA can certainly be viewed as an abstraction procedure that discards non-difference-making factors. On the other hand, it is perhaps not so clear the RGA respects the cohesiveness requirements that Strevens proposes since the upshot is that systems that are very different at the level of fundamental physics are given a common explanation. That is, the RGA does not seem to work by showing (at least in any obvious way) that the systems to which it applies are contiguous with respect to the underlying physics. [ 9 ]

Another related issue is this: a number of philosophers claim that the RGA provides a non-causal explanation (Batterman 2002, 2010a; Reutlinger 2014). As we have seen, Strevens denies that there are non-causal explanations in his extended sense of “causal” but, in addition, if it is thought the RGA implements Strevens’ abstraction procedure, this raises the question of whether (contrary to Strevens’ expectations) this procedure can take causal information as input and yield a non-causal explanation as output. A contrary view, which may be Strevens’, is that as long as the explanation is the result of applying the kairetic procedure to causal input, that result must be causal.

The issue that we have been addressing so far has to do with whether causal contiguity is a defensible requirement to impose on upper-level explanations. There is also a related question – assuming that the requirement is defensible, how can we tell whether it is satisfied? The contiguity requirement as well as the whole abstraction procedure with which it is associated is characterized with reference to fundamental physics but, as we have noted, users of upper-level explanations usually have little or no knowledge of how to connect these with the underlying physics. If Strevens’ model is to be applicable to the assessment of upper-level explanations it must be possible to tell, from the vantage point of those explanations and the available information that surrounds their use, whether they satisfy the contiguity and other requirements but without knowing in detail how they connect to the underlying physics. Strevens clearly thinks this is possible (as he should, given his views) and in some cases this seems plausible. For example, it seems fairly plausible, as we take Strevens to assume, that predator/prey pairs consisting of lions and zebras are disparate from pairs consisting of spiders and house flies from the point of view of the underlying physics and thus constitute heterogeneous realizers of the LV equations. [ 10 ] On the other hand, in a case of pre-emption in which Billy’s rock shatters a bottle very shortly before Suzy’s rock arrives at the same space, Strevens seems committed to the claim that these two causal processes are non-contiguous – indeed he needs this result to avoid counting Suzy’s throw as a cause of the shattering [ 11 ] (Non-contiguity must hold even if the throws involve rocks with the same mass and velocity following very similar trajectories, differing only slightly in their timing.) In other examples, Strevens claims that airfoils of different flexibility and different materials satisfy the contiguity constraint, as do different molecular scattering processes in gases – apparently this is so even if the latter are governed by rather different potential functions (as they sometimes are) (Strevens 2008: 165–6). The issue here is not that these judgments are obviously wrong but rather that one would like to have a more systematic and principled story about the basis on which they are to be made.

That said, we think that Strevens has put his finger on an important issue that deserves more philosophical attention. This is that there is something explanatorily puzzling or incomplete about a stable upper-level generalization that appears to have very disparate realizers: one naturally wants a further explanation of how this comes about – one that does not leave it as a kind of unexplained coincidence that this uniformity of behavior occurs. [ 12 ] The RGA purports to do this for certain aspects of behavior around critical points and it does not seem unreasonable to hope for accounts (perhaps involving some apparatus very different from the RGA) for other cases. What is less clear is whether such an explanation will always appeal to causal contiguity at the level of fundamental physics – for example in the case of the RGA the relevant factors (and where causal contiguity appears to obtain) are relatively abstract and high-level, although certainly “physical”.

Interventionist theories are intended both as theories of causation and of causal explanation. Here we provide only a very quick overview of the former, referring readers to the entry causation and manipulability for more detailed discussion of the former and instead focus on causal explanation. Consider a causal claim (generalization) of the form

where “ C ” and “ E ” are variables – that is, they refer to properties or quantities that can take at least two values. Examples are “forces cause accelerations” and “Smoking causes lung cancer”. According to interventionist accounts (G) is true if and only if there is a possible intervention I such that if I were to change the value of C , the value of E or the probability distribution of E would change (Woodward 2003). The notion of an intervention is described in more detail in the causation and manipulability entry, but the basic idea is that this is an unconfounded experimental manipulation of C that changes E , if at all, via a route that goes through C and not in any other way. Counterfactuals that describe would happen if an intervention were to be performed are called interventionist counterfactuals . A randomized experiment provides one paradigm of an intervention.

Causal explanations can take several different forms within an interventionist framework [ 13 ] – for instance, a causal explanation of some explanandum \(E =e\) requires:

and also meeting the condition

By meeting these conditions (and especially in virtue of satisfying (3.3)) an explanation answers what Woodward (2003) calls “what-if-things-had-been-different questions” (w-questions) about E – it tells us how E would have been different under changes in the values of the C variable from the value specified in (3.2).

As an example, consider an explanation of why the strength (E) of the electrical field created by a long straight wire along which the charge is uniformly distributed is described by \(E= \lambda/2 \pi r \epsilon_{o}\) where \(\lambda\) is the charge density and \(r\) is the distance from the wire. An explanation of this can be constructed by appealing to Coulomb’s law (playing the role of (3.1) above) in conjunction with information about the shape of the wire and the charge distribution along it ( (3.2) above). This information allows for the derivation of \(E= \lambda/2 \pi r \epsilon_{o}\) but it also can be used to provide answers to a number of other w-questions. For example, Coulomb’s law and a similar modeling strategy can be used to answer questions about what the field would be if the wire had a different shape (e.g., if twisted to form a loop) or if it was somehow flattened into a plane or deformed into a sphere.

The condition that the explanans answer a range of w-questions is intended to capture the requirement that the explanans must be explanatorily relevant to the explanandum. That is, factors having to do with the charge density and the shape of the conductor are explanatorily relevant to the field intensity because changes in these factors would lead to changes in the field intensity. Other factors such as the color of the conductor are irrelevant and should be omitted from the explanation because changes in them will not lead to changes in the field intensity. As an additional illustration, consider Salmon’s (1971a: 34) example of a purported explanation of ( F ) a male’s failure to get pregnant that appeals to his taking birth control pills ( B ). Intuitively ( B ) is explanatorily irrelevant to ( F ). The interventionist model captures this by observing that B fails to satisfy the what-if-things-had-been-different requirement with respect to F : F would not change if B were to change. (Note the contrast with the rather different way in which the kairetic model captures explanatory relevance.)

Another key idea of the interventionist model is the notion of invariance of a causal generalization (Woodward & Hitchcock 2003). Consider again a generalization (G) relating \(C\) to \(E\), \(E= f(C)\). As we have seen, for (G) to describe a causal relationship at all it must at least be the case that (G) correctly tells how E would change under at least some interventions on C . However, causal generalizations can vary according to the range of interventions over which this is true. It might be that (G) correctly describes how E would change under some substantial range R of interventions that set C to different values or this might instead be true only for some restricted range of interventions on C . The interventions on C over which (G) continues to hold are the interventions over which (G) is invariant. As an illustration consider a type of spring for which the restoring force F under extensions X is correctly described by Hooke’s law:

for some range R of interventions on X . Extending the spring too much will cause it to break so that its behavior will no longer be described by Hooke’s law. (3.4) is invariant under interventions in R but not so for interventions outside of R . (3.4) is, intuitively, invariant only under a somewhat narrow range of interventions. Contrast (3.4) with the gravitational inverse square law:

(3.5) is invariant under a rather wide range of interventions that set \(m_1,\) \(m_2,\) and \(r\) to different values but there are also values for these variables for which (3.5) fails to hold – e.g., values at which general relativistic effects become important. Moreover, invariance under interventions is just one variety of invariance. One may also talk about the invariance of a generalization under many other sorts of changes – for example, changes in background conditions, understood as conditions that are not explicitly included in the generalization itself. As an illustration, the causal connection between smoking and lung cancer holds for subjects with different diets, in different environmental conditions, with different demographic characteristics and so on. [ 14 ] However, as explained below, it is invariance under interventions that is most crucial to evaluating whether an explanation is good or deep within the interventionist framework.

Given the account of causal explanation above it follows that for a generalization to figure in a causal explanation it must be invariant under at least some interventions. As a general rule a generalization that is invariant under a wider range of interventions and other changes will be such that it can be used to answer a wider range of w-questions. (See section 4 below.) In this respect such a generalization might be regarded as having superior explanatory credentials – it at least explains more than generalizations with a narrower range of invariance. Generalizations that are invariant under a very wide range of interventions and that have the sort of mathematical formulation that allows for precise predictions are those that we tend to regard as laws of nature. Generalizations that have a narrower range of invariance like Hooke’s “law” capture causal information but are not plausible candidates for laws of nature. An interventionist model of form (3.1–3.3) above thus requires generalizations with some degree of invariance or relationships that support interventionist counterfactuals, but it does not require laws. In this respect, like the other models considered in this entry, it departs from the DN model which does require laws for successful explanation (see the entry on scientific explanation ).

Turning now to criticisms of the interventionist model, some of these are also criticisms of interventionist accounts of causation. Several of these (and particularly the delicate question of what it means for an intervention to be “possible”) are addressed if not resolved in the causation and manipulability entry.

Another criticism, not addressed in the above entry, concerns the “truth makers” or “grounds” for the interventionist counterfactuals that figure in causal explanation. Many philosophers hold that it is necessary to provide a metaphysical account of some kind for these. There are a variety of different proposals – perhaps interventionist counterfactuals or causal claims more generally are made true by “powers” or “dispositions”. Perhaps instead such counterfactuals are grounded in laws of nature, with the latter being understood in terms of some metaphysical framework, as in the Best Systems Analysis. For the most part interventionists, have declined to provide truth conditions of this sort and this has struck some metaphysically minded philosophers as a serious omission. One response is that while it certainly makes sense to ask for deeper explanations of why various interventionist counterfactuals hold, the only explanation that is needed is an ordinary scientific explanation in terms of some deeper theory, rather than any kind of distinctively “metaphysical” explanation (Woodward 2017b). For example, one might explain why the interventionist counterfactual “if I were to drop this bottle it will fall to the ground” is true by appealing to Newtonian gravitational theory and “grounding” it in this way. (There is also the task of providing a semantics for interventionist counterfactuals and here there have been a variety of proposals – see, e.g., Briggs 2012. But again, this needn’t take the form of providing metaphysical grounding.) This response raises the question of whether in addition to ordinary scientific explanations there are metaphysical explanations (of counterfactuals, laws and so on) that it is the task of philosophy to provide – a very large topic that is beyond the scope of this entry.

Yet another criticism (pressed by Franklin-Hall 2016 and Weslake 2010) is that the w-condition implies that explanations at the lowest level of detail are always superior to explanations employing upper-level variables – the argument being that lower-level explanations will always answer more w-questions than upper-level explanations. (But see Woodward (2021) for further discussion.)

Presumably all models of causal explanation (and certainly all of the models considered above) agree that a causal explanation involves the assembly of causal information that is relevant to the explanandum of interest, although different models may disagree about how to understand causation, causal relevance, and exactly what causal information is needed for explanation. There is also widespread agreement (at least among the models considered above) that causal explanations can differ in how deep or good they are. Capturing what is involved in variations in depth is thus an important task for a theory of causal explanation (or for that matter, for any theory of explanation, causal or non-causal). Unsurprisingly different treatments of causal explanation provide different accounts of what explanatory depth consists in. One common idea is that explanations that drill down (provide information) about lower-level realizing detail are (to that extent) better – this is taken to be one dimension of depth even if not the only one.

This idea is discussed by Sober (1999) in the context of reduction, multiple realizability, and causal explanations in biology. Sober suggests that lower-level details provide objectively superior explanations compared to higher-level ones and he supports this in three main ways. First, he suggests that for any explanatory target, lower-level details can always be included without detracting from an explanation. The worst offense committed by this extra detail is that it “explains too much,” while the same cannot be said for higher-level detail (Sober 1999: 547). Second, Sober claims that lower-level details do the “work” in producing higher-level phenomena and that this justifies their privilege or priority in explanations. A similar view is expressed by Waters, who claims that higher-level detail, while more general, provides “shallow explanations” compared to the “deeper accounts” provided by lower-level detail (1990: 131). A third reason is that physics has a kind of “causal completeness” that other sciences do not have. It is argued that this causal completeness provides an objective measure of explanatory strength, in contrast to the more “subjective” measures sometimes invoked in defenses of the explanatory credentials of upper level-sciences. As Sober (1999: 561) puts it,

illumination is to some degree in the eye of the beholder; however, the sense in which physics can provide complete explanations is supposed to be perfectly objective.

Furthermore,

if singular occurrences can be explained by citing their causes, then the causal completeness of physics [ensures] that physics has a variety of explanatory completeness that other sciences do not possess. (1999: 562)

Cases where some type-level effect (e.g., a disease) has a shared causal etiology at higher-levels, but where this etiology is multiply-realized at lower ones present challenges for such views (Ross 2020). In Sober’s example, “smoking causes lung cancer” is a higher-level (macro) causal relationship. He suggests that lower-level realizers of smoking (distinct carcinogens) provide deeper explanations of this outcome. One problem with this claim is that any single lower-level carcinogen only “makes a difference to” and explains a narrow subset of all cases of the disease. By contrast, the higher-level causal factor “smoking” makes a difference to all (or most) cases of this disease. This is reflected in the fact that biomedical researchers and nonexperts appeal to smoking as the cause of lung cancer and explicitly target smoking cessation in efforts to control and prevent this disease. This suggests that there can be drawbacks to including too much lower-level detail.

The kairetic theory also incorporates, in some respects, the idea that explanatory depth is connected to tracking lower-level detail. This is reflected in the requirement that deeper explanations are those that are cohesive with respect to fundamental physics – at the very least we will be in a better position to see that this requirement is satisfied when there is supporting information about low-level realizers. [ 15 ] On the other hand, as we have seen, the kairetic abstraction procedure taken in itself pushes away from the inclusion of specific lower-level detail in the direction of greater generality which, in some form or other, is also regarded by most as a desirable feature in explanations, the result being a trade-off between these two desiderata. The role of lower-level detail is somewhat different in mechanistic models since in typical formulations generality per se is not given independent weight, and depth is associated with the provision of more rather than less relevant detail. Of course a great deal depends on what is meant by “relevant detail”. As noted above, this issue is taken up by Craver in several papers, including most recently, Craver and Kaplan (2020) who discuss what they call “norms of completeness” for mechanistic explanations, the idea being that there needs to be some “stopping point” at which a mechanistic explanation is complete in the sense that no further detail needs to be provided. Clearly, whatever “relevant detail” in this connection means it cannot mean all factors any variation in which would make a difference to some feature of the phenomenon P which is the explanatory target. After all, in a molecular level explanation of some P , variations at the quantum mechanical level – say in the potential functions governing the behavior of individual atoms will often make some difference to P , thus requiring (on this understanding of relevance) the addition of this information. Typically, however, such an explanation is taken by mechanists to be complete just at the molecular level – no need to drill down further. Similarly, from a mechanistic point of view an explanation T of the behavior of a gas in terms of thermodynamic variables like pressure and temperature is presumably less than fully adequate since the gas laws are regarded by some if not most mechanists as merely “phenomenological” and not as describing a mechanism. A statistical mechanical explanation (SM) of the behavior of the gas is better qua mechanistic explanation but ordinarily such explanations don’t advert to, say, the details of the potentials (DP) governing molecular interactions, even though variations in these would make some difference to some aspects of the behavior of the gas. The problem is thus to describe a norm of completeness that allows one to say that SM is superior to T without requiring DP rather than SM. Craver and Kaplan’s discussion (2020) is complex and we will not try to summarize it further here except to say that it does try to find this happy medium of capturing how a norm of completeness can be met, despite its being legitimate to omit some detail.

A closely related issue is this: fine-grained details can be relevant to an explanandum in the sense that variations in those details may make a difference to the explanandum but it can also be the case that those details sometimes can be “screened off” from or rendered conditionally irrelevant to this explanandum (or approximately so) by other, more coarse grained variables that provide less detail, as described in Woodward 2021. For example, thermodynamic variables can approximately screen off statistical mechanical variables from one another. In such a case is it legitimate to omit (do norms about completeness permit omitting) the more fine-grained details as long as the more coarse-grained but screening off detail is included?

Interventionist accounts, at least in the form described by Woodward (2003), Hitchcock and Woodward (2003) offer a somewhat different treatment of explanatory depth. Some candidate explanations will answer no w-questions and thus fail to be explanatory at all. Above this threshold explanations may differ in degree of goodness or depth, depending on the extent to which they provide more rather than less information relevant to answering w-questions about the explanandum – and thus more information about what the explanandum depends on. For example, an explanation of the behavior of a body falling near the earth’s surface in terms of Galileo’s law \(v=gt\) is less deep than an explanation in terms of the Newtonian law of gravitation since the latter makes explicit how the rate of fall depends on the mass of the earth and the distance of the body above the earth’s surface. That is, the Newtonian explanation provides answers to questions about how the velocity of the fall would have been different if the mass of the earth had been different, if the body was falling some substantial distance away from the earth’s surface and so on, thus answering more w-questions than the explanation appealing to Galileo’s law.

This account associates generality with explanatory depth but this connection holds only for a particular kind of generality. Consider the conjunction of Galileo’s law and Boyle’s law. In one obvious sense, this conjunction is more general than either Galileo’s law or Boyle’s law taken alone – more systems will satisfy either the antecedent of Galileo’s law or the antecedent of Boyle’s law than one of these generalizations alone. On the other hand, given an explanandum having to do with the pressure P exerted by a particular gas, the conjunctive law will tell us no more about what P depends on than Boyle’s law by itself does. In other words, the addition of Galileo’s law does not allow us to answer any additional w-questions about the pressure than are answered by Boyle’s law alone. For this reason, this version of interventionism judges that the conjunctive law does not provide a deeper explanation of P than Boyle’s law despite the conjunctive law being in one sense more general (Hitchcock & Woodward 2003).

To develop this idea in a bit more detail, let us say that the scope of a generalization has to do with the number of different systems or kinds of systems to which the generalization applies (in the sense that the systems satisfy the antecedent and consequents of the generalization). Then the interventionist analysis claims that greater scope per se does not contribute to explanatory depth. The conjunction of Galileo’s and Boyle’s law has greater scope than either law alone, but it does not provide deeper explanations.

As another, perhaps more controversial, illustration consider a set of generalizations N1 that successfully explain (by interventionist criteria) the behavior of a kind of neural circuit found only in a certain kind K of animal. Would the explanatory credentials of N1 or the depth of the explanations it provides be improved if this kind of neural circuit was instead found in many different kinds of animals or if N1 had many more instances? According to the interventionist treatment of depth under consideration, the answer to this question is “no” (Woodward 2003: 367). Such an extension of the application of N1 is a mere increase in scope. Learning that N1 applies to other kinds of animals does not tell us anything more about what the behavior of the original circuit depends on than if N1 applied just to a single kind of animal.

It is interesting that philosophical discussions of the explanatory credentials of various generalizations often assume (perhaps tacitly) that greater scope (or even greater potential scope in the sense that there are possible – perhaps merely metaphysically possible – but not actual systems to which the generalization would apply) per se contributes to explanatory goodness. For example, Fodor and many others argue for the explanatory value of folk psychology on the grounds that its generalizations apply not just to humans but would apply to other systems with the appropriate structure were these to exist (perhaps certain AI systems, Martians if appropriately similar to humans etc.) (Fodor 1981: 8–9). The interventionist treatment of depth denies there is any reason to think the explanatory value of folk psychology would be better in the circumstances imagined above than if it applied only to humans. As another illustration, Weslake (2010) argues that upper-level generalizations can provide better or deeper explanations of the same explananda than lower-level generalizations if there are physically impossible [but metaphysically possible] systems to which the upper-level explanation applies but to which the lower-level explanation does not (2010: 287), the reason being that in such cases the upper- level explanation is more general in the sense of applying to a wider variety of systems. Suppose for example, that for some systems governed by the laws of thermodynamics, the underlying micro theory is Newtonian mechanics and for other “possible” or actual systems governed by the same thermodynamic laws, the correct underlying micro-theory is quite different. Then, according to Weslake, thermodynamics provides a deeper explanation than the either of the two micro-theories. This is also an argument that identifies greater depth with greater scope. The underlying intuition about depth here is, so to speak, the opposite of Strevens’ since he would presumably draw the conclusion that in this scenario the generalizations of thermodynamics would lack causal cohesion if the different realizing microsystems were actual.

This section has focused on recent discussion of the roles played by the provision of more underlying detail, and generality (in several interpretations of that notion) in assessments of the depth of causal explanation. It is arguable that there are a number of other dimensions of depth that we do not discuss – readers are referred to Glymour (1980), Wigner (1967), Woodward (2010), Deutsch (2011) among many others.

We noted above that there has been considerable recent interest in the question of whether there are non-causal explanations (of the “why” variety) or whether instead all explanations are causal. Although this entry does not discuss non-causal explanations in detail, this issue raises the question of whether there is anything general that might be said about what makes an explanation “causal” as opposed to “non-causal”. In what follows we review some proposals about the causal/non-causal contrast, including ideas that abstract somewhat from the details of the theories described in previous sections.

We will follow the philosophical literature on this topic by focusing on candidate explanations that target empirical explananda within empirical science but (it is claimed) explain these non-causally. These contrast with explanations within mathematics, as when some mathematical proofs are regarded as explanatory (of mathematical facts). Accounts of non-causal explanation in empirical science typically focus on explanatory factors that seem “mathematical”, that abstract from lower-level causal details, and/or that are related to the explanatory target via dependency relations that are (in some sense) non-empirical, even though the explanatory target appears to be an empirical claim. A common suggestion is that explanations exhibiting one or more of these features, qualify as non-causal. Purported examples include appeals to mathematical facts to explain various traits in biological systems, such as the prime-number life cycles of cicadas, the hexagonal-shape of the bee’s honeycomb, and the fact that seeds on a sunflower head are described by the golden angle (Baker 2005; Lyon & Colyvan 2008; Lyon 2012). An additional illustration is Lange’s claim (e.g., 2013: 488) that one can explain why 23 strawberries cannot be evenly divided among three children by appealing to the mathematical fact that 23 is not evenly divisible by three. It is claimed that in these cases, explaining the outcome of interest requires appealing to mathematical relationships, which are distinct from causal relationships, in the sense that the former are non-contingent and part of some mathematical theory (e.g., arithmetic, geometry, graph theory, calculus) or a consequence of some mathematical axiom system.

A closely related idea is that in addition to appealing to mathematical relationships, non-causal explanations abstract from lower-level detail, with the implication that although these details may be causal, they are unnecessary for the explanation which is consequently taken to be non-causal. The question of whether it is possible to traverse each bridge in the city of Königsberg exactly once (hereafter just “traverse”) is a much-discussed example. Euler provided a mathematical proof that whether such traversability is possible depends on higher-level topological or graph-theoretical properties concerning the connectivity of the bridges, as opposed to any lower-level causal details of the system (Euler 1736 [1956]; Pincock 2012). This explanatory pattern is similar to other topological or network explanations in the literature, which explain despite abstracting from lower-level causal detail (Huneman 2012; Kostic 2020; Ross 2021b). Other candidates for non-causal explanations are minimal model explanations, in which the removal of at least some or perhaps all causal detail is used to explain why systems which differ microphysically all exhibit the same behavior in some respects (Batterman 2002; Chirimuuta 2014; Ross 2015; and the entry on models in science ).

Still other accounts (not necessarily inconsistent with those described above) attempt to characterize some non-causal explanations in terms of the absence of other features (besides those described above). Woodward (2018) discusses two types of cases.

An example of (5.1) is a purported explanation relating the possibility of stable planetary orbits to the dimensionality of space – given natural assumptions, stable orbits are possible in a three-dimensional space but not possible in a space of dimensionality greater than three, so that the possibility of stable orbits in this sense seems to depend on the dimensionality of space. (For discussion see Ehrenfest 1917; Büchel 1963 [1969]; Callendar 2005). Assuming it is not possible to intervene to change the dimensionality of space, this explanation (if that is what it is) is treated as non-causal within an interventionist framework because of this impossibility. In other words, the distinction between explanations that appeal to factors that are targets of possible interventions and those that appeal to factors that are not targets of possible interventions is taken to mark one dividing line between causal and non-causal explanations.

In the second set of cases (5.2) , there are factors cited in the explanans that can be changed under interventions but the relationship between this property and the explanandum is non-contingent and “mathematical”. For example, it is certainly possible to intervene to change the configuration of bridges in Königsberg and in this way to change their traversability but the relation between the bridge configuration and their traversability is, as we have seen, non-contingent. Many of the examples mentioned earlier – the cicada, honeybee, and sunflower cases – are similar. In these cases, the non-contingent character of the dependency relation between explanans and explanandum is claimed to mark off these explanations as non-causal.

A feature of many of the candidates for non-causal explanation discussed above (and arguably another consideration that distinguishes causal from non-causal explanations) is that the non-causal explanations often seem to explain why some outcome is possible or impossible (e.g., why stable orbits are possible or impossible in spaces of different dimensions, why it is possible or not to traverse various configurations of bridges). By contrast it seems characteristic of causal explanations that they are concerned with a range of outcomes all of which are taken to be possible and instead explain why one such outcome in contrast to an alternative is realized (why an electric field has a certain strength rather than some alternative strength.)

While many have taken the above examples to represent clear cases of non-causal, mathematical explanation, others have argued that these explanations remain causal through-and-through. One example of this expansive position about causal explanation is Strevens (2018). According to Strevens, the Königsberg and other examples are cases in which mathematics plays a merely representational role, for example the role of representing difference-makers that dictate the movement of causal processes in the world. Strevens refers to these as “non-tracking” explanations, which identify limitations on causal processes that can explain their final outcome, but not the exact path taken to them (Strevens 2018: 112). For Strevens the topological structure represented in the Königsberg’s case captures information about causal structure or the web of causal influence – in this way the information relevant to the explanation, although abstract, is claimed to be causal. While this argument is suggestive, one open question is how the kairetic account can capture the fact that some of these cases involve explanations of impossibilities, where the source of the impossibility is not obviously “structural” (Lange 2013, 2016). For example, the impossibility of evenly dividing 23 by 3 does not appear to be a consequence of the way in which a structure influences some causal process. [ 16 ]

In addition to the examples and considerations just described, the philosophical literature contains many other proposed contrasts between causal and non-causal explanations, with accompanying claims about how to classify particular cases. For example, Sober (1983) claims that “equilibrium explanations” are non-causal. These are explanations in which an outcome is explained by showing that, because it is an equilibrium (or better, a unique equilibrium) , any one of a large number of different more specific processes would have led to that outcome. As an illustration, for sexually reproducing populations meeting certain additional conditions (see below), natural selection will produce an equilibrium in which there are equal numbers of males and females, although the detailed paths by which this outcome is produced (which conception events lead to males or females) will vary on different occasions. The underlying intuition here is that causal explanations are those that track specific trajectories or concrete processes, while equilibrium explanations do not do this. By contrast the kairetic theory treats at least some equilibrium explanations as causal in an extended sense (Strevens 2008: 267). Interventionist accounts at least in form described in Woodward (2003) also take equilibrium explanations to be causal to the extent that information is provided about what the equilibrium itself depends on. (That is, the interventionist framework takes the explanandum to be why this equilibrium rather than some alternative equilibrium obtains.) For example, the sex ratio equilibrium depends on such factors as the amount of parental investment required to produce each sex. Differences in required investment can lead to equilibria in which there are unequal numbers of males and females. On interventionist accounts, parental investment is thus among the causes of the sex ratio because it makes a difference for which equilibrium is realized. Interventionist accounts are able to reach this conclusion because they treat relatively “abstract” factors like parental investment as causes as long as interventions on these are systematically associated with associated with changes in outcomes. Thus, in contrast to some of the accounts described above, interventionism does not regard the abstractness per se of an explanatory factor as a bar to interpreting it as causal.

There has also been considerable discussion of whether computational explanations of the sort found in cognitive psychology and cognitive neuroscience that relate inputs to outputs via computations are causal or mechanistic. Many advocates (Piccinini 2006; Piccinini & Craver 2011) of mechanistic models of explanation have regarded such explanations as at best mechanism sketches, since they say little or nothing about realizing (e.g., neurobiological) detail. Since these writers tend to treat “mechanistic explanation”, “causal explanation” and even “explanation” as co-extensional, at least in the biomedical sciences, they seem to leave no room for a notion of non-causal explanation. By contrast computational explanations count as causal by interventionist lights as long as they correctly describe how outputs vary under interventions on inputs (Rescorla 2014). But other analyses of computational models suggest that they are similar to non-causal forms of explanation (Chirimuuta 2014, 2018).

Besides the authors discussed above, there is a great deal of additional recent work related to causal explanation that we lack the space to discuss. For additional work on the role of abstraction and idealization in causal explanation (and whether the presence of various sorts of abstraction and idealization in an explanation implies that it is non-causal) see Janssen and Saatsi (2019), Reutlinger and Andersen (2016), Blanchard (2020), Rice (2021), and Pincock (2022). Another set of issues that has received a great deal of recent attention concerns causal explanation in contexts in which different “levels” are present (Craver & Bechtel 2007; Baumgartner 2010; Woodward 2020) This literature addresses questions of the following sort. Can there be “upper-level” causation at all or does all causal action occur at some lower, microphysical level, with upper-level variables being casually inert? Can there be “cross-level” causation – e.g., “downward” causation from upper to lower levels? Finally, in addition to the work on explanatory depth discussed in Section 4 , there has been a substantial amount of recent work on distinctions among different sorts of causal claims (Woodward 2010; Ross 2021a; Ross & Woodward 2022) and on what makes some causes more explanatorily significant than others (e.g., Potochnik 2015).

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causal models | causation: and manipulability | causation: regularity and inferential theories of | mathematical: explanation | models in science | scientific explanation

Acknowledgments

Thanks to Carl Craver, Michael Strevens and an anonymous referee for helpful comments on a draft of this entry.

Copyright © 2023 by Lauren Ross < rossl @ uci . edu > James Woodward < jfw @ pitt . edu >

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Assessing causality in epidemiology: revisiting Bradford Hill to incorporate developments in causal thinking

Michal shimonovich.

1 MRC/CSO Social and Public Health Sciences Unit, University of Glasgow, Glasgow, UK

Anna Pearce

Hilary thomson, katherine keyes.

2 Mailman School of Public Health, Columbia University, New York, NY USA

Srinivasa Vittal Katikireddi

The nine Bradford Hill (BH) viewpoints (sometimes referred to as criteria) are commonly used to assess causality within epidemiology. However, causal thinking has since developed, with three of the most prominent approaches implicitly or explicitly building on the potential outcomes framework: directed acyclic graphs (DAGs), sufficient-component cause models (SCC models, also referred to as ‘causal pies’) and the grading of recommendations, assessment, development and evaluation (GRADE) methodology. This paper explores how these approaches relate to BH’s viewpoints and considers implications for improving causal assessment. We mapped the three approaches above against each BH viewpoint. We found overlap across the approaches and BH viewpoints, underscoring BH viewpoints’ enduring importance. Mapping the approaches helped elucidate the theoretical underpinning of each viewpoint and articulate the conditions when the viewpoint would be relevant. Our comparisons identified commonality on four viewpoints: strength of association (including analysis of plausible confounding); temporality; plausibility (encoded by DAGs or SCC models to articulate mediation and interaction, respectively); and experiments (including implications of study design on exchangeability). Consistency may be more usefully operationalised by considering an effect size’s transportability to a different population or unexplained inconsistency in effect sizes (statistical heterogeneity). Because specificity rarely occurs, falsification exposures or outcomes (i.e., negative controls) may be more useful. The presence of a dose-response relationship may be less than widely perceived as it can easily arise from confounding. We found limited utility for coherence and analogy. This study highlights a need for greater clarity on BH viewpoints to improve causal assessment.

Introduction

Causal assessment is fundamental to epidemiology as it may inform policy and practice to improve population health. A leading figure in epidemiology, Sir Austin Bradford Hill, suggested the goal of causal assessment is to understand if there is “any other way of explaining the set of facts before us … any other answer equally, or more, likely than cause and effect” [ 1 ]. Causal assessment may be applied to a body of evidence or a single study to interrogate the “set of facts” underlying a relationship. Bradford Hill notably laid out a set of such facts. Although commonly described as Bradford Hill criteria, he described them as ‘viewpoints’ and emphasised they should not be used as a checklist, but as considerations for assessing causality. As a result, we refer to them as ‘BH viewpoints’ [ 2 ].

Since Bradford Hill first introduced his viewpoints, causal thinking in epidemiology has increasingly incorporated the potential outcomes framework [ 3 – 8 ]. Informally, the potential outcomes framework posits that a true causal effect is the difference between the observed outcome when the individual was exposed and the unobserved potential outcome had the individual not been exposed, all other things being equal [ 6 ]. Because the unobserved potential outcome of an individual cannot be known, investigators often compare the outcomes of exposed and unexposed groups [ 6 ]. Application of the potential outcomes framework asks investigators to consider exchangeability between these groups i.e., if the unexposed group would have the same risk of the outcome as the exposed group had they also been exposed [ 6 ]. In practice, this means considering if groups are comparable. Investigators may be more confident that the observed effect equals the true causal effect if the groups are exchangeable [ 9 ].

We focus on three approaches that implicitly or explicitly incorporate the potential outcomes framework but operationalise it differently [ 4 , 10 – 12 ]. Firstly, directed acyclic graphs (DAGs) help articulate assumptions about the interrelationships between variables of interest and therefore threats to valid causal inference. Sufficient-component cause (SCC) models highlight the multi-factorial nature of causality, drawing attention to how different exposures interact to produce the outcome. Finally, the Grading of Recommendations, Assessment, Development and Evaluation (GRADE) methodology provides a systematic approach to assessing the certainty of a causal relationship based on a body of evidence (i.e., the existing studies available used to assess whether a causal relationship between an exposure and outcome exists). Epidemiologists have proposed that causal assessment may be improved by combining approaches such as these [ 7 , 13 – 15 ].

To draw on the strengths of each of these potential outcomes framework approaches, we compared the extent to which they overlap or complement each other. There is limited literature comparing the potential outcomes framework in SCC models and DAGs [ 4 , 5 , 11 ] and one study comparing BH viewpoints to GRADE [ 10 ]. While BH viewpoints have been revisited to critically reflect on the theory and application of each viewpoint [ 2 , 16 – 20 ], we have not identified any attempts to compare it to DAGs and SCC models, with the former particularly important given the growing influence of DAGs in epidemiology [ 21 ].

Our main aims are to examine: 1) if and how each BH viewpoint is considered by each of the three potential outcomes framework approaches (referred to simply as ‘approaches’ hereafter); and 2) the extent they elucidate the underpinning theory of BH viewpoints. BH viewpoints serve as the foundation for this comparison because of its influential status within epidemiology [ 19 , 20 , 22 ]. Additionally, there is agreement in the literature that the BH viewpoints account for the most relevant considerations in causal assessment [ 17 ]. To facilitate comparisons, we drew DAGs and SCC models for each BH viewpoint and mapped each BH viewpoint against each GRADE domain. We use the example of alcohol consumption and active-tuberculosis where relevant to illustrate the elements of each approach. Mycobacterium tuberculosis (MTB) is the bacterium responsible for tuberculosis (TB). MTB causes latent-TB, which can turn into active-TB in individuals with low immunity [ 23 ]. Alcohol consumption is hypothesised to cause a weaker immune system, resulting in active-TB [ 24 ]. The example is purposefully simplified and may not reflect real-world scenarios.

In the next section, we summarise the BH viewpoints and key characteristics of the three approaches they are being compared against. Our aim is to introduce the commonalities and distinctions within these approaches as approaches to causal inference, rather than to provide a detailed explanation or critical assessment of each approach. Following this, we compare each of the nine BH viewpoints against the three approaches and critically reflect on the theoretical implications for assessing causal relationships. We finish by summarising our key findings, make tentative suggestions about how causal assessment could be conducted in the future and note some areas for future research.

Causal assessment approaches

Bradford hill viewpoints.

Bradford Hill’s explanation of the nine viewpoints is summarised in Table ​ Table1. 1 . These were not intended to be “hard and fast rules of evidence that must be obeyed before we accept cause and effect,” but characteristics to keep in mind while considering if an observed association is due to something other than causality [ 1 ]. In current practice, BH viewpoints are applied together or separately to a body of evidence or a single empirical study.

Bradford Hill viewpoints and explanatory quotations

Directed acyclic graphs

DAGs are diagrams that illustrate the putative causal relationship between an exposure and outcome [ 6 ]. DAGs include the variables that might bias the relationship in question and their development is based on background knowledge of the topic [ 25 ]. Detailed explanations of DAGs can be found elsewhere [ 5 , 6 , 25 – 27 ]. DAGs are commonly applied to a single study, but it has been proposed that they can be applied to a body of evidence [ 62 ].

The simplified DAG below (Fig.  1 ) shows the pathway between the exposure and outcome, alcohol consumption and active-TB, respectively. Alcohol consumption may result in active-TB, for example, by lowering an individual’s immune system (mediator not shown) [ 23 ]. Overcrowding is a confounding variable, causing both alcohol consumption and active-TB. If there was no causal effect of alcohol consumption on active-TB (i.e. no edge between those two variables in the DAG), an association would still be observed between them in the data due to the common cause overcrowding [ 4 , 25 , 28 , 29 ]. Thus, overcrowding must be conditioned upon, indicated by a square around the variable, to obtain an unbiased estimate of alcohol consumption on active-TB. If investigators condition on the appropriate variables using a DAG that accurately represents a causal relationship, they may be more confident of exchangeability and thus estimating the true causal effect [ 9 , 30 ].

Directed acyclic graph representing relationship between alcohol consumption and active-TB. The confounding variable, overcrowding, effects both the exposure and outcome and should be conditioned on, as indicated by the bold square around overcrowding

Sufficient-component cause (SCC) models

SCC models (also known as causal pies) illustrate the multi-factorial nature of causality through pie charts [ 31 ]. SCC models view each of the variables that contribute to the outcome occurring as causal components [ 32 ], with many different combinations of components potentially bringing about the outcome of interest. Taken together, the components for each ‘complete pie’ are sufficient to produce the outcome. Necessary components are those without which the outcome could not occur [ 33 ]. For example, MTB is a necessary (but insufficient) component of tuberculosis and will therefore be a component for all of the causal pies for tuberculosis (but never features as a sole component of a causal pie). The origins of SCC models can be traced to Mackie’s definition of causality. This introduced the idea of INUS causation, that is a cause can be “an insufficient but necessary part of a condition which is itself unnecessary but sufficient for the result” [ 34 ] p. 45.

Causal pies are useful for understanding causal mechanisms and interactions of causal components [ 33 ]. Table ​ Table2 2 illustrates four pies ( S 1 , S 2 , S 3 , S 4 ) for two different populations (population 1 and population 2) which represent the possible combination of selected causal components (alcohol, overcrowding and unknown factors) for the development of active TB.

Sufficient component cause models and corresponding prevalence rates and risk ratios (RRs) for each sufficient-cause between two populations

The prevalence of each causal pie differs in each population, and as a result the RR differs in each population

Unknown factors may differ in each combination of components, as indicated by the different subscripts of U corresponding to each SCC model. In a hypothetical dataset of 400 individuals, A and O are measured and U is not. The causal pies can be found in column one (see label). Columns two and three indicate if the individual has been exposed to each measured causal component ( A and O , where A  = 1 indicates individuals represented in the corresponding SCC models have been exposed). Columns four and five for population 1 and columns eight and nine for population 2 show the number of individuals in the example dataset who developed active-TB ( T  = 1) and who did not ( T  = 0), respectively. The sum of columns four and five for population 1 and eight and nine for population 2 is the total number of individuals exposed to each causal pie for each population. Finally, column seven for population 1 and eleven for population 2 is the risk ratio (RR) for each pie calculated using S 1 as the reference group

GRADE methodology

GRADE is the most widely adopted approach for assessing certainty of evidence in systematic reviews, guideline development and evidence-informed recommendations [ 35 ]. Certainty has been defined by the GRADE Working Group as the “extent of our confidence that the estimates of the effect are correct” [ 10 , 36 – 38 ]. Certainty is based both on assessing the risk of bias of individual studies and an evaluation across studies [ 35 ]. GRADE typically considers evidence from randomised controlled trials (RCTs) as providing a higher level of certainty than evidence from nonrandomised studies (NRSs), although the appropriateness of this has been critiqued [ 39 ]. Certainty may be modified according to different GRADE domains (summarised in Table ​ Table3). 3 ). Large associations, dose-response relationships and adjusting for plausible confounding upgrade certainty.

The initial level of certainty, according to GRADE, differs between randomised controlled trials (RCTs) and nonrandomised studies (NRSs)

The level of certainty indicates the confidence of investigators that the estimated effect is close to the true causal effect. GRADE provides domains that may upgrade or downgrade the level of certainty. Based on tables in [ 38 ]

Concerns about directness, inconsistency, imprecision and publication bias may reduce certainty. Directness refers to how closely the research evidence relates to the research question of interest, with different study populations (such as available evidence only focusing on adults, rather than children) or the use of surrogate outcomes being examples of ‘indirectness’. Inconsistency reflects differences in the effect size across studies (often identified through high levels of heterogeneity in a meta-analysis) which cannot be adequately explained. Imprecision occurs when effect estimates have wide confidence interval. Publication bias may arise if studies with a positive or exciting result are more likely to be published than those without a large association

Comparisons against Bradford Hill’s viewpoints

Table ​ Table4 4 summarises the overlapping elements between BH viewpoints and the potential outcomes framework approaches, with subsequent text providing additional detail.

Summary of utilisation of each Bradford Hill (BH) viewpoint by each causal assessment approach: BH viewpoints, directed acyclic graphs (DAGs), sufficient-component cause models and GRADE methodology. Based on comparative analysis of causal assessment approaches

Strength of association

Bradford Hill argued that a large association suggests the observed effect is less likely to be due to bias [ 1 , 40 ], but he acknowledged that weak (or small) associations may still reflect causal relationships. As noted by Greenland and Robins, large associations can still arise from confounding and a weak association does not mean there is an absence of causality[ 33 ]. In practice, investigators may rely on existing tools and guidelines, or their own interpretation, to determine what constitutes a strong association.

Although DAGs cannot represent the size of an association, they facilitate “bias analysis” (see Fig.  1 ) [ 14 ]. Investigators may use DAGs to highlight important variables that they were unable to condition on and consider their implications for the effect estimate, including residual confounding (from inaccurately or poorly measured variables, including confounders) [ 41 ].

SCC models draw attention to the impact of disease prevalence and the prevalence of competing causes on the strenth of association or effect estimate. For example, the RR of S 3 is attenuated as the prevalence of a competing sufficient cause (S 4 ) or the prevalence of the outcome in the reference group (S 1 ) increases (see Table ​ Table2 2 ).

According to the GRADE Working Group, a strong association is indicated by a risk ratio (RR) of 2–5 or 0.2–0.5 [ 17 , 17 , 17 ]. Evidence from NRSs that estimate a large effect will be upgraded on the basis that confounding is less likely to entirely remove the observed association [ 43 ].

Consistency

Bradford Hill argued that consistent estimates observed in different circumstances reduce the likelihood that the effect is due to chance or bias [ 1 ]. Comparison with the three approaches demonstrate that differences in effect size across studies which may be due to variations in causal structures, variable interactions, or biases of the relevant studies.

Transportability refers to the extent to which a causal effect in one context can be used to infer a causal effect in different circumstances, such as different populations or study designs [ 44 ]. Investigators can use DAGs to understand how differences in causal structures may explain different observed effect sizes. For example, investigators may want to understand if the causal effect of alcohol consumption on active-TB can be extrapolated to a target population with a high baseline risk of HIV (represented in Fig.  2 ). In other words, to understand if the different effect size in the target population is due to HIV modifying the effect of alcohol consumption on active-TB by reducing immunity [ 45 , 46 ]. To represent the target population’s exposure to a stratum of HIV (i.e., a higher risk of HIV), there is a square around HIV [ 44 , 46 ]. If the likelihood of active-TB for a given level of alcohol consumption is equivalent between the populations, the estimated effect of alcohol on active-TB is transportable and any statistical heterogeneity observed is likely due to HIV risk modifying the effect of alcohol on active-TB[ 46 ].

Directed acyclic graph (DAG) of target population with high baseline risk of HIV. The high baseline risk of HIV means that HIV has been conditioned upon, indicated by square around HIV. The estimated effect of alcohol consumption on active-TB in this population will be

modified by the higher risk of HIV. This needs to be considered when comparing the effect estimates between this target population and the one described in Fig.  1 with low risk of HIV

Investigators can use SCC models to understand differences in variable interactions and if that can explain different observed effect sizes observed between populations [ 44 , 47 – 49 ]. For example, investigators may want to understand if the RR of individuals in population 1 in Table ​ Table2 2 can be transported to population 2. According to Table ​ Table2, 2 , the RR of active-TB when individuals are exposed only to overcrowding (S 3 ) is lower in population 2 than population 1. i.e., the effect of overcrowding on active-TB differs between populations when alcohol is not consumed. It may be that the unknown factors of S 3 differ between populations. However, because the RRs are the same for other causal pies, investigators may assume that the reason for different prevalence and RRs for S 3 is that unknown factors and overcrowding are interacting differently between the populations, in which case the effect sizes cannot be transported from population 1 to population 2.

In GRADE, unexplained inconsistency (typically, statistical heterogeneity) suggests lower confidence about the likely effect of the exposure under different circumstances. GRADE considers unexplained inconsistency rather than consistent effect estimates, as Bradford Hill suggested, to highlight that consistent estimates in different circumstances may be subject to the same bias and do not necessarily increase confidence in causality [ 50 ].

Specificity

According to Bradford Hill, a relationship is specific if the exposure is associated with the outcome in question and no others, and if the outcome is associated with the exposure in question and no others. He emphasised that a non-specific relationship does not undermine causality. Specificity originated in Robert Koch’s postulates to evaluate causality in infectious diseases, but is rare in epidemiology and usually arises when the outcome is defined based on the exposure status (e.g., tuberculosis being defined by the presence of the tubercle bacillus) [ 17 , 51 , 52 ]. Comparisons highlighted how multiple causation (where one exposure may affect many outcomes and one outcome may be effected by many exposures) limits the utility of directly applying specificity in epidemiological practice, but extending the concept to the related idea of ‘falsification’ may improve its usefulness.

The DAG in Fig.  1 illustrates a non-specific relationship as active-TB is caused by at least two exposures: alcohol-consumption and overcrowding [ 53 ]. The relationship is also non-specific because alcohol consumption may cause many other outcomes such as cancer, cardiovascular disease and injuries [ 54 ]. This is not shown in the DAG in Fig.  1 because DAGs typically include the main variables related to the relationship of interest (i.e., an exposure, outcome and any potential confounders) [ 55 ]. This is also the reason why DAGs are not used to demonstrate specific relationships; a variable may be left out of a DAG because it is not of interest, not because the relationship illustrated in the DAG is specific.

One important reason for specificity is multiple causation suggests a higher likelihood that the observed association is due to confounding. Rather than seeking evidence of specificity, DAGs can be used to help identify and assess falsification (or negative control) outcomes and exposures. A falsification outcome is expected to be both independent of the outcome and associated with the exposure only through the confounding variable [ 56 ]. If investigators accurately condition on the confounding variable, they would not observe an effect of the exposure on the falsification outcome.

A hypothetical falsification outcome is head lice (Fig. ​ (Fig.3). 3 ). Alcohol consumption does not have a causal effect on head lice. If investigators observe an effect of alcohol consumption on head lice despite conditioning upon overcrowding, this is likely due to residual confounding due to overcrowding being inaccurately measured. Therefore, it is possible that the relationship between alcohol and active-TB is also subject to residual confounding of overcrowding and investigators should adjust their conclusions accordingly. An absence of association between alcohol consumption and head lice does not suggest specificity, but investigators may be more confident that in this study, the association between alcohol consumption and active-TB is not confounded by overcrowding.

The directed acyclic graphs (DAG) shows the relationship between the exposure (alcohol consumption), the outcome (active-TB), the confounding variable (overcrowding) and the falsification outcome (head lice). The bold square around overcrowding indicates that it has been conditioned on. If there is no effect of alcohol consumption on head lice, there is a greater likelihood that overcrowding has been accurately conditioned upon

Finding falsification variables can be challenging. Take the example of identifying a falsification exposure (which is independent of the exposure and associated with the outcome only through the confounding variable). Many possible exposures associated with the confounder (overcrowding), such as smoking, air pollution, experiences of homelessness and malnutrition are also associated with the outcome (active-TB) and therefore would fail as a falsification exposure [ 57 , 58 ]. Put another way, the lack of specificity in most causal relationships in epidemiology limits our ability to carry out falsification tests. However, where they do exist they can offer a powerful tool for assessing bias.

Causal pies illustrate the multi-factorial nature of causal relationship that limits the likelihood of specificity because a range of causal pies (and causal components) may produce the same outcome (see Table ​ Table2). 2 ). One causal pie may also be used to represent a possible sufficient-cause for various exposures[ 59 ]. The causal pie would represent a specific relationship only if a component is both necessary and sufficient to produce the outcome and the outcome could only be produced by this necessary and sufficient cause [ 31 , 33 ]. These limitations are among the reasons why some, including the originators of GRADE methodology, argue that specificity should be excluded from causal assessment [ 7 , 10 , 31 , 60 ].

Temporality

Temporality is considered fundamental to causality; an exposure must precede an outcome. Bradford Hill alluded to how reverse causality skews temporality: “does a particular occupation or occupational environment promote infection by the tubercle bacillus … or, indeed, have they already contracted it?” [ 1 ]. Two of the three approaches explicitly incorporate temporality, with the order of cause and effect being fundamental to DAGs.

DAGs can highlight reverse causality [ 20 , 61 ]. For example, in a cross-sectional study, the observed effect of alcohol consumption is based on measurements after individuals were diagnosed with active-TB. However, active-TB may have actually occurred prior to diagnosis of active-TB and been a cause of alcohol consumption, via social marginalisation [ 62 ]. Given a longitudinal study that has information on previous diagnoses, investigators could test for reverse causation by considering if active-TB was present before the diagnosis that was observed after alcohol consumption (see Fig. ​ Fig.4). 4 ). If investigators conditioned upon active-TB before diagnosis and continued to observe an effect of consuming alcohol on active-TB after diagnosis, or if they found no effect of active-TB before diagnosis on alcohol consumption, then the estimated effect of alcohol consumption on active-TB after diagnosis is less likely due to reverse causation.

Temporality using directed acyclic graphs (DAGs). Investigators may be more confident that the effect of alcohol consumption on active-TB is not due to reverse causality if (1) they condition upon active-TB before diagnosis and continue to observe an effect of alcohol consumption on active-TB after diagnosis or (2) if they do not observe an effect of active-TB before diagnosis on alcohol consumption

Time may be one component of a causal pie but temporality is not considered in the synergy, antagonism and interaction of the components [ 2 ]. Temporality is not directly considered by GRADE. RCTs, which guarantee that the exposure precedes the outcome through study design, are upgraded. However, the favouring of RCTs is not only about temporality but also about the achievement of exchangeability through randomisation. Additionally temporality is not explicitly considered for NRSs (which include longitudinal studies and so may also be able to ensure that the exposure precedes the outcome).([ 10 ].

Dose-response

A dose-response gradient exists when incremental increases (or decreases) of the exposure produce incremental increases (or decreases) of the outcome. Dose-response is fundamental to causal assessment in pharmacology and toxicology [ 63 ]. Bradford Hill argued that a dose-response gradient provides a “simpler explanation” of the causal relationship than if it were not observed (see Table ​ Table1) 1 ) [ 1 ]. However, there are many reasons investigators may not observe a dose-response gradient including exposure threshold effects, as in the case of allergens [ 17 ]. Furthermore, a dose-response relationship may be induced by a confounding variable [ 64 , 65 ]. For example, an incremental increase in alcohol consumption that corresponds to an incremental increase in active-TB may be due to incremental increases in overcrowding (see Fig.  1 ) [ 66 ]. While DAGs non-parametric (and so cannot show the structure of the relationship between any two variables), they can be used to consider the plausibility of one or more confounding variables undermining a dose-response relationship.

Unknown components limit the utility of SCC models to assess dose-response gradients. Evidence from NRSs is upgraded in GRADE if a dose-response relationship has been observed on the basis that confounding is less likely [ 35 ]. However, as noted above, a dose-response relationship may easily arise from confounding.

Plausibility

Investigators develop assumptions about a causal relationship based on background knowledge. Thus, the plausibility of the causal relationship is both dependent on and limited by knowledge available at the time [ 1 ]. It may be further limited by assumptions based on investigators’ beliefs rather than empirical evidence [ 67 ].

The process of developing DAGs and SCC models forces investigators to explicitly articulate assumptions about the causal relationships relevant to the research question of interest, making it transparent to other investigators [ 44 , 68 ] [ 69 ]. DAGs may include mediators, which lie on the causal path between the exposure and outcome; a weakened immunity is the mediator by which alcohol consumption causes active-TB. Mediation analysis considers the direct and indirect effect of mediators [ 70 ]. Interrogating background knowledge to develop a DAG encourages a more systematic exploration of the plausibility of the causal chain.

For SCC models, investigators make explicit the nature of variable interaction [ 71 ]. GRADE upgrades for appropriate adjustment for all plausible confounding variables, but does not consider the broader variables relevant to the plausibility of a causal relationship across a body of evidence [ 35 ].

Coherence is an assessment of how the putative relationship fits into existing theory and empirical evidence [ 1 , 60 ]. Our comparisons suggest that coherence is not considered by the other approaches and may have limited utility, partly because it is poorly delineated from plausibility [ 72 ]. Investigators evaluating the coherence of a DAG or SCC model may consider how the assumptions illustrated by either approach fit existing theory, however, neither consider or illustrate coherence. Schünemann and colleagues argue that GRADE considers coherence by assessing indirectness [ 10 ]. However, in considering indirectness, investigators determine how applicable the population and interventions of identified studies are to the putative causal relationship under study. Coherence, on the other hand, asks investigators to consider how applicable the putative causal relationship is to broader evidence, including studies that do not investigate that specific relationship.

Bradford Hill argued that “strong support for the causation hypothesis might be revealed” from “experimental, or semi-experimental data” [ 1 ]. He alluded to natural experiment studies, where the exposure is determined by nature or other factors outside of the control of investigators and where exchangeability between comparison groups is more likely [ 29 ].

Investigators have used DAGs to elucidate why randomisation results in exchangeability. Randomisation is an example of an instrumental variable; it causes (and is not caused by) the exposure and only impacts the outcome through the exposure [ 73 ]. If consuming alcohol was completely random and randomisation was independent of active-TB (see Fig.  5 ), the risk of overcrowding would be the same for individuals allocated to consume alcohol and those allocated to not [ 74 ]. Thus, the effect estimated would be based on exchangeable groups, but bounded by the proportion of individuals exposed due to randomisation, potentially limiting the transportability of the effect estimate [ 44 , 75 ].

Directed acyclic graph (DAG) with randomisation as the instrumental variable. According to this DAG, randomisation causes alcohol consumption. If this were true, there is a greater likelihood that the effect estimated would be similar or equivalent to the true causal effect

Due to limitations on randomisation, epidemiologists rely largely on observational data. Investigators can use DAGs to interrogate the plausibility of “naturally occurring” instrumental variables, and how likely it is that individuals were truly randomly exposed [ 29 , 73 ]. Clarity about study design, particularly procedures for assigning exposure, has been assisted by DAGs through the development of the ‘target trial’ (or ‘emulated trial’) where observational data analysis emulates randomised trial data analysis [ 76 ]. While it has several advantages, this does not seem to be directly comparable with the original BH viewpoint.

The causal pies that result in a given disease include both known and unknown components, as shown in Table ​ Table2. 2 . As investigators are unable to measure unknown variables for each causal pie, they cannot be certain that the groups exposed to each causal pie are exchangeable because they may differ in other characteristics that affect the outcome [ 4 , 11 ]. GRADE privileges effect estimates from randomised (experimental) studies which are more likely to be “causally attributable to the intervention” by initially grading RCTs higher than NRSs [ 43 ]. At present, no distinction is made between natural experiment studies and other NRSs on the basis of study design.

Bradford Hill argued that the likelihood of a causal relationship may be strengthened if a comparable association is observed between the same outcome and an analogous exposure or the same exposure and an analogous outcome. DAGs and SCC models do not account for analogous relationships in their assessment, but analogous relationships may be part of developing the assumptions and theories encoded in the diagrams. In GRADE, downgrading would be prevented if there was certainty in a causal relationship between the same exposure and similar outcomes in the same body of evidence [ 10 ]. While this has been conflated with analogy, this is more to do with the directness of the evidence to the research question rather than the transportability of the assumptions of an analogous, confirmed causal relationship to the one under study [ 77 ].

Discussion and conclusions

Epidemiologists evaluate evidence to understand how likely it is the observed effect is equal to the causal effect. We mapped DAGs, SCC models and GRADE against each BH viewpoint by comparing each tool to identify the overlap between different perspectives on causal assessment. The summary of these comparisons and the potential implications for causal assessment can be found in Table ​ Table5 5 .

Summary of conclusions. Interpretation of each BH based on mapping of DAGs, SCC models and GRADE

The comparisons highlight the overlap between BH viewpoints and other approaches. This underscores the ongoing influence of BH viewpoints in causal assessment alongside developments in causal thinking. It also highlights the importance of other approaches in understanding BH viewpoints. DAGs help explain the theoretical underpinning of strength of association, consistency, temporality, specificity, dose-response, plausibility, and experiment. GRADE provides guidance on how causal assessment can be applied in practice, particularly for considering strength of association, consistency, temporality, dose-response and experiment. While the inclusion of SCC models can be debated as they can be considered a framework to describe causal reality and are least used of the approaches we studied, their inclusion has been useful for understanding strength of association and plausibility in our analysis. Despite their seemingly limited utility for understanding BH viewpoints, SCC models, along with GRADE, also help explain why specificity may have limited usefulness in causal inference.

Our analysis is the first to compare insights from advancements in causal assessment with BH viewpoints [ 7 ]. This is an area that requires further research and we hope our study will encourage debate and discussion on overlapping approaches to causal inference. Further research and discussion is necessary to develop a new and comprehensive set of causal criteria that incorporates both traditional and recently developed approaches in causal inference. Such work would likely benefit from applying these different approaches to specific research questions, with a view to identifying their relative capacity to facilitate causal assessment. However, we did not critique the individual approaches as this has been done in previous works [ 4 , 5 , 10 , 11 ]. We did not investigate all potential approaches to assessing causality (e.g. International Agency for Research on Cancer and criteria for teratogenicity) due to limited time and resources. Instead, we focused on GRADE, DAGs and SCC models which are perhaps the best-known causal assessment approaches outside of BH viewpoints.

This study underscores the need for greater clarity on causal assessment in epidemiology. This is an initial attempt to demonstrate how recent approaches can be used to elucidate BH viewpoints, which remain fundamental to causal assessment and to tentatively suggest how their application could be improved. Our findings are preliminary and we welcome debate about our comparisons and the suggested implications for causal assessment.

Wellcome Trust (GB) (205412/Z/16/Z) Dr Anna Pearce; Chief Scientist Office, Scottish Government Health and Social Care Directorate (SPHSU13) Dr Anna Pearce Dr Srinivasa Vittal Katikireddi; Medical Research Council (MC_UU_12017/13) Dr Anna Pearce Dr Srinivasa Vittal Katikireddi; Chief Scientist Office (SPHSU15) Dr Hilary Thomson; NHS Health Scotland (SCAF/15/02) Dr Srinivasa Vittal Katikireddi; Medical Research Council MC_UU_12017/15 Dr Hilary Thomson; Medical Research Council MC_ST_U18004 Michal Shimonovich.

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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7.2: Causal relationships

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• Page ID 25639

• Matthew DeCarlo
• Radford University via Open Social Work Education

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Learning Objectives

• Define and provide an example of idiographic and nomothetic causal relationships
• Describe the role of causality in quantitative research as compared to qualitative research
• Identify, define, and describe each of the main criteria for nomothetic causal relationships
• Describe the difference between and provide examples of independent, dependent, and control variables
• Define hypothesis, be able to state a clear hypothesis, and discuss the respective roles of quantitative and qualitative research when it comes to hypotheses

Most social scientific studies attempt to provide some kind of causal explanation. A study on an intervention to prevent child abuse is trying to draw a connection between the intervention and changes in child abuse. Causality refers to the idea that one event, behavior, or belief will result in the occurrence of another, subsequent event, behavior, or belief. In other words, it is about cause and effect. It seems simple, but you may be surprised to learn there is more than one way to explain how one thing causes another. How can that be? How could there be many ways to understand causality?

Think back to our chapter on paradigms, which were analytic lenses comprised of assumptions about the world. You’ll remember the positivist paradigm as the one that believes in objectivity and social constructionist paradigm as the one that believes in subjectivity. Both paradigms are correct, though incomplete, viewpoints on the social world and social science.

A researcher operating in the social constructionist paradigm would view truth as subjective. In causality, that means that in order to try to understand what caused what, we would need to report what people tell us. Well, that seems pretty straightforward, right? Well, what if two different people saw the same event from the exact same viewpoint and came up with two totally different explanations about what caused what? A social constructionist would say that both people are correct. There is not one singular truth that is true for everyone, but many truths created and shared by people.

When social constructionists engage in science, they are trying to establish one type of causality—idiographic causality. An idiographic causal explanation means that you will attempt to explain or describe your phenomenon exhaustively, based on the subjective understandings of your participants. These explanations are bound with the narratives people create about their lives and experience, and are embedded in a cultural, historical, and environmental context. Idiographic causal explanations are so powerful because they convey a deep understanding of a phenomenon and its context. From a social constructionist perspective, the truth is messy. Idiographic research involves finding patterns and themes in the causal relationships established by your research participants.

If that doesn’t sound like what you normally think of as “science,” you’re not alone. Although the ideas behind idiographic research are quite old in philosophy, they were only applied to the sciences at the start of the last century. If we think of famous scientists like Newton or Darwin, they never saw truth as subjective. There were objectively true laws of science that were applicable in all situations. Another paradigm was dominant and continues its dominance today, the positivist paradigm. When positivists try to establish causality, they are like Newton and Darwin, trying to come up with a broad, sweeping explanation that is universally true for all people. This is the hallmark of a nomothetic causal explanation .

Nomothetic causal explanations are also incredibly powerful. They allow scientists to make predictions about what will happen in the future, with a certain margin of error. Moreover, they allow scientists to generalize —that is, make claims about a large population based on a smaller sample of people or items. Generalizing is important. We clearly do not have time to ask everyone their opinion on a topic, nor do we have the ability to look at every interaction in the social world. We need a type of causal explanation that helps us predict and estimate truth in all situations.

If these still seem like obscure philosophy terms, let’s consider an example. Imagine you are working for a community-based non-profit agency serving people with disabilities. You are putting together a report to help lobby the state government for additional funding for community support programs, and you need to support your argument for additional funding at your agency. If you looked at nomothetic research, you might learn how previous studies have shown that, in general, community-based programs like yours are linked with better health and employment outcomes for people with disabilities. Nomothetic research seeks to explain that community-based programs are better for everyone with disabilities. If you looked at idiographic research, you would get stories and experiences of people in community-based programs. These individual stories are full of detail about the lived experience of being in a community-based program. Using idiographic research, you can understand what it’s like to be a person with a disability and then communicate that to the state government. For example, a person might say “I feel at home when I’m at this agency because they treat me like a family member” or “this is the agency that helped me get my first paycheck.”

Neither kind of causal explanation is better than the other. A decision to conduct idiographic research means that you will attempt to explain or describe your phenomenon exhaustively, attending to cultural context and subjective interpretations. A decision to conduct nomothetic research, on the other hand, means that you will try to explain what is true for everyone and predict what will be true in the future. In short, idiographic explanations have greater depth, and nomothetic explanations have greater breadth. More importantly, social workers understand the value of both approaches to understanding the social world. A social worker helping a client with substance abuse issues seeks idiographic knowledge when they ask about that client’s life story, investigate their unique physical environment, or probe how they understand their addiction. At the same time, a social worker also uses nomothetic knowledge to guide their interventions. Nomothetic research may help guide them to minimize risk factors and maximize protective factors or use an evidence-based therapy, relying on knowledge about what in general helps people with substance abuse issues.

Nomothetic causal relationships

One of my favorite classroom moments occurred in the early moments of my teaching career. Students were providing peer feedback on research questions. I overheard one group who was helping someone rephrase their research question. A student asked, “Are you trying to generalize or nah?” Teaching is full of fun moments like that one.

Answering that one question can help you understand how to conceptualize and design your research project. If you are trying to generalize, or create a nomothetic causal relationship, then the rest of these statements are likely to be true: you will use quantitative methods, reason deductively, and engage in explanatory research. How can I know all of that? Let’s take it part by part.

Because nomothetic causal relationships try to generalize, they must be able to reduce phenomena to a universal language, mathematics. Mathematics allows us to precisely measure, in universal terms, phenomena in the social world. Not all quantitative studies are explanatory. For example, a descriptive study could reveal the number of people without homes in your county, though it won’t tell you why they are homeless. But nearly all explanatory studies are quantitative. Because explanatory researchers want a clean “x causes y” explanation, they need to use the universal language of mathematics to achieve their goal. That’s why nomothetic causal relationships use quantitative methods.

What we’ve been talking about here is relationships between variables. When one variable causes another, we have what researchers call independent and dependent variables. For our example on spanking and aggressive behavior, spanking would be the independent variable and aggressive behavior addiction would be the dependent variable. An independent variable is the cause, and a dependent variable is the effect. Why are they called that? Dependent variables depend on independent variables. If all of that gets confusing, just remember this graphical relationship:

Relationship strength is another important factor to take into consideration when attempting to make causal claims when your research approach is nomothetic. I’m not talking strength of your friendships or marriage. In this context, relationship strength refers to statistical significance. The more statistically significant a relationship between two variables is shown to be, the greater confidence we can have in the strength of that relationship. You’ll remember from our discussion of statistical significance in Chapter 3, that it is usually represented in statistics as the p value.

A hypothesis is a statement describing a researcher’s expectation regarding what she anticipates finding. Hypotheses in quantitative research are a nomothetic causal relationship that the researcher expects to demonstrate. It is written to describe the expected relationship between the independent and dependent variables. Your prediction should be taken from a theory or model of the social world. For example, you may hypothesize that treating clinical clients with warmth and positive regard is likely to help them achieve their therapeutic goals. That hypothesis would be using the humanistic theories of Carl Rogers. Using previous theories to generate hypotheses is an example of deductive research. If Rogers’ theory of unconditional positive regard is accurate, your hypothesis should be true. This is how we know that all nomothetic causal relationships must use deductive reasoning.

Let’s consider a couple of examples. In research on sexual harassment (Uggen & Blackstone, 2004), [1] one might hypothesize, based on feminist theories of sexual harassment, that more females than males will experience specific sexually harassing behaviors. What is the causal relationship being predicted here? Which is the independent and which is the dependent variable? In this case, we hypothesized that a person’s gender (independent variable) would predict their likelihood to experience sexual harassment (dependent variable).

Sometimes researchers will hypothesize that a relationship will take a specific direction. As a result, an increase or decrease in one area might be said to cause an increase or decrease in another. For example, you might choose to study the relationship between age and support for legalization of marijuana. Perhaps you’ve taken a sociology class and, based on the theories you’ve read, you hypothesize that age is negatively related to support for marijuana legalization. [2] What have you just hypothesized? You have hypothesized that as people get older, the likelihood of their supporting marijuana legalization decreases. Thus, as age (your independent variable) moves in one direction (up), support for marijuana legalization (your dependent variable) moves in another direction (down). So, positive relationships involve two variables going in the same direction and negative relationships involve two variables going in opposite directions. If writing hypotheses feels tricky, it is sometimes helpful to draw them out and depict each of the two hypotheses we have just discussed.

It’s important to note that once a study starts, it is unethical to change your hypothesis to match the data that you found. For example, what happens if you conduct a study to test the hypothesis from Figure 7.3 on support for marijuana legalization, but you find no relationship between age and support for legalization? It means that your hypothesis was wrong, but that’s still valuable information. It would challenge what the existing literature says on your topic, demonstrating that more research needs to be done to figure out the factors that impact support for marijuana legalization. Don’t be embarrassed by negative results, and definitely don’t change your hypothesis to make it appear correct all along!

Let’s say you conduct your study and you find evidence that supports your hypothesis, as age increases, support for marijuana legalization decreases. Success! Causal explanation complete, right? Not quite. You’ve only established one of the criteria for causality. The main criteria for causality have to do with covariation, plausibility, temporality, and spuriousness. In our example from Figure 7.3, we have established only one criteria—covariation. When variables covary , they vary together. Both age and support for marijuana legalization vary in our study. Our sample contains people of varying ages and varying levels of support for marijuana legalization.

Just because there might be some correlation between two variables does not mean that a causal relationship between the two is really plausible. Plausibility means that in order to make the claim that one event, behavior, or belief causes another, the claim has to make sense. It makes sense that people from previous generations would have different attitudes towards marijuana than younger generations. People who grew up in the time of Reefer Madness or the hippies may hold different views than those raised in an era of legalized medicinal and recreational use of marijuana.

Once we’ve established that there is a plausible relationship between the two variables, we also need to establish whether the cause happened before the effect, the criterion of temporality . A person’s age is a quality that appears long before any opinions on drug policy, so temporally the cause comes before the effect. It wouldn’t make any sense to say that support for marijuana legalization makes a person’s age increase. Even if you could predict someone’s age based on their support for marijuana legalization, you couldn’t say someone’s age was caused by their support for legalization.

Finally, scientists must establish nonspuriousness. A spurious relationship is one in which an association between two variables appears to be causal but can in fact be explained by some third variable. For example, we could point to the fact that older cohorts are less likely to have used marijuana. Maybe it is actually use of marijuana that leads people to be more open to legalization, not their age. This is often referred to as the third variable problem, where a seemingly true causal relationship is actually caused by a third variable not in the hypothesis. In this example, the relationship between age and support for legalization could be more about having tried marijuana than the age of the person.

Quantitative researchers are sensitive to the effects of potentially spurious relationships. They are an important form of critique of scientific work. As a result, they will often measure these third variables in their study, so they can control for their effects. These are called control variables , and they refer to variables whose effects are controlled for mathematically in the data analysis process. Control variables can be a bit confusing, but think about it as an argument between you, the researcher, and a critic.

Researcher: “The older a person is, the less likely they are to support marijuana legalization.”

Critic: “Actually, it’s more about whether a person has used marijuana before. That is what truly determines whether someone supports marijuana legalization.”

Researcher: “Well, I measured previous marijuana use in my study and mathematically controlled for its effects in my analysis. The relationship between age and support for marijuana legalization is still statistically significant and is the most important relationship here.”

Let’s consider a few additional, real-world examples of spuriousness. Did you know, for example, that high rates of ice cream sales have been shown to cause drowning? Of course, that’s not really true, but there is a positive relationship between the two. In this case, the third variable that causes both high ice cream sales and increased deaths by drowning is time of year, as the summer season sees increases in both (Babbie, 2010). [4] Here’s another good one: it is true that as the salaries of Presbyterian ministers in Massachusetts rise, so too does the price of rum in Havana, Cuba. Well, duh, you might be saying to yourself. Everyone knows how much ministers in Massachusetts love their rum, right? Not so fast. Both salaries and rum prices have increased, true, but so has the price of just about everything else (Huff & Geis, 1993). [5] Finally, research shows that the more firefighters present at a fire, the more damage is done at the scene. What this statement leaves out, of course, is that as the size of a fire increases so too does the amount of damage caused as does the number of firefighters called on to help (Frankfort-Nachmias & Leon-Guerrero, 2011). [6] In each of these examples, it is the presence of a third variable that explains the apparent relationship between the two original variables.

In sum, the following criteria must be met for a correlation to be considered causal:

• The two variables must vary together.
• The relationship must be plausible.
• The cause must precede the effect in time.
• The relationship must be nonspurious (not due to a third variable).

Once these criteria are met, a researcher can say they have achieved a nomothetic causal explanation, one that is objectively true. It’s a difficult challenge for researchers to meet. You will almost never hear researchers say that they have proven their hypotheses. A statement that bold implies that a relationship has been shown to exist with absolute certainty and that there is no chance that there are conditions under which the hypothesis would not be true. Instead, researchers tend to say that their hypotheses have been supported (or not). This more cautious way of discussing findings allows for the possibility that new evidence or new ways of examining a relationship will be discovered. Researchers may also discuss a null hypothesis. We covered in Chapter 3 that the null hypothesis is one that predicts no relationship between the variables being studied. If a researcher rejects the null hypothesis, she is saying that the variables in question are somehow related to one another.

Idiographic causal relationships

Remember our question, “Are you trying to generalize or nah?” If you answered no, you are trying to establish an idiographic causal relationship. I can guess that if you are trying to establish an idiographic causal relationship, you are likely going to use qualitative methods, reason inductively, and engage in exploratory or descriptive research. We can understand these assumptions by walking through them, one by one.

Researchers seeking idiographic causal relationships are not trying to generalize, so they have no need to reduce phenomena to mathematics. In fact, using the language of mathematics to reduce the social world down is a bad thing, as it robs the causal relationship of its meaning and context. Idiographic causal relationships are bound within people’s stories and interpretations. Usually, these are expressed through words. Not all qualitative studies use word data, as some can use interpretations of visual or performance art, though the vast majority of social science studies do use word data.

But wait, I predicted that an idiographic causal relationship would use descriptive or exploratory research. How can we build causal relationships if we are just describing or exploring a topic? Wouldn’t we need to do explanatory research to build any kind of causal explanation? Explanatory research attempts to establish nomothetic causal relationships—an independent variable is demonstrated to cause changes a dependent variable. Exploratory and descriptive qualitative research contains some causal relationships, but they are actually descriptions of the causal relationships established by the participants in your study. Instead of saying “x causes y,” your participants will describe their experiences with “x,” which they will tell you was caused by and influenced a variety of other factors, depending on time, environment, and subjective experience. As we stated before, idiographic causal explanations are messy. Your job as a social science researcher is to accurately describe the patterns in what your participants tell you.

Let’s consider an example. If I asked you why you decided to become a social worker, what might you say? For me, I would say that I wanted to be a mental health clinician since I was in high school. I was interested in how people thought. At my second internship in my undergraduate program, I got the advice to become a social worker because the license provided greater authority for insurance reimbursement and flexibility for career change. That’s not a simple explanation at all! But it does provide a description of the deeper understanding of the many factors that led me to become a social worker. If we interviewed many social workers about their decisions to become social workers, we might begin to notice patterns. We might find out that many social workers begin their careers based on a variety of factors, such as: personal experience with a disability or social injustice, positive experiences with social workers, or a desire to help others. No one factor is the “most important factor,” like with nomothetic causal relationships. Instead, a complex web of factors, contingent on context, emerge in the dataset when you interpret what people have said.

Finding patterns in data, as you’ll remember from Chapter 6, is what inductive reasoning is all about. A researcher collects data, usually word data, and notices patterns. Those patterns inform the theories we use in social work. In many ways, the idiographic causal relationships you create in qualitative research are like the social theories we reviewed in Chapter 6 (e.g. social exchange theory) and other theories you use in your practice and theory courses. Theories are explanations about how different concepts are associated with each other how that network of relationships works in the real world. While you can think of theories like Systems Theory as Theory (with a capital “T”), inductive causal relationships are like theory with a small “t.” They may apply only to the participants, environment, and moment in time in which you gathered your data. Nevertheless, they contribute important information to the body of knowledge on the topic you studied.

Over time, as more qualitative studies are done and patterns emerge across different studies and locations, more sophisticated theories emerge that explain phenomena across multiple contexts. In this way, qualitative researchers use idiographic causal explanations for theory building or the creation of new theories based on inductive reasoning. Quantitative researchers, on the other hand, use nomothetic causal relationships for theory testing , wherein a hypothesis is created from existing theory (big T or small t) and tested mathematically (i.e., deductive reasoning).

If you plan to study domestic and sexual violence, you will likely encounter the Power and Control Wheel. [6] The wheel is a model of how power and control operate in relationships with physical violence. The wheel was developed based on qualitative focus groups conducted by sexual and domestic violence advocates in Duluth, MN. While advocates likely had some tentative hypotheses about what was important in a relationship with domestic violence, participants in these focus groups provided the information that became the Power and Control Wheel. As qualitative inquiry like this one unfolds, hypotheses get more specific and clear, as researchers learn from what their participants share.

Once a theory is developed from qualitative data, a quantitative researcher can seek to test that theory. For example, a quantitative researcher may hypothesize that men who hold traditional gender roles are more likely to engage in domestic violence. That would make sense based on the Power and Control Wheel model, as the category of “using male privilege” speaks to this relationship. In this way, qualitatively-derived theory can inspire a hypothesis for a quantitative research project.

Unlike nomothetic causal relationships, there are no formal criteria (e.g., covariation) for establishing causality in idiographic causal relationships. In fact, some criteria like temporality and nonspuriousness may be violated. For example, if an adolescent client says, “It’s hard for me to tell whether my depression began before my drinking, but both got worse when I was expelled from my first high school,” they are recognizing that oftentimes it’s not so simple that one thing causes another. Sometimes, there is a reciprocal relationship where one variable (depression) impacts another (alcohol abuse), which then feeds back into the first variable (depression) and also into other variables (school). Other criteria, such as covariation and plausibility still make sense, as the relationships you highlight as part of your idiographic causal explanation should still be plausibly true and it elements should vary together.

Similarly, idiographic causal explanations differ in terms of hypotheses. If you recall from the last section, hypotheses in nomothetic causal explanations are testable predictions based on previous theory. In idiographic research, a researcher likely has hypotheses, but they are more tentative. Instead of predicting that “x will decrease y,” researchers will use previous literature to figure out what concepts might be important to participants and how they believe participants might respond during the study. Based on an analysis of the literature a researcher may formulate a few tentative hypotheses about what they expect to find in their qualitative study. Unlike nomothetic hypotheses, these are likely to change during the research process. As the researcher learns more from their participants, they might introduce new concepts that participants talk about. Because the participants are the experts in idiographic causal relationships, a researcher should be open to emerging topics and shift their research questions and hypotheses accordingly.

Two different baskets

Idiographic and nomothetic causal explanations form the “two baskets” of research design elements pictured in Figure 7.4 below. Later on, they will also determine the sampling approach, measures, and data analysis in your study.

In most cases, mixing components from one basket with the other would not make sense. If you are using quantitative methods with an idiographic question, you wouldn’t get the deep understanding you need to answer an idiographic question. Knowing, for example, that someone scores 20/35 on a numerical index of depression symptoms does not tell you what depression means to that person. Similarly, qualitative methods are not often used to deductive reasoning because qualitative methods usually seek to understand a participant’s perspective, rather than test what existing theory says about a concept.

However, these are not hard-and-fast rules. There are plenty of qualitative studies that attempt to test a theory. There are fewer social constructionist studies with quantitative methods, though studies will sometimes include quantitative information about participants. Researchers in the critical paradigm can fit into either bucket, depending on their research question, as they focus on the liberation of people from oppressive internal (subjective) or external (objective) forces.

We will explore later on in this chapter how researchers can use both buckets simultaneously in mixed methods research. For now, it’s important that you understand the logic that connects the ideas in each bucket. Not only is this fundamental to how knowledge is created and tested in social work, it speaks to the very assumptions and foundations upon which all theories of the social world are built!

Key Takeaways

• Idiographic research focuses on subjectivity, context, and meaning.
• Nomothetic research focuses on objectivity, prediction, and generalizing.
• In qualitative studies, the goal is generally to understand the multitude of causes that account for the specific instance the researcher is investigating.
• In quantitative studies, the goal may be to understand the more general causes of some phenomenon rather than the idiosyncrasies of one particular instance.
• For nomothetic causal relationships, a relationship must be plausible and nonspurious, and the cause must precede the effect in time.
• In a nomothetic causal relationship, the independent variable causes changes in a dependent variable.
• Hypotheses are statements, drawn from theory, which describe a researcher’s expectation about a relationship between two or more variables.
• Qualitative research may create theories that can be tested quantitatively.
• The choice of idiographic or nomothetic causal relationships requires a consideration of methods, paradigm, and reasoning.
• Depending on whether you seek a nomothetic or idiographic causal explanation, you are likely to employ specific research design components.
• Causality-the idea that one event, behavior, or belief will result in the occurrence of another, subsequent event, behavior, or belief
• Control variables- potential “third variables” effects are controlled for mathematically in the data analysis process to highlight the relationship between the independent and dependent variable
• Covariation- the degree to which two variables vary together
• Dependent variable- a variable that depends on changes in the independent variable
• Generalize- to make claims about a larger population based on an examination of a smaller sample
• Hypothesis- a statement describing a researcher’s expectation regarding what she anticipates finding
• Idiographic research- attempts to explain or describe your phenomenon exhaustively, based on the subjective understandings of your participants
• Independent variable- causes a change in the dependent variable
• Nomothetic research- provides a more general, sweeping explanation that is universally true for all people
• Plausibility- in order to make the claim that one event, behavior, or belief causes another, the claim has to make sense
• Spurious relationship- an association between two variables appears to be causal but can in fact be explained by some third variable
• Statistical significance- confidence researchers have in a mathematical relationship
• Temporality- whatever cause you identify must happen before the effect
• Theory building- the creation of new theories based on inductive reasoning
• Theory testing- when a hypothesis is created from existing theory and tested mathematically

Image attributions

Mikado by 3dman_eu CC-0

Weather TV Forecast by mohamed_hassan CC-0

Beatrice Birra Storytelling at African Art Museum by Anthony Cross public domain

• Uggen, C., & Blackstone, A. (2004). Sexual harassment as a gendered expression of power. American Sociological Review, 69 , 64–92. ↵
• In fact, there are empirical data that support this hypothesis. Gallup has conducted research on this very question since the 1960s. For more on their findings, see Carroll, J. (2005). Who supports marijuana legalization? Retrieved from http://www.gallup.com/poll/19561/who-supports-marijuana-legalization.aspx ↵
• Figures 7.2 and 7.3 were copied from Blackstone, A. (2012) Principles of sociological inquiry: Qualitative and quantitative methods. Saylor Foundation. Retrieved from: https://saylordotorg.github.io/text_...ative-methods/ Shared under CC-BY-NC-SA 3.0 License ( https://creativecommons.org/licenses/by-nc-sa/3.0/ ) ↵
• Babbie, E. (2010). The practice of social research (12th ed.) . Belmont, CA: Wadsworth. ↵
• Huff, D. & Geis, I. (1993). How to lie with statistics . New York, NY: W. W. Norton & Co. ↵
• Frankfort-Nachmias, C. & Leon-Guerrero, A. (2011). Social statistics for a diverse society . Washington, DC: Pine Forge Press. ↵

Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

Related Articles

Research Methodology

Qualitative Data Coding

What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

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12 Causal Learning

Department of Psychology University of California, Los Angeles Los Angeles, California, USA

School of Psychology Cardiff University Cardiff, Wales, UK

• Published: 21 November 2012
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This chapter is an introduction to the psychology of causal inference using a computational perspective, with the focus on causal discovery. It explains the nature of the problem of causal discovery and illustrates the goal of the process with everyday and hypothetical examples. It reviews psychological research under two approaches to causal discovery, an associative approach and a causal approach that incorporates causal assumptions in the inference process. The latter approach provides a framework within which to answer different questions regarding causal inference coherently. The chapter ends with a consideration of causality as unfolding over time. We conclude with a sketch of future directions for the field.

Why Causality?

The central question of this chapter is: “How can any intelligent system put on Planet Earth, if given cognitive resources and types of information similar to those available to us, discover how the world works so that it can best achieve its goals?” Before we attempt to answer this question, let us imagine that our cognition were different in various respects. First, suppose we were unable to learn associations between events (i.e., detect statistical regularity in the occurrence of events). We would be unable to predict any events, causal or otherwise. For example, we would be unable to predict that if the traffic light turns red, we should stop or an accident is likely to happen, or that if we hear a knock on our door, someone will be on the other side when we open the door. Nor would we be able to predict the weather, even imperfectly. We would be unable to learn the sequences of sound in language or music, or the meaning of words. We would behave as if we had prosopagnosia, unable to relate our parents' faces, or the face of the person we have been dating for the past month, to their past history. A nonassociative world would be grim.

Now, imagine a world where we were able to learn associations but unable to reason about causes and effects. What would it be like? In that world, for a child growing up on a farm who has always experienced sunrise after the rooster crows, if the rooster is sick one morning and does not crow, she would predict that the sun would not rise until the rooster crows. Similarly, if the rooster has been deceived into crowing, say, by artificial lighting in the middle of the night, the child would predict that the sun would rise soon after. Notice that under normal conditions noncausal associations do enable one to reliably predict a subsequent event from an observation (e.g., sunrise from a rooster's crowing, a storm soon to come from a drop in the barometric reading, or from ants migrating uphill). They do not, however, support predictions about the event (e.g., sunrise) when the observation (crowing or no crowing) is produced by an action or an extraneous cause (respectively, artificial light and the rooster's sickness). An associative world without causation would be exasperating.

A causal tree and the implied associative links. Nodes represent variables, labeled by letters. Arrows represent direct causal links. Dotted lines represent implied associations, which include indirect causal links as well as associations between direct and indirect effects of a common cause.

Consider how often we would be wrong, and how inefficient we would be, were we to store all associations, both causal and noncausal. We illustrate the problem with the causal tree in Figure 12.1 . In the figure, each node represents a variable, and each arrow represents a causal relation. There are four causal links, but six additional associations (the dotted lines). 1 These additional associations can be inferred from the causal links, and thus are redundant. In an associative world, if information on any of the six extra associations is salient (e.g., as information on a rooster's crowing and sunrise might be), they would be indistinguishable from the causal links. Thus, not only would the extra associations be inefficient to store, many would yield erroneous predictions based on actions. For example, node D in the figure is linked by a single arrow, but by three additional associations, to nodes B, C, and E; manipulating any of these variables would not lead to D, the “desired” outcome predicted by these three associations.

Finally, not only would we be unable to achieve our goals, but we would be unable to structure an otherwise chaotic flux of events into meaningful episodes. We explain events by causation. Returning to our storm example, whereas we might explain that a car skidded and rolled down the mountainside because of the rainstorm, it would be odd to explain that the car skidded because of the low barometric reading. Causal explanations are universal, as anthropologists who study everyday narratives across cultures have observed; they serve to imbue life events with an orderliness, to demystify unexpected events, and establish coherence (Ochs & Capps, 2001 ).

Predicting the Consequences of Actions to Achieve Goals: A Framework for Causal Learning, Category Formation, and Hypothesis Revision

For the just mentioned reasons, it is easy to see why it is important to distinguish between causation and mere association. A less obvious reason, one that has implications for the formulation of the problem to be solved, is that whereas associations are observable, causal relations are inherently unobservable and can only be inferred. For example, one can observe the number of lung cancer patients among cigarette smokers and among nonsmokers and see the association between cigarette smoking and lung cancer, but the association can be causal or noncausal. It may, for example, be due to confounding by the higher incidence of radon in the smokers' dwellings, and the exposure to radon is what caused the smokers' lung cancer. The challenge is how to encapsulate causal relations, even though they are unobservable, so that the causal knowledge can be applied to best achieve desired outcomes.

We have so far implicitly assumed that cause-and-effect variables, such as “sunrise,” “drop in barometric reading,” and “storm,” are predefined, given to the causal learner, and only the relations between them are to be discovered. A more realistic description of the situation is: In order for our causal knowledge to be generalizable from the learning context (e.g., prior experience, whether one's own or that of others, shows that icy roads cause skidding) to the application context (I don't want my car to skid, so I will wait until the ice has melted before I drive), we construct a representation of the world in which cause-and-effect variables are so defined that they enable ideally invariant causal relations to be constructed. As the philosopher C. I. Lewis (1929) observed, “Categories are what obey laws.” Defining the objects, events, and categories linked by causal relations is part of the problem of causal discovery. Fortunately for cognitive psychologists studying human causal discovery, some of the work defining variables is already taken care of by evolution, prewired into our perceptual system and emotions. For example, we see a rooster as figure against the ground of the farm landscape. Strong gusts of wind alarm us, and getting wet in the rain is unpleasant. But there is definitely remaining work; for example, what determines that “ants migrating uphill” should be defined as a variable?

Whenever we apply causal knowledge to achieve a goal, we are assuming that the causal relations in question remain invariant from the learning context to the application context. Because of our limited causal knowledge, however, a causal relation that we assume to be invariant would no doubt in fact often change (e.g., a scientist might hypothesize “vitamin E has antioxidant effects” but find instead that whereas natural foods rich in vitamin E have antioxidant effects, vitamin E pills do not). The assumption of causal invariance in our everyday application of causal knowledge might seem too strong. Although simplistic as a static hypothesis, however, this assumption is rational as a defeasible default within the dynamic process of hypothesis testing and hypothesis revision. Given our limited access to information at any particular moment, the criterion of causal invariance serves as a compass aimed at formulating the simplest explanation of a phenomenon that allows invariance to obtain (e.g., the scientist might search for other substances in natural foods that in conjunction with vitamin E consistently produce the effects). Observed deviation from the default indicates a need for hypothesis revision, a change in direction aimed at capturing causal invariance (Carroll & Cheng, 2010 ).

Cheng (2000) showed that an alternative assumption that would also justify generalization of a causal relation regarding an outcome to a new context is that enabling conditions (causal factors in the contextual background interacting with the hypothesized cause) and preventive causes that occur in the background (all of which are often unobserved) occur just as frequently in the generalization context as in the learning context. She also showed that with respect to the accuracy of generalization to new contexts, the two assumptions are equivalent. In the rest of our chapter, we use causal invariance (which we term “independent causal influence” when we define it mathematically) because it is the simpler of the two equivalent conceptions.

Now that we have considered some goals and constraints of causal inference, let us rephrase the question of causal learning with respect to those goals and constraints: How can any intelligent agent given the information and resources available to humans discover ideally invariant causal relations that support generalization from the learning context to an application context? In particular, would it suffice to have a powerful statistical process that detects regularities among events but lacks any a priori assumptions about how the world works? Because humans have limited access to information, an accompanying question is, What hypothesis testing and revision process would allow the ideally invariant causal relations to be constructed?

By posing our question in terms of discovery, we by no means rule out the possibility that there exist some innate domain-specific biases. Classic studies by Garcia, McGowan, Ervin, and Koelling (1968) demonstrated two such biases. In each of four groups of rats, one of two cues, either a novel size or a novel flavor of food pellets, was conditionally paired with either gastrointestinal malaise induced by X-ray or with pain induced by electrical shock. The combination of flavor and illness produced a conditioned decrement in the amount consumed but that of the size of the pellet and illness did not. Conversely, the combination of size and pain produced hesitation before eating, but flavor and pain did not. Apparently, the novelty had to be of the right kind for effective causal learning regarding the malaise and shock to occur.

Most of what we do know about the world, however, must have been acquired due to experience. How else could we have come to know that exposure to the sun causes tanning in skin but causes bleaching in fabrics? Or come to know that billiard ball A in motion hitting billiard ball B at rest would not jump over B, rebound leaving B still, or explode (Hume, 1739 / 1888 )? Notice that it is not necessary for the causal learner to know how sunlight causes tanning in skin or bleaching in fabrics to discover that it does. Neither was it necessary, for that matter, for the rats to know how the X-ray or electricity caused their respective effects for their learning to occur. We will return to the issue of adding intervening nodes in a causal network to explain how an outcome is achieved via a causal mechanism.

Proposed Solutions: Two Dominant Approaches

We have only gone so far as posing the problem to be solved. Hopefully, posing the problem clearly will mean much of the work has been done. In the rest of this chapter, we review proposed solutions according to two dominant approaches: the associative approach, including its statistical variants, and the causal approach. We follow each of these accounts with a review of main empirical tests of the approach. (For a discussion of how the perceptual view [Michotte, 1946 / 1963 ], the mechanism view [Ahn, Kalish, Medin, & Gelman, 1995 ], and the coherence view [Thagard, 2000 ] relate to these approaches, see Buehner and Cheng [2005] .) We then broaden our scope to consider the role of temporal information in causal learning. We end the chapter with a sketch of future research directions.

The Associative Approach

An intuitive approach that has dominated psychological research on learning is the associative approach (e.g., Allan & Jenkins, 1980 ; Jenkins & Ward, 1965 ; Rescorla & Wagner, 1972 ), which traces its roots to the philosopher David Hume (1739 / 1888 ). Hume made a distinction between analytic and empirical knowledge, and argued that causal knowledge is empirical. Only experience tells us what effect a cause has. The strong conviction of causality linking two constituent events is but a mental construct. The problem of causal learning posed by Hume radically shaped subsequent research on the topic and set the agenda for the study of causal learning from a cognitive science perspective. Both the associative and causal approaches are predicated on his posing of the problem.

To Hume, the relevant observed aspects of experience that give rise to the mentally constructed causal relations were the repeated association between the observed states of a cause and its effect, their temporal order and contiguity, and spatial proximity. Our examples have illustrated that one can predict a future event from a covariation —the concerted variation among events—provided that causes of that event remain unperturbed. Predictions of this kind are clearly useful; we appreciate weather reports, for example. To early associative theorists, causality is nothing more than a fictional epiphenomenon floating unnecessarily on the surface of indisputable facts. 2 After all, causal relations are unobservable. In fact, Karl Pearson, one of the fathers of modern statistics, subscribed to a positivist view and concluded that calculating correlations is the ultimate and only meaningful transformation of evidence at our disposal: “Beyond such discarded fundamentals as ‘matter’ and ‘force’ lies still another fetish amidst the inscrutable arcana of modern science, namely, the category of cause and effect” (Pearson, 1911 , p. iv).

But, as we saw earlier, mere associations are inadequate for predicting the consequences of actions and would also be inefficient to store. Thus, in addition to dissecting the traditional associative view to understand its shortcomings, we will also consider a more viable augmented variant of the associative view, one similar to how scientists infer causation. The augmented view assumes that rational causal learning requires not only a sophisticated detector of covariations among events but also the use of actions as a causality marker: When the observed states of events are obtained by an action, by oneself or others, intervening in the normal course of events, the observed associations are causal; otherwise, they are noncausal. After all, one can observe that actions are what they are; there is therefore no deviation from Hume's constraint that causal discovery begins with observable events as input. In entertaining this variant, we are taking the perspective of the design of an intelligent causal learner on our planet, rather than adhering to how the associative view has been traditionally interpreted. This more viable variant of the associative view implicitly underlies the use of associative statistics in typical tests of causal hypotheses in medicine, business, and other fields. It retains the strong appeal of the associative approach, namely, its objectivity. Other things being equal, positing unobservable events, as the causal view does, seems objectionable.

A growing body of research is dedicated to the role of intervention in causal learning, discovery, and reasoning (e.g., Blaisdell, Sawa, Leising, & Waldmann, 2006 ; Gopnik et al., 2004 ; Lagnado & Sloman, 2004 ; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003 ). Indeed, the general pattern reported is that observations based on intervention allow causal inferences that are not possible based on mere observations.

A Statistical Model

For situations involving only one varying candidate cause, an influential decision rule for more than four decades has been the ΔP rule:

according to which the strength of the relation between binary causes c and effects e is determined by their contingency or probabilistic contrast —the difference between the probabilities of e in the presence and absence of c (see, e.g., Allan & Jenkins, 1980 ; Jenkins & Ward, 1965 ). ΔP is estimated by relative frequencies. In our equations, we denote the “presence” value of a binary variable by a “+” superscript and the “absence” value by a “−” superscript (e.g., c+ denotes the presence of c). Figure 12.2 displays a standard contingency table where cells A and B respectively, represent the frequencies of the occurrence, and nonoccurrence, of e in the presence of c; cells C and D represent, respectively, the frequencies the occurrence, and of nonoccurrence, of e in the absence of c .

A standard 2 x 2 contingency table; a through d are labels for event types resulting from factorial combination of the presence and absence of cause c and effect e .

If ΔP is noticeably positive, then c is thought to produce e ; if it is noticeably negative, then c is thought to prevent e ; and if ΔP is not noticeably different from zero, then c and e are thought not to be causally related to each other. Several modifications of the ΔP rule to include various parameters have been proposed (e.g., Anderson & Sheu, 1995 ; Perales & Shanks, 2007 ; Schustack & Sternberg, 1981 ; White, 2002 ). By allowing extra degrees of freedom, these modified models fit certain aspects of human judgment data better than the original rule. Another type of modification is to compute the ΔP value of a candidate cause conditioned on constant values of alternative causes (Cheng & Holyoak, 1995 ). This modification allows the model to better account for the influence of alternative causes (as illustrated later). Like all other psychological models of causal learning, all variants of the ΔP model assume that the candidate causes are perceived to occur before the effect in question.

An Associationist Model

In the domain of animal learning, an organism's capacity to track contingencies in its environment has long been of central interest, and apparent parallels between conditioning and causal learning have led many researchers (see Shanks & Dickinson, 1987 ; for a review see De Houwer & Beckers, 2002 ) to search for explanations of human causal learning in neural-network models that specify the algorithm of learning. The most influential associationist theory, the Rescorla-Wagner (RW) model (Rescorla & Wagner, 1972 ), and all its later variants, is based on an algorithm of error correction driven by a discrepancy between the expected and actual outcomes. For each learning trial where a cue was presented the model specifies

where ΔV is the change in the strength of a given CS-US association on a given trial (CS stands for conditioned stimulus, e.g., a tone; US stands for unconditioned stimulus, e.g., a footshock), α and β represent learning rate parameters reflecting the saliencies of the CS and US, respectively, λ stands for the actual outcome of each trial (usually 1.0 if it is present and 0 if it is absent), and ΣV is the expected outcome defined as the sum of all associative strengths of all CSs present on that trial.

For situations involving only one varying cue, its mean weight at equilibrium according to the RW algorithm has been shown to equal ΔP if the value of β remains the same when the US is present and when it is absent for the λ values just mentioned (Chapman & Robins, 1990 ; Danks, 2003 ). In other words, this simple and intuitive algorithm elegantly explains why causal learning is a function of contingency. It also explains a range of results for designs involving multiple cues, such as blocking (see section on “Blocking” to follow), conditioned inhibition , overshadowing , and cue validity (Miller, Barnet, & Grahame, 1995 ).

Blocking: Illustrating an Associationist Explanation

“Blocking” (Kamin, 1969 ) occurs after a cue (A) is established as a perfect predictor (A+, with “+” representing the occurrence of the outcome), followed by exposure to a compound consisting of A and a new, redundant, cue B. If AB is also always followed by the outcome (AB+), cue B receives very little conditioning; its conditioning is blocked by cue A. According to RW, A initially acquires the maximum associative strength supported by the stimulus. Because the association between A and the outcome is already at asymptote when B is introduced, there is no error left for B to explain, hence the lack of conditioning to B. What RW computes is the ΔP for B conditioned on the constant presence of A. Shanks (1985) replicated the same finding in a causal reasoning experiment with human participants, although the human responses seemed to reflect uncertainty of the causal status of cue B rather than certainty that it is noncausal (e.g., Waldmann & Holyoak, 1992 ).

Failure of the RW Algorithm to Track Covariation When a Cue Is Absent

However, Shanks' (1985) results also revealed evidence for backward blocking; in fact, there is evidence for backward blocking even in young children (Gopnik et al., 2004 ). In this procedure, the order of learning phases is simply reversed; participants first learn about the perfect relation between AB and the outcome (AB+), and subsequently learn that A by itself is also a perfect predictor (A+). Conceptually, forward and backward blocking are identical, at least from a causal perspective. A causal explanation might go: If one knows that A and B together always produce an effect, and one also knows that A by itself also always produces the effect, one can infer that A is a strong cause. B, however, might be a cause, even a strong one, or noncausal; its causal status is unclear. Typically, participants express such uncertainty with low to medium ratings relative to ratings for control cues that have been paired with the effect an equal number of times (see Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008 , for a review).

Beyond increasing susceptibility to attention and memory biases (primacy and recency; see, e.g., Dennis & Ahn, 2001 ), there is no reason why the temporal order in which knowledge about AB and A is acquired should play a role from a rational standpoint. This is not so for the RW model, however. The model assumes that the strength of a cue can only be updated when that cue is present. In the backward blocking paradigm, however, participants retrospectively alter their estimate of B on the A+ trials in phase 2. In other words, the ΔP of B, conditioned on the presence of A, decreases over a course of trials in which B is actually absent, and the algorithm therefore fails to track its covariation.

Several modifications of RW have been proposed to allow the strengths of absent cues to be changed, for instance, by setting the learning parameter α negative on trials where the cue is absent: Van Hamme and Wasserman's (1994) modified RW model, Dickinson and Burke's modified sometimes-opponent-process model (1996), and the comparator hypothesis (Denniston, Savastano, & Miller, 2001 ; Miller & Matzel, 1988 ; Stout & Miller, 2007 ). Such modifications can explain backward blocking and some other findings showing retrospective revaluation (for an extensive review of modifications to associative learning models applicable to human learning see De Houwer & Beckers, 2002 ). But these modifications also oddly predict that one will have difficulty learning that there are multiple sufficient causes of an effect. For example, if one drinks tea by itself and finds it quenching, but one sometimes drinks both tea and lemonade, then learning subsequently that lemonade alone can quench thirst will cause one to unlearn that tea can quench thirst. Carroll, Cheng, and Lu (2010) found that in such situations human subjects do not revise causal relations for which they have unambiguous evidence (e.g., that tea is quenching).

Causal Inference: Empirical Findings on Humans and Rats

Association does not equal causation, as we illustrated earlier and as every introductory statistics text warns. We now review how humans and rats reason causally rather than merely associatively.

The Direction of Causality

The concept of causality is fundamentally directional (Reichenbach, 1956 ) in that causes produce effects, but effects cannot produce causes. Thus, whereas we might say that, given the angle of the sun at a certain time of the day, the height of a flagpole explains the length of its shadow on the ground, it would be odd to say the reverse. 3 A straightforward demonstration that humans make use of the direction of the causal arrow was provided by Waldmann and Holyoak (1992) , who reasoned that only causes, but not effects, should “compete” for explanatory power. If P is a perfect cause of an outcome A, and R, a redundant cue, is only presented preceding A in conjunction with P, one has no basis of knowing to what extent, if at all, R actually produces A. Consequently, the predictiveness of R should be depressed relative to P in a predictive situation. But if P is instead a consistent effect of A, there is no reason why R cannot also be an equally consistent effect of A. Alternative causes need to be kept constant to allow causal inference, but alternative effects do not. Consequently, the predictiveness of R should not be depressed in a diagnostic situation.

This asymmetry prediction was tested with the blocking design, using scenarios to manipulate whether a variable is interpreted as a candidate cause or as an effect. Participants in Waldmann and Holyoak's (1992) Experiment 3 had to learn the relation between several light buttons and the state of an alarm system. The instructions introduced the buttons as causes for the alarm in the predictive condition, but as potential consequences of the state of the alarm system in the diagnostic condition.

Waldmann and Holyoak found exactly the pattern of results they predicted: There was blocking in the predictive condition, but not the diagnostic condition. These results reveal that humans make use of the direction of the causal arrow. Follow-up work from Waldmann's lab (Waldmann & Holyoak, 1997 ; Waldmann, 2000 , 2001 ) as well as others (Booth & Buehner, 2007 ; López, Cobos, & Caño, 2005 ) has demonstrated that the asymmetry in cue competition is indeed a robust finding.

Ceiling Effects

One might think that augmenting statistical models with intervention would solve the problem of the directionality of causation. But although intervention generally allows causal inference, it does not guarantee it. Consider a food allergy test that introduces samples of food into the body by needle punctures on the skin. The patient may react with hives on all punctured spots, and yet one may not know whether the patient is allergic to any of the foods. Suppose her skin is allergic to needle punctures, so that hives appear also on punctured spots without food. In this example, there is an intervention, but no causal inference regarding food allergy seems warranted (Cheng, 1997 ). More generally, interventions are subject to the problem of the well-known placebo effect , in which the intended intervention is accompanied by a concurrent intervention (as adding allergens into the bloodstream is accompanied by the puncturing the skin), resulting in confounding. Our example illustrates that intervention does not guarantee causal inference. Not only is intervention insufficient for differentiating causation from association, it is also unnecessary. Mariners since ancient times have known that the position and phase of the moon is associated with the rising and falling of the tides (Salmon, 1989 ). Notably, they did not consider the association causal, and they had no explanation for the ebb and flow of the tides, until Newton proposed his law of universal gravitation. No intervention on the moon and the tides is possible, but there was nonetheless a dramatic change in causal assessment.

A revealing case of the distinction between covariation and causation that does not involve confounding has to do with what is known in experimental design as a ceiling effect . We illustrate this effect with the preventive version of it (a principle never covered in courses on experimental design); the underlying intuition is so powerful it needs no instruction. Imagine that a scientist conducts an experiment to find out whether a new allergy drug relieves migraine as a side effect. She follows the usual procedure and administers the medicine to an experimental group of patients, while an equivalent control group receives a placebo. At the end of the study, the scientist discovers that none of the patients in the experimental group but also none of the patients in the control group suffered from migraine. The effect never occurred, regardless of the intervention. If we enter this information into the ΔP rule, we see that P( e + | c + ) = 0 and P( e + | c − ) = 0, yielding ΔP = 0. According to the ΔP rule and RW, this would indicate that there is no causal relation, that is, the drug does not relieve migraine. Would the scientist really conclude that? No, the scientist would instead recognize that she has conducted a poor experiment and hence withhold judgment on whether the drug relieve migraine. If the effect never occurs in the first place, how can a preventive intervention be expected to prove its effectiveness?

Even rats seem to appreciate this argument (Zimmer-Hart & Rescorla, 1974 ). For associative models, however, when an inhibitory cue (i.e., one with negative associative strength) is repeatedly presented without the outcome, so that the actual outcome is 0 whereas the expected outcome is negative, the prediction is that the cue reduces its strength toward 0. That is, in a noncausal world, we would unlearn our preventive causes whenever they are not accompanied by a generative cause. For example, if we inoculate child after child with polio vaccine in a country, and there is no occurrence of polio in that country, we would come to believe that the polio vaccine does not function anymore, rather than merely that it is not needed. To the contrary, even for rats, the inhibitory cue retains its negative strength (Zimmer-Hart & Rescorla, 1974 ). In other words, when an outcome in question never occurs, either when a conditioned inhibitory cue is present or when it is not, rats apparently treat the zero ΔP value as uninformative, retaining the inhibitory status of the cue. In this case, in spite of a discrepancy between the expected and actual outcomes, there is no revision of causal strength.

Notice that given the aforementioned hypothetical migraine-relief experiment, from the same exact data, showing that migraine never occurs one can conclude that the drug does not cause migraine rather than withhold judgment. Thus, given the exact same covariation, the causal learner can simultaneously have two conclusions depending on the direction of influence under evaluation (generative vs. preventive). Wu and Cheng (1999) conducted an experiment that showed that beginning college students, just like experienced scientists, do and do not refrain from making causal inferences in the generative and preventive ceiling effects situations depending (in opposite ways) on the direction of influence to be evaluated. We are not aware of any convincing modification of associationist models that can accommodate the finding.

Definition of Causal Invariance: Beyond Augmentation of Associations With Intervention and Other Principles of Experimental Design

The same problem that leads to the ceiling effect—namely, the lack of representation of causal relations—manifests itself even when all the principles of experimental design are obeyed. Even in that case, the associative view makes anomalous predictions. Liljeholm and Cheng (2007 , Experiment 2) presented college students with a scenario involving three studies of a single specific cue A (Medicine A, an allergy medicine) as a potential cause of an outcome (headache as a potential side-effect of the allergy medicine). In the scenario, allergy patients in the studies were randomly assigned to an experimental group that received Medicine A and a control group that received a placebo. In the three studies, the probability of the outcome was higher by, respectively, ¼, ½, and ¾ in the experimental group than in the control group (i.e., ΔP = ¼, ½, and ¾; see Table 12.1 ). In a varying-base-rate condition, the base rate of headache differed across the three studies. In a constant-base-rate condition, the base rate of the effect remained constant: Headache never occurred without the medicine. The students were asked to assess whether the medicine interacted with unobserved causes in the background across the studies or influenced headache the same way across them. As intuition suggests, more students in the constant-base-rate condition than in the varying-base-rate condition (13 out of 15, vs. 5 out of 15, respectively) judged the medicine to interact with the background causes.

Because the changes in covariation, as measured by associative models such as Δ P (Jenkins & Ward, 1965 ) or RW (Rescorla & Wagner, 1972 ), were the same across conditions, these associative models could not explain the observed pattern of judgments. Thus, even when there is an effective intervention and there is no violation of the principles of experimental design, a statistical account will not suffice. We return to discuss the implications of these results later.

Intervention Versus Observation

Following analogous work on humans (Waldmann & Hagmayer, 2005 ), Blaisdell et al. (2006) reported a result that challenges associative models: Rats are capable of distinguishing between observations and interventions. In Experiment 1, during a Pavlovian learning phase rats were trained on two interspersed pairs of associations: A light cue (L) is repeatedly followed by either a tone (T) or food (F). If the rats learned that L is a common cause of T and F (see Fig. 12.5 a), then in the test phase, observing T should lead them to infer that L must have occurred (because L was the only cause of T), which should in turn lead them to predict F (because L causes F). The number of nose pokes into the food bin measures prediction of F. Consider an alternative condition in which during a test phase the rats learn that pressing on a newly introduced lever turns on T. Because generating T by means of an alternative cause does not influence its cause (L), turning T on by pressing a lever should not lead the rats to predict F. After the learning phase, rats were allocated to either the observation or the intervention condition. The occurrences of T in the test phase were equated across the two conditions by yoking the observation rats to the intervention rats, so that when a rat in the intervention condition pressed the lever and T followed, a rat in the observation condition heard T at the same time, independently of their lever pressing. L and F never occurred during the test phase. Remarkably, the observation rats nose-poked more often than the intervention rats in the interval following T, even though during the learning phase, T and F never occurred simultaneously on the same trial.

Because all occurrences of L, T, and F were identical across the observation and intervention groups, associations alone cannot explain the difference between observing T and intervening to obtain T. Even if augmented with the assumption that interventions have special status, so that the pairing between lever pressing and T, for example, is learned at a much faster rate than purely observed pairings, there would still be no explanation for why the intervention rats apparently associate T with L less than did the observation rats. We will return to discuss a causal account of the observed difference.

A Causal Approach

A solution to the puzzles posed by the distinction between covariation and causation is to have a leap of faith that causal relations exist, even though they are unobservable (Kant, 1781 / 1965 ). This leap of faith distinguishes the diverse variants of the causal approach from all variants of the associative approach. Some psychologists have proposed that human causal learning involves positing candidate causal relations and using deductive propositional reasoning to arrive at possible explanations of observed data (De Houwer, Beckers, & Vandorpe, 2005 ; Lovibond, Been, Mitchell, Bouton, & Frohardt, 2003 ; Mitchell, De Houwer, & Lovibond, 2009 ). Others (Gopnik et al., 2004 ) have proposed that human causal learning is described by causal Bayes nets , a formal framework in which causal structures are represented as directed acyclic graphs (Pearl, 2000 ; Spirtes, Glymour, & Scheines, 1993 / 2000 ; see Sloman, 2005 , for a more accessible exposition). The graphs consist of arrows connecting some nodes to other nodes, where the nodes represent variables and each arrow represents a direct causal relation between two variables; “acyclic” refers to the constraint that the paths formed by the arrows are never loops. Others have proposed a variant of causal Bayes nets that makes stronger causal assumptions; for example, assume as a defeasible default that causes do not interact, and revise that assumption only when there is evidence against it. The stronger assumptions enable the learner to construct causal knowledge incrementally (Buehner, Cheng, & Clifford, 2003 ; Cheng, 1997 , 2000 ; Griffiths & Tenenbaum, 2005 ; Lu, Yuille, Liljeholm, Cheng, & Holyoak, 2008 ; Waldmann, Cheng, Hagmayer, & Blaisdell, 2008 ).

These variants of the causal view, in addition to their explicit representation of causal relations, share a rational perspective (see Chater & Oaksford, Chapter 2 ). Thus, they all have a goal of inferring causal relations that best explain observed data. They all make use of deductive inference (for examples of the role of analytic reasoning in empirical learning, see Mermin, 2005 ; Shepard, 2008 ). It may be said that they all assume that the causal learner deduces when to induce! Our focus in this chapter is on explaining basic ways in which the causal approach provides a solution to what appears to be impasses from an associative perspective.

A Theory of Causal Induction

We use Cheng (1997) 's causal power theory (also called the power PC theory, short for “a causal power theory of the probabilistic contrast model”) to illustrate how a causal theory explains many of the puzzles mentioned earlier. This theory starts with the Humean constraint that causality can only be inferred, using observable evidence (e.g., covariations, temporal ordering, and spatial information) as input to the reasoning process. It combines that constraint with Kant's (1781 / 1965 ) postulate that reasoners have a priori notions that types of causal relations exist in the universe.

This unification can best be illustrated with an analogy. The relation between a causal relation and a covariation is like the relation between a scientific theory and a model. Scientists postulate theories (involving unobservable entities) to explain models (i.e., observed regularities or laws); the kinetic theory of gases, for instance, is used to explain Boyle's law. Boyle's law describes an observable phenomenon, namely that pressure × volume = constant (under certain boundary conditions), and the kinetic theory of gases explains in terms of unobservable entities why Boyle's law holds (gases consist of small particles moving at a speed proportional to their temperature, and pressure is generated by the particles colliding with the walls of the container). Likewise, a causal relation is the unobservable entity that reasoners strive to infer in order to explain observable regularities between events. This distinction between a causal relation as an unobserved, distal, postulated entity and covariation as an observable, proximal stimulus property implies that there can be situations where evidence is observable, but inference is not licensed, and the goal of causal inference thus cannot be met. Specifically, this means that the desired distal unknown, such as causal strength, is represented as a variable (cf. Doumas & Hummel, Chapter 4 ; Holyoak & Hummel, 2000 ), separately from covariation, allowing situations where covariation has a definite value (e.g., 0, as in the ceiling effect), but the causal variable has no value.

How, then, does the causal power theory (Cheng, 1997 ) go beyond the proximal stimulus and explain the various ways in which covariation does not imply causation? The path through the derivation of the estimation of causal strength reveals the answers. For inferring simple (i.e., elemental) causal relations, the theory partitions all causes of effect e into the candidate cause in question, c , and a , a composite of all (observed and unobserved) alternative causes of e . “Alternative causes” of e include all and only those causes of e that are not on the same causal path to e as c . Thus, c can be thought of as a composite that includes all causes on the same causal path as c preceding e . This partitioning is a general structure that maps onto all learning situations involving candidate causes and effects that are binary variables with a “present” and an “absent” value. We focus on this type of variables because they best reveal how the associative and causal views differ.

The unobservable probability with which c produces e (i.e., the probability that e occurs as a result of c occurring), termed the generative causal power of c with respect to e , is represented by a variable, q c . When Δ P ≥ 0, q c is the desired unknown. Likewise, when Δ P ≤ 0, the preventive causal power of c , denoted by p c , is the desired unknown. Two other relevant theoretical unknowns are q a , the probability with which a produces e when it occurs, and P( a ), the probability with which a occurs. The composite a may include unknown or unobservable causes. Because any causal power variable may have a value of 0, or an unknown or undefined value, these variables are merely hypotheses—they do not presuppose that c and a indeed have causal influence on e . The idea of a cause producing an effect and of a cause preventing an effect are primitives in the theory (see Goodman, Ullman, & Tenenbaum, 2011 , and Tenenbaum, Kemp, Griffiths & Goodman, 2011 , for an alternative view).

The theory assumes four general simplifying beliefs (Cheng, 1997 ; Novick & Cheng, 2004 ):

c and a influence e independently,

a could produce e but not prevent it,

causal powers are independent of the frequency of occurrences of the causes (e.g., the causal power of c is independent of the frequency of occurrence of c ), and

e does not occur unless it is caused.

Assumption 1 is a leap of faith inherent to this incremental learning variant of causal discovery. This is the defeasible default assumption we termed “causal invariance” earlier. Two causes influencing effect e “independently” means that the influence of each on e remains unchanged regardless of whether e is influenced by the other cause. Assumption 2 is likewise a default hypothesis, adopted unless evidence discredits it. (Alternative models apply if assumption 1 or 2 is discredited; see Novick & Cheng 2004 ; see Cheng, 2000 , for implications of the relaxation of these assumptions.) This set of assumptions, which is stronger than that assumed in standard Bayes nets, enables causal relations to be learned one at a time, when there is information on only the occurrences of two variables, a single candidate cause and an effect. The type of learning described by the theory therefore requires less processing capacity. It is assumed that, as in associative models, when there is information on which variable is an effect, the causal learner iterates through candidate causes of the effect, grouping all potential causes other than the candidate in question as the composite alternative cause. Otherwise, the causal learner iterates through all possible variable pairs of candidate causes and effects.

These assumptions imply a specific function for integrating the influences of multiple causes (Cheng, 1997 ; Glymour, 2001 ), different from the additive function assumed by associative models. For the situation in which a potentially generative candidate cause c occurs independently of other causes, the probability of observing the effect e is given by a noisy-OR function,

where c Σ {0,1} denotes the absence and the presence of the candidate cause c . Recall that in our equations we denote the “presence” value of a binary variable by a “+” superscript and the “absence” value by a “−” superscript. In contrast, variables have no superscripts. As just mentioned, variable q c represents the generative power of the candidate cause c . Because it is not possible to estimate the causal power of unobserved causes, variable w a represents P( a + ) · q a . In the preventive case, the same assumptions are made except that c is potentially preventive. The resulting noisy-AND-NOT integration function for preventive causes is

where p c is the preventive causal power of c .

Using these “noisy-logical” integration functions (terminology due to Yuille & Lu 2008 ), Cheng (1997) derived normative quantitative predictions for judgments of causal strength. Under the aforementioned set of assumptions, the causal power theory explains the two conditional probabilities defining ΔP as follows:

Equation 5 “explains” that given that c has occurred, e is produced by c or by the composite a , nonexclusively ( e is jointly produced by both with a probability that followsfrom the independent influence of c and a on e ). Equation 6 “explains” that given that c did not occur, e is produced by a alone.

Explaining the Role of “No Confounding” and Why Manipulation Encourages Causal Inference But Does Not Guarantee Success

It follows from Equation 3 and 4 that

From Equation 7 , it can be seen that there are four unknowns: q c , q a , P(a + |c − ), and P(a + |c − )! It follows that in general, despite Δ P having a definite value, there is no unique solution for q c . This failure to solve for q c corresponds to our intuition that covariation need not imply causation.

When there is no confounding . Now, in the special case in which a occurs independently of c (e.g., when alternative causes are held constant), P(a + | c + ) = P(a + | c − ). If one is willing to assume “no confounding,” then making use of Equation 6 , Equation 7 simplifies to Equation 8 ,

in which all variables besides q c are observable. In this case, q c can be solved. Being able to solve for q c only under the condition of independent occurrence explains why manipulation by free will encourages causal inference in everyday reasoning—alternative causes are unlikely to covary with one's decision to manipulate. For the same reason, it explains the role of the principle of control in experimental design.

At the same time, the necessity of the “ no confounding ” condition explains why causal inferences resulting from interventions are not always correct; although alternative causes are unlikely to covary with one's decision to manipulate, they still may do so, as our needle-puncture allergy example illustrates. Note that the “no confounding” condition is a result in this theory, rather than an unexplained axiomatic assumption, as it is in current scientific methodology (also see Dunbar & Klahr, Chapter 35 ).

An analogous explanation yields p c , the power of c to prevent e

Griffiths and Tenenbaum (2005) showed that if one represents uncertainty about the estimates of causal power by a distribution of the likelihood of each possible strength given the data, then Equation 8 and 9 , respectively, are maximum likelihood point estimates of the generative and preventive powers of the candidate cause; that is, they are the peak of the posterior likelihood distributions.

Explaining Two Ceiling Effects

Equation 8 and 9 explain why ceiling effects block causal inference and do so under different conditions for evaluating generative and preventive causal influence. When the outcome does not occur at either a ceiling (i.e., extreme) level, both equations yield either causal power of 0 when the occurrence of c makes no difference to the occurrence of e (ΔP = 0). When e always occurs (i.e., P(e + |c + ) = P(e + |c + ) =1) regardless of the manipulation, however, q c in Equation 8 (the generative case) is left with an undefined value. In contrast, in the preventive case, when e never occurs (i.e., P(e + |c + ) = P(e + |c − ) = 0), again regardless of the manipulation, p c in Equation 9 is left with an undefined value. 4

As we mentioned, most causes are complex, involving not just a single factor but a conjunction of factors operating in concert, and the assumption that c and a influence e independently may be false most of the time. When this assumption is violated, if an alternative cause (part of a ) is observable, the independent influence assumption can be given up for the observable alternative cause, and progressively more complex causes can be evaluated using the same distal approach that represents causal powers (see Novick & Cheng, 2004 , for an extension of this approach to evaluate conjunctive causes involving two factors). Even if alternative causes are unknown, however, Cheng (2000) showed that as long as they occur with about the same probability in the learning context as in the generalization context, predictions according to simple causal power involving a single factor will hold.

Some have claimed that the causal power approach cannot account for reasoning that combines observations with interventions. As just shown, however, this approach explains the role of interventions in causal learning and how it differs from observation. Likewise indicating that this approach readily accommodates the combination, Waldmann et al. (2008) derived an equation under the causal power assumptions that explains Blaisdell et al.'s results regarding the distinction between observations and interventions in diagnostic reasoning.

Experimental Tests of a Causal Approach

We examine three findings in support of the causal approach. None of these findings can be explained by the associative view, even when augmented with the assumption that only interventions enable causal inference. The first two findings test the two leaps of faith: that causal relations exist and that they are invariant across contexts. The first finding concerns the independent causal influence assumption as manifested in a qualitative pattern of the influence of P(e + |c + ), the base rate of e , for candidate causes with the same ΔP. The second illustrates the parsimony of a causal explanation that assumes independent causal influence across different types of “effect” variables, specifically, dichotomous and continuous (Beckers, De Houwer, Pineno, & Miller, 2005 ; Beckers, Miller, De Houwer, & Urushihara, 2006 ;Lovibond et al., 2003 ). The third concerns the test reviewed earlier of the distinction between observation and intervention (“seeing” vs. “doing”) in diagnostic causal inference (Blaisdell et al., 2006 ; Waldmann & Hagmayer, 2005 ). We consider explanations of this distinction as an illustration of the compositionality of the causal view and of the role of deductive reasoning in causal inference.

The Independent Causal Influence Assumption Affects Causal Judgments: Base- Rate Influence on Conditions With Identical ΔP

As we noted, a major purpose of causal discovery is to apply the acquired causal knowledge to achieve goals, and that the independent causal influence assumption is a leap of faith that justifies generalization from the learning context to the application context. Here, we see that the assumption leads to causal judgments that differ from those predicted by associative models, even those augmented with a privileged status for interventions and other principles of experimental design. In other words, this assumption not only affects the application of causal knowledge, it affects the very discovery of that knowledge itself.

Do people have this leap of faith? Let us examine the predictions based on the causal power assumptions in greater detail. If we consider Equation 8 , for any constant positive ΔP, generative causal ratings should increase as P(e + |c − ) increases. Conversely, according to Equation 9 , for any constant negative ΔP, preventive causal ratings should decrease as P(e + |c − ) increases. On the other hand, according to both equations, zero contingencies should be judged as noncausal regardless of the base rate of e except when the base rate is at the respective ceiling levels.

No associative model of causal inference, descriptive or prescriptive, predicts this qualitative pattern of the influence of the base rate of e . Normative models are symmetric around the probability of .5 and therefore do not predict an asymmetric pattern either for generative causes alone or for preventive causes alone. Although some psychological associative learning models can explain one or another part of this pattern given felicitous parameter values, the same parameter values will predict notable deviations from the rest of the pattern. For example, in the RW, if β US 〉 β ¬US causal ratings for generative and preventive causes will both increase as base-rate increases , whereas they will both decrease as base-rate increases if the parameter ordering was reversed. No consistent parameter setting will predict opposite trends for generative as for preventive causes for the same change in the base rate of e . Another prominent associative learning model, Pearce's (1987) model of stimulus generalization, can account for opposite base rate influences in positive and negative contingencies if the parameters are set accordingly, but this model would then predict a base-rate influence on noncontingent conditions.

Example stimulus materials from a condition in Buehner et al. (2003) .

Figure 12.3 illustrates the intuitiveness of a deviation from ΔP. The reasoning is counterfactual. P(e + |c − ), 1/3 in the figure, estimates the “expected” probability of e in the presence of c , if c had been absent so that only causes other than c exerted an influence on e . A deviation from this counterfactual probability is evidence for c being a simple cause of e . Under the assumption that the patients represented in the figure were randomly assigned to the two groups, one that received the drug and another that did not, one would reason that about 1/3 of the patients in the “drug” group would be expected to have headache if they had not received the drug. For the remaining patients—the 2/3 who did not have already have headaches caused by other factors—the drug would be the sole cause of headaches. In this subgroup, headache occurred in 3/4 of the patients. One might therefore reason, one's best guess for the probability of the drug producing headache is 3/4. If one assumes that for every patient in the control group, regardless of whether the patient had a headache, the drug causes headache with a probability of 3/4, this estimate would result. Among those who already had a headache produced by alternative causes, headache due to the drug is not observable.

In contrast, consider what estimate would result if one assumes instead that the drug causes headache with a probability of 1/2, the estimated causal strength according to associative models such as the ΔP model. Applying that probability to every patient, one's best guess would be that 2/3 of the patients would have headaches after receiving the medicine, rather than the 5/6 shown in Figure 12.3 . As should be clear, associative models give estimates that are inconsistent with the assumption that the causes involved influenced headache independently, even though the additivity in those models is generally assumed to represent independence, and thus to justify generalization to new contexts. This inconsistency, due to the outcome variable being dichotomous, leads to irrational applications of causal knowledge to achieve desired outcomes.

Are people rational or irrational in their estimation of causal strength? To discriminate between the causal power theory and the associative approach, Buehner, Cheng, and Clifford (2003 , Experiment 2) made use of the pattern of causal-strength predictions according to Equation 8 and 9 just discussed. They gave subjects a task of assessing whether various allergy medicines have a side effect on headaches, potentially causing headaches or preventing them, when presented with fictitious results of studies on allergy patients (see Fig. 12.3 for an example) in which the patients were randomly assigned to two groups, one receiving the medicine and the other not. The subjects were also asked to rate the causal strengths of each candidate after viewing the results for each fictitious study, using a frequentist counterfactual causal question that specified a novel transfer context: “Imagine 100 patients who do not suffer from headaches. How many would have headaches if given the medicine?” The novel context for assessing generative causal power, as just illustrated, is one in which there are no alternative generative causes of headache. By varying the base rate of the target effect, for both generative and preventive causes, the experiment manipulated (1) causal power while keeping ΔP constant, (2) ΔP while keeping causal power constant. The experiment also manipulated the base rate of e for noncontingent candidate causes. Their results clearly indicate that people make the leaps of faith assumed by the causal power theory, contrary to the predictions of all associative models, including normative associative models.

Integrating Causal Representation With Bayesian Inference: Representing Uncertainty and Evaluating Causal Structure

The reader might have noticed that, just like the Δ P rule, the point estimate of causal power in the causal power theory (Equation 8 and 9 ) is insensitive to sample size. As initially formulated, the theory did not provide any general account of how uncertainty impacts causal judgments. The point estimates are the most likely strength of the causal link that would have produced the observed data, but causal links with other strength values, although less likely to have produced the data, could well have also, for smaller sample sizes more so than for larger sizes. The lack of an account of uncertainty in early models of human causal learning, together with methodological problems in some initial experiments testing the causal power theory (see Buehner et al., 2003 ), contributed to prolonging the debate between proponents of associationist treatments and of the causal power theory. For some data sets (e.g., Buehner & Cheng, 1997 ; Lober & Shanks, 2000 ), human causal-strength judgments for some conditions were found to lie intermediate between the values predicted by causal power versus Δ P . This pattern was especially salient for studies in which the causal question, which was ambiguously worded, could be interpreted to concern confidence in the existence of a causal link. Intriguingly, a subtle, statistically insignificant, but consistent trend toward this pattern seemed to occur even for the disambiguated counterfactual question illustrated earlier. These deviations from the predictions of the causal power theory perhaps reflect the role of uncertainty, which is outside the scope of the theory.

An important methodological advance in the past decade is to apply powerful Bayesian probabilistic inference to causal graphs to explain psychological results (e.g., Griffiths & Tenenbaum, 2005 ; Lu et al., 2008 ; Tenenbaum et al., 2011 ; see Griffiths, Tenenbaum, & Kemp, Chapter 3 ; for a review of recent work, see Holyoak & Cheng, 2011 ). This new tool enables rationality in causal inference to be addressed more fully. For example, it enables a rich representation of uncertainty and a formulation of qualitative queries regarding causal structure.

Griffiths and Tenenbaum (2005 ; Tenenbaum & Griffiths, 2001 ) proposed the causal support model, a Bayesian model that addresses the causal query, termed a “structure” judgment, which aims to answer, “How likely is it that a causal link exists between these two variables?” This is in contrast to the causal query regarding causal strength that has been emphasized in previous psychological research on causal learning. Strength judgment concerns the weight on a causal link, which aims to answer the query, “What is the probability with which a cause produces (alternatively, prevents) an effect?”

In terms of the graphs in Figure 12.4 , the causal support model aims to account for judgments as to whether a set of observations ( D ) was generated by Graph 1, a causal structure in which a link may exist between candidate cause C and effect E or by a causal structure in which no link exists between C and E (Graph 0). Causal-strength models, by contrast, aim to account for people's best estimates of the weight w 1 on the link from C to effect E in Graph 1 that generated D , with w 1 ranging from 0 to 1.

Candidate causal structures varying in whether c causes e .

In the causal support model, the decision variable is based on the posterior probability ratio of Graphs 1 and 0 by applying Bayes' rule. Support is defined as:

Associative Versus Causal Bayesian Models: Uniform Versus Sparse and Strong Priors

Note that adopting Bayesian inference is entirely orthogonal to the longstanding debate between causal and associationist approaches. Because mathematics is a tool rather than an empirical theory, the Bayesian approach can be causal or associative depending on whether causal assumptions are made, even while they are applied to supposedly causal graphs. As Griffiths and Tenenbaum (2005) had noted, a Bayesian model can incorporate either the noisy-logical integration functions derived from the causal power theory or the linear function underlying the Rescorla-Wagner model and the Δ P rule. In addition, a Bayesian analysis can be applied to both strength and structure judgments, as well as to other types of causal queries, such as causal attribution. For strength judgments, rather than basing predictions on the peak of the posterior distribution of w 1 in Graph 1, which corresponds to causal power andthose estimates.

Lu et al. (2008) developed and compared several variants of Bayesian models as accounts of human judgments about both strength and structure. In addition to directly comparing predictions based on these alternatives, Lu et al. considered two different sets of priors on causal strength. One possible prior is simply a uniform distribution, as assumed in the causal support model. The alternative “generic” (i.e., domain-general) prior tested by Lu et al. is based on the assumption that people prefer parsimonious causal models (Chater & Vitányi, 2003 ; Lombrozo, 2007 ; Novick & Cheng, 2004 ). Sparse and strong (SS) priors imply that people prefer causal models that minimize the number of causes of a particular polarity (generative or preventive) while maximizing the strength of each individual cause that is in fact potent (i.e., of nonzero strength).

The sparse and strong priors, although admitted post hoc, point to the role of parsimony in explanation, an interesting issue for future research. When one is presented with a Necker cube, for example, one perceives two possible orientations. The human perceptual system has implicitly screened out the infinitely many other possible non-cube-shaped objects that would project the same eight corners onto our retina. The visual system makes a parsimony assumption: It favors the simplest “explanations” of the input on our retina. The human causal learning appears to similarly favor parsimonious causal explanations.

For all four Bayesian models, Lu et al. (2008) compared the average observed human strength rating for a given contingency condition with the mean of w 1 computed using the posterior distribution. Model fits revealed that the two causal variants based on the noisy-logical integration function were much more successful overall than the associative variants. For datasets from a meta-analysis based on 17 experiments selected from 10 studies in the literature (Perales & Shanks, 2007 ; see also Hattori & Oaksford, 2007 ), the causal Bayesian models (with one or zero free parameters) performed at least as well as the most successful nonnormative model of causal learning (with four free parameters) and much better than the Rescorla-Wagner model. Thus, although both causal and associative approaches can be given a Bayesian formulation, the empirical tests of human causal learning reported by Lu et al. favor the causal Bayesian formulation, providing further evidence for the rationality of human causal inference.

Lu et al. (2008) also evaluated structure analogs of the two causal variants of Bayesian strength models as accounts for observed structure judgments from experiments in which participants were explicitly asked to judge whether the candidate was indeed a cause. Relative to the support model, human reasoners appear to place greater emphasis on causal power and the base rate of the effect, and less emphasis on sample size.

The Independent Causal Influence Assumption for Dichotomous and Continuous Outcome Variables

Across multiple studies on humans (Beckers, de Houwer, Pineno, & Miller, 2005 ; De Houwer, Beckers, & Glautier, 2002 ; Lovibond et al., 2003 ) and even rats (Beckers, Miller, De Houwer, & Urushihara, 2006 ), an intriguing set of findings has emerged, showing that information regarding the additivity of the causal influences of two causes and the range of magnitudes of the outcome both influence judgments regarding unrelated candidate causes of that outcome. We illustrate the finding with parts of a broader study by Lovibond et al. (2003) . In a backward blocking design, cues A and B (two food items) in combination were paired with an outcome (an allergic reaction); in a second phase, cue B alone was paired with the outcome. Thus, target cue A made no difference to the occurrence of the outcome (holding B constant, there was always an allergic reaction regardless of whether A was there). The critical manipulation in Lovibond et al. was a “pretraining compound” phase during which one group of subjects, the ceiling group, saw that a combination of two allergens produced an outcome at the same level (“an allergic reaction”) as a single allergen (i.e., the ceiling level). In contrast, the nonceiling group saw that a combination of two allergens produced a stronger reaction (“a STRONG allergic reaction”) than a single allergen (“an allergic reaction”). Following this pretraining phase, all subjects were presented with information regarding novel cues in the main training phase. Critically, the outcome in this training phase always only occurred at the intermediate level (“an allergic reaction”), both for subjects in the ceiling and nonceiling groups.

As a result of pretraining, however, subjects' perception of the nature of the outcome in this phase would be expected to differ. For the exact same outcome, “an allergic reaction,” the only form of the outcome in that phase, whereas the ceiling group would perceive it to occur at the ceiling level, the nonceiling group would perceive it to occur at an intermediate level. As mentioned, for both groups, cue A made no difference to the occurrence of the outcome. Because the causal view represents causal relations separately from covariation, it explains why when the outcome occurs at a ceiling level, the generative effect of a cause has no observable manifestation. At a nonceiling level, causal and associative accounts coincide: The most parsimonious explanation for no observable difference is noncausality. However, at the ceiling level, observing no difference does not allow causal inference, as explained by the causal power theory. In support of this interpretation, the mean causal rating for cue A was reliably lower for the nonceiling group than for the ceiling group.

Beckers et al. (2005) manipulated pretraining on possible levels of the outcome and on the additivity of the influences of the cues separately and found that each type of pretraining had an enormous effect on the amount of blocking. Beckers et al. (2006) obtained similar results in rats. These and other researchers have explained these results in terms of the use of propositional reasoning to draw conclusions regarding the target cue (Beckers et al., 2005 , 2006 ; Lovibond et al., 2003 ; Mitchell et al., 2009 ). For example, a subject might reason: “If A and B are each a cause of an outcome, the outcome should occur with a greater magnitude when both A and B are present than when either occurs by itself. The outcome in fact was not stronger when A and B were both present as when B occurred alone. Therefore, A must not be a cause of the outcome.” These researchers have explained the impact of the pretraining in terms of learning the appropriate function for integrating the influences of multiple causes in the experimental materials (e.g., additivity vs. subadditivity) from experiences during the pretraining phase, in line with proposals by Griffiths and Tenenbaum (2005) and Lucas and Griffiths (2010) .

It is important to distinguish between domain-specific integrating functions that are the outputs of causal learning, and domain-independent integrating functions that enable an output, in view of the essential role they play in the inference process. In the causal power theory, the latter are the noisy-logicals: functions representing independent causal influence. As seen in the preceding section, whether independent causal influence is assumed in the inference process leads to different causal judgments. Moreover, independent causal influence enables compositionality. Even if we were to disregard the role of that assumption in the inference process, without it generalization of the acquired causal knowledge to new contexts would be problematic: If integrating functions were purely empirically learned, every new combination of causes, such as the combination of a target cause with unobserved causes in a new context, would require new learning (i.e., causal inference would not be compositional).

An alternative interpretation of Lovibond et al.'s (2003) results is that for all types of outcome variables, independent causal influence is always the default assumed in the causal discovery process, but the mathematical function defining independent influence differs for different types of outcome variables. For continuous outcome variables, independent causal influence is represented by additivity, as is generally known; for dichotomous outcome variables, independent causal influence is represented by the noisy-logicals, as explained earlier (see pp. 219–220 & 222–223). The unifying underlying concept is the superposition of the influences, a concept borrowed from physics. Under this interpretation, the pretraining conveys information on the nature of the outcome variable: continuous or dichotomous. Thus, subjects in their ceiling group, who received pretraining showing that two food items in combination produced an “allergic reaction” just as each item alone did, learned that the outcome is dichotomous. But subjects in their nonceiling group, who received pretraining showing that two food items in combination produced a stronger allergic reaction than each item alone, learned that the outcome is continuous.

Intervention Versus Observation and Diagnostic Causal Inference

A hallmark of a rational causal reasoner is the ability to formulate flexible and coherent answers to different causal queries. A goal of accounts of causal inference is to explain that ability. We have illustrated the causal view's answers to queries regarding causal strength and structure. (For formulations of answers to questions regarding causal attribution [how much an target outcome is due to certain causes], see Cheng & Novick, 2005 ; for answers to questions regarding enabling conditions, see Cheng & Novick, 1992 .) Let us consider here answers to queries involving diagnostic causal inference, inference from the occurrence of the effect to the occurrence of its causes. Recall Blaisdell et al's (2006) finding regarding rats' ability to distinguish between an event that is merely observed and one that follows an intervention. When a tone that occurred only when a light occurred during the learning phase was merely observed in the test phase, the rats in the experiment (the Observe group) nose-poked into the food bin more often than when the tone occurred immediately after that rats pressed a lever newly inserted in the test phase (the Intervene group). The Observe rats apparently diagnosed that the light must have occurred, whereas the Intervene rats diagnosed that it need not have occurred; light was never followed by food in the test phase.

Blaisdell et al.'s (2006) results were initially interpreted as support for causal Bayes nets. Note that the different diagnostic inferences in the two groups are consistent with simple deductive inference. For the Observe group, because the light was the only cause of the tone, when the tone occurred, the light must have occurred. For the Intervene group, because both the lever press and the light caused the tone, the tone occurring need not imply that the light occurred. Because causal Bayes nets (Pearl, 2000 ; Spirtes et al., 1993 / 2000 ) and the causal power approach (Waldmann et al., 2008 ) both make use of deductive inference, it is not surprising that they can also explain diagnostic reasoning.

The graphs in causal Bayes nets are assumed to satisfy the Markov condition, which states that for any variable X in the graph, conditional on its parents (i.e., the set of variables that are direct causes of X), X is independent of all variables in the graph except its descendents (i.e., its direct or indirect effects). A direct effect of X is a variable that has an arrow directly from X pointing into it, and an indirect effect of X is a variable that has a pathway of arrows originating from X pointing into it. Candidate causal networks are evaluated by assessing patterns of conditional independence and dependence entailed by the networks using the Markov and other assumptions. Candidate causal networks that are inconsistent with the observed pattern of conditional independence are eliminated, and the remaining candidate causal networks form the basis of causal judgments.

The causal Bayes nets approach explains Blaisdell et al.'s results by a distinction it makes between intervening to set a variable at a specific value and merely observing that value. As illustrated in Figure 12.5 a, observing T allows diagnostic inference regarding L because of the arrow from L to T. But intervening to produce T severs all other incoming arrows into T, a result called graph surgery, so that the resulting causal network no longer has the arrow from L to T (see Fig. 12.5 b).

( a ) L (Light) causes T (tone) and F (food). ( b ) Lever press and L each causes T.

Although this approach explains the results in the test phase if one assumes that the rats inferred the causal structure intended by the researchers, namely, that L is the common cause of T and F (see Fig. 12.5 a), the perfect negative correlation between T and F conditional on L during the learning phase in fact violates the Markov assumption applied to this causal structure (see Rehder & Burnett, 2005 ; Steyvers et al., 2003 for human results indicating violations of the Markov assumption). Causal Bayes nets therefore predict from the learning phase data that there is some inhibitory connection between T and F, and that both the Intervention and Observation rats should equally avoid going to the food bin when T occurred, contrary to the responses observed.

An alternative solution, one that causal psychological theories (e.g., Cheng, 1997 , 2000 ; Waldmann et al., 2008 ) inherited from traditional associative accounts (e.g., Rescorla & Wagner, 1972 ) is that people (and perhaps other species) incrementally construct causal networks by evaluating one (possibly conjunctive or otherwise complex) causal relation involving a single target effect at a time, while taking into consideration other causes of the effect. Motivated by consideration of limited processing capacity and of limited access to information at any one time, the incremental feature is shared by associative theorists (e.g., Jenkins & Ward, 1965 Rescorla & Wagner, 1972 ). Notably, whereas standard Bayes nets fail to explain Blaisdell et al.'s results, the incremental approach fully explains them. One difference is that the Markov assumption plays a different role in the latter approach: It is the consequence of the causal power assumptions (specifically, the independence assumptions), rather than a constraint used for generating the inferences. Thus, noticing the negative correlation takes effort and thus need not occur until there is sufficient training, as is consistent with the findings in rats (Savastano & Miller, 1998 ; Yin, Barnet, & Miller, 1994 ).

In summary, the three lines of evidence just discussed all lie beyond even the augmented associative view. They converge in their support for the two leaps of faith underlying the causal view, as well as for the conviction that the causal world is logically consistent.

Time and Causality: Mutual Constraints

We have concentrated on theoretical approaches that specify how humans take the mental leap from covariation to causation. Irrespective of any differences in theoretical perspective, all these approaches have in common that they assume that covariation can be readily assessed. This assumption is reflected in the experimental paradigms most commonly used; typically, participants are presented with evidence structured in the form of discrete, simultaneous or sequential learning trials in which each trial contains observations on whether the cause occurred and whether the effect occurred. In other words, in these tasks it is always perfectly clear whether a cause is followed by an effect on a given occasion. Such tasks grossly oversimplify the complexities of causal induction in some situations outside experimental laboratories: Some events have immediate outcomes, and others do not reveal their consequences until much later. Before an organism can evaluate whether a specific covariation licenses causal conjecture, the covariation needs to be detected and parsed in the first place.

Although the problem had been neglected for many years, the last decade has seen interesting and important developments. It has long been documented that cause-effect contiguity (one of Hume's cues toward causality) appears to be essential for causal discovery. Shanks, Pearson, and Dickinson (1989) , for example, reported that in an impoverished computerized instrumental learning task, people failed to discriminate between conditions where they had strong control over an outcome (ΔP = .75) and noncontingent control conditions, when their actions and the associated outcomes were separated by more than 2 seconds. In a completely different domain, Michotte (1946 / 1963 ) found that impressions of causal “launching” only occur when the collision of the launcher with the launchee is followed immediately by motion onset in the launchee: Temporal gaps of 150 ms or more destroy the impression.

From a computational perspective, it is easy to see why delays would produce decrements in causal reasoning performance. Contiguous event pairings are less demanding on attention and memory. They are also much easier to parse. When there is a temporal delay, and there are no constraints on how the potential causes and effects are bundled, as in Shanks et al. (1989) , the basic question on which contingency depends no longer has a clear answer: Should this particular instance of e be classified as occurring in the presence of c or in its absence? Each possible value of temporal lag results in a different value of contingency. The problem is analogous to that of the possible levels of abstractions of the candidate causes and the effects at which to evaluate contingency (and may have an analogous solution). Moreover, for a given e , when alternative intervening events occur, the number of hypotheses to be considered multiplies. The result is a harder, more complex inferential problem, one with a larger search space.

Buehner and May (2002 , 2003 , 2004 ) have demonstrated that prior knowledge about delayed time frames constrains the search process, such that noncontiguous relations are judged to be just as causal as contiguous ones. Buehner and McGregor (2006) have further shown that when prior assumptions about delays are sufficiently salient, contiguous relations are perceived as less causal than delayed ones—an apparent contradiction to Hume's tenets.

If causal learning operates according to the principles of Bayesian evidence integration, then these results on contiguous and delayed causation make sense: Reasoners may focus on the expected delay for a type of causal relation and evaluate observations with respect to it. In Bayesian terms, they evaluate likelihoods, the probability of the observations resulting from a hypothesis. In the earlier demonstrations of detrimental effects of delay (Michotte, 1946 / 1963 ; Shanks et al., 1989 ), the prior assumption would have been that there is no delay: Michotte's stimuli were simulations of well-known physical interactions (collisions), while Shanks et al. used computers, which (even in those days!) were expected to operate fast. Once these prior assumptions are modified via instructions (Buehner & May, 2002 , 2003 , 2004 ), or via constraints in the environment (Buehner & McGregor, 2006 ), then delayed relations pose no problem.

More recent work has found that prior expectations about time frames are relevant not only for the extent of delays but also with respect to their variability . Consider two hypothetical treatments against headache. Drug A always provides relief 2 hours after ingestion, while drug B sometimes starts working after just 1 hour, while other times it can take 3 hours to kick in. Which would we deem as a more effective drug? The answer to that question depends on how exactly temporal extent is interpreted when drawing causal conclusions. One possibility would be that causal attribution decays over time, similarly to discounting functions found in intertemporal choice (for an overview, see Green & Myerson, 2004 ). Under such an account, the appeal of a causal relation would decay over time according to a hyperbolic function.

One consequence of hyperbolic discounting is that variable relations may appear more attractive than stable ones, even when they are equated for mean expected delay. This conjecture is rooted in the diminishing sensitivity to delay: Variable relations accrue more net strength than constant relations matched for mean delay. And indeed, Cicerone (1976) has found that pigeons preferred variable over constant delays of reinforcement. Thus, if human causal learners approach time in a similar manner (and apply well-established principles of discounting as regards to intertemporal choice), we would expect drug B to emerge as the favorite. Interestingly, the opposite is the case: Greville and Buehner (2010) found that causal reasoners consistently prefer stable, predictable relations. Presumably we have strong a priori expectations that (most) causal relations are associated with a particular, relatively constant time frame. Where such expectations are violated, less learning takes place.

Cause-effect timing not only impacts assessments of causal strength but critically also constrains our ability to infer structure. Pace Hume, causes must occur before their effects, even though the intervening interval may extremely closely approximate 0 (e.g., the interval between a fist's contact with a pillow and the pillow's indentation, the interval between a cat walking into the sun and its shadow appearing on the ground). While such considerations are relatively trivial when there are only two variables involved, finding structure in multivariable causal systems gets increasingly difficult as the size of the system grows. Moreover, many structures are Markov-equivalent (Pearl, 2000 ), meaning that they cannot be distinguished by mere observation of the statistical patterns they produce. Lagnado and Sloman (2004 , 2006 ) have shown that in such situations, people rely on temporal ordering to infer causal structure. More specifically, temporal order constrains structure inference to a greater extent than the observed patterns of statistical dependencies.

As we highlighted earlier, cognitive science approaches to causality are rooted in the Humean conjecture that causality is a mental construct, inferred from hard, observable facts. Recent evidence suggests that Hume's route from sensory experience to causal knowledge is not a one-way street but in fact goes in both directions. Not only does our sensory experience determine our causal knowledge, but causal knowledge also determines our sensory experience. The latter direction of influence was first documented by Haggard, Clark, and Kalogeras (2002) , who showed that sensory awareness of actions and resultant consequences are shifted in time, such that actions are perceived as later, and consequences as earlier (with reference to a baseline judgment error). Causes and effects thus mutually attract each other in our subjective experience. Originally, the effect was thought to be specific to motor action and intentional action control (Wohlschläger, Haggard, Gesierich, & Prinz, 2003 ). Buehner and Humphreys (2009) , however, have shown that causality is the critical component of temporal binding: Intentional actions without a clear causal relation do not afford attraction to subsequent (uncaused) events. Moreover, Humphreys and Buehner (2009 , 2010 ) have shown that the causal binding effect exists over time frames much longer than originally reported, and outside the range of motor adaptation (Stetson, Cui, Montague, & Eagleman, 2006 ), as would be required for action-control based approaches. Buehner and Humphreys (2010) have furthermore demonstrated a binding effect in spatial perception using Michottean stimuli—a finding that is completely outside the scope of motor-specific accounts of binding. It appears as if our perception of time and space, and our understanding of causality, mutually constrain each other to afford a maximally coherent and parsimonious experience.

Our chapter has reviewed multiple lines of evidence showing a strong preference for parsimonious causal explanations. This preference holds for scientific as well as everyday explanations. Among the many alternative representations of the world that may support predictions equally well, we select the most parsimonious. Hawking and Mlodinow (2010) note that, although people often say that Copernicus's sun-centered model of the cosmos proved Ptoloemy's earth-centered model wrong, that is not true; one can explain observations of the heavens assuming either Earth or the sun to be at rest. Likewise, although the city council of Monza, Italy, barred pet owners from keeping goldfish in curved fishbowls—on the grounds that it is cruel to give the fish a distorted view of reality through the curved sides of the bowl—the goldfish could potentially formulate a model of the motion of objects outside the bowl no less valid as ours. The laws of motion in our frame are simpler than the fish's, but theirs are potentially just as coherent and useful for prediction. But the members of the city council of Monza, like the rest of us, have such an overpowering preference for the more parsimonious model of the world that they perceive it as “truth.”

Conclusions and Future Directions

Our chapter began with the question: With what cognitive assets would we endow an intelligent agent—one that has processing and informational resources similar to humans—so that the agent would be able to achieve its goals? We have taken the perspective that generalization from the learning context to the application context is central to the achievement of its goals. From this perspective, we first examined the crippling inadequacies of the associative view, which attempts to maintain objectivity by restricting its inference process to computations on observable events only. We considered variants of the associative view augmented with a special status for interventions and other principles of experimental design, in line with typical scientific causal inference.

We then considered the causal view, which resolves major apparent impasses by endowing the agent with two leaps of faith, that (1) the world is causal even though causal relations are never observable, and (2) causal laws are uniform and compositional. These empirical leaps are grounded in the conviction that existence is logically consistent. They enable the agent to incrementally construct an understanding of how the world works and coherently generalize its acquired causal knowledge. Analysis in cognitive research shows that the common belief that justifies the augmented associative view—that assumptions about independent causal influence justify the application of causal knowledge to new contexts but do not influence the output of statistical analyses—is mistaken. Likewise, the common belief that assumptions about estimations of causal strength are secondary, and do not affect judgments regarding causal structure, is mistaken.

Remarkably, observed causal judgments reveal that humans make those leaps of faith, and that their causal judgments are based on a definition of independent causal influence that is logically consistent across the learning and application contexts. The use of the sharper tool of Bayesian mathematics shows even more unequivocal support for the causal view. This tool also extends the capability to formulate answers to different kinds of causal queries.

The potential to discover how the world works must of course be accompanied by the requisite computational capabilities. We have identified three intertwined capabilities so far. The agent must be able to (1) make deductive logical inferences, (2) compute statistical regularities, and (3) represent uncertainty. The last two allow the agent to make progress in the face of errors in even its best hypotheses. The first is an essential component of the parsimony assumption and of coherent and flexible reasoning.

Three outstanding issues seem especially pertinent to us in view of our analysis and review. For each issue, a rational analysis in tandem with empirical work differentiating between alternative plausible explanations would deepen our understanding of causal learning.

Hypothesis revision: If causal learning is incremental, by what criteria do causal learners revise their hypotheses, and what do their criteria and revisions reveal about the intended destination of the revision process? Recent research found that for preventers with a narrow scope, which violate the independent influence assumption, people are more likely to posit a hidden cause to explain and remove the violation (Carroll & Cheng, 2010 ). Standard causal Bayes nets would not interpret the violation to signal a need for representation revision.

Category formation and causal learning: We have taken the perspective that causal discovery is the driving force underlying our mental representation of the world, not just in the sense that we need to know how things influence each other but also in the sense that causal relations define what should be considered things in our mental universe (Lewis, 1929 ). Are causal learning and category formation two aspects of the same challenge, as the goal of generalization of causal beliefs to application contexts would suggest? How do people arrive at their partitioning of the continuous stream of events into candidate causes and effects? Likewise, how do people arrive at their partitioning of events into candidate causes and effects at particular levels of abstraction? In Lien and Cheng's (2000) experiments, human subjects were presented with causal events involving visual stimuli for which candidate-cause categories were undefined; there was no specification of either the potential critical features or the relevant level of abstraction of the features. It was found that subjects seemed to form candidate-cause categories that maximized ΔP, perhaps in an attempt to maximize the necessity and sufficiency of the cause to produce the effect in question. The topic awaits better formulations of explanations as well as additional empirical work.

Parsimony in causal explanations: We have encountered the critical role of parsimony in causal explanations multiple times in our chapter. Although models of parsimony (e.g., Chater & Vitányi, 2003 ; Lombrozo, 2007 ) are consistent with the psychological findings, they do not predict them. Better integration of theories of simplicity with theories and findings in causal learning would be a major advance.

Acknowledgments

Preparation of this chapter was supported by AFOSR FA 9950-08-1-0489. We thank Jessica Walker and Keith Holyoak for comments on an earlier draft.

More generally, for a causal tree with n nodes, the number of direct causal links would be n - 1 (because every node other than the root node has one and only one arrow going into it). But the number of associations between nodes (including causal ones) would be n(n - 1)/2, because every node in the tree is linked by an arrow to at least one other node, so that there is an non-zero association between every pair of nodes.

Ulrike Hahn provided this interpretation.

The example was provided by Sylvain Bromberger.

Although the theory obtains different equations for estimating generative and preventive causal powers, the choice between the two equations does not constitute a free parameter. Which of the two equations applies follows from the value of ΔP. On occasions where ΔP = 0, both equations apply and make the same prediction, namely, that causal power should be 0, except in ceiling-effect situations. Here, the reasoner does have to make a pragmatic decision on whether she is evaluating the evidence to assess a preventive or generative relation, and whether the evidence at hand is meaningful for that purpose.

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Causal research: definition, examples and how to use it.

16 min read Causal research enables market researchers to predict hypothetical occurrences & outcomes while improving existing strategies. Discover how this research can decrease employee retention & increase customer success for your business.

What is causal research?

Causal research, also known as explanatory research or causal-comparative research, identifies the extent and nature of cause-and-effect relationships between two or more variables.

It’s often used by companies to determine the impact of changes in products, features, or services process on critical company metrics. Some examples:

• How does rebranding of a product influence intent to purchase?
• How would expansion to a new market segment affect projected sales?
• What would be the impact of a price increase or decrease on customer loyalty?

To maintain the accuracy of causal research, ‘confounding variables’ or influences — e.g. those that could distort the results — are controlled. This is done either by keeping them constant in the creation of data, or by using statistical methods. These variables are identified before the start of the research experiment.

As well as the above, research teams will outline several other variables and principles in causal research:

• Independent variables

The variables that may cause direct changes in another variable. For example, the effect of truancy on a student’s grade point average. The independent variable is therefore class attendance.

• Control variables

These are the components that remain unchanged during the experiment so researchers can better understand what conditions create a cause-and-effect relationship.  

This describes the cause-and-effect relationship. When researchers find causation (or the cause), they’ve conducted all the processes necessary to prove it exists.

• Correlation

Any relationship between two variables in the experiment. It’s important to note that correlation doesn’t automatically mean causation. Researchers will typically establish correlation before proving cause-and-effect.

• Experimental design

Researchers use experimental design to define the parameters of the experiment — e.g. categorizing participants into different groups.

• Dependent variables

These are measurable variables that may change or are influenced by the independent variable. For example, in an experiment about whether or not terrain influences running speed, your dependent variable is the terrain.  

Why is causal research useful?

It’s useful because it enables market researchers to predict hypothetical occurrences and outcomes while improving existing strategies. This allows businesses to create plans that benefit the company. It’s also a great research method because researchers can immediately see how variables affect each other and under what circumstances.

Also, once the first experiment has been completed, researchers can use the learnings from the analysis to repeat the experiment or apply the findings to other scenarios. Because of this, it’s widely used to help understand the impact of changes in internal or commercial strategy to the business bottom line.

Some examples include:

• Understanding how overall training levels are improved by introducing new courses
• Examining which variations in wording make potential customers more interested in buying a product
• Testing a market’s response to a brand-new line of products and/or services

So, how does causal research compare and differ from other research types?

Well, there are a few research types that are used to find answers to some of the examples above:

1. Exploratory research

As its name suggests, exploratory research involves assessing a situation (or situations) where the problem isn’t clear. Through this approach, researchers can test different avenues and ideas to establish facts and gain a better understanding.

Researchers can also use it to first navigate a topic and identify which variables are important. Because no area is off-limits, the research is flexible and adapts to the investigations as it progresses.

Finally, this approach is unstructured and often involves gathering qualitative data, giving the researcher freedom to progress the research according to their thoughts and assessment. However, this may make results susceptible to researcher bias and may limit the extent to which a topic is explored.

2. Descriptive research

Descriptive research is all about describing the characteristics of the population, phenomenon or scenario studied. It focuses more on the “what” of the research subject than the “why”.

For example, a clothing brand wants to understand the fashion purchasing trends amongst buyers in California — so they conduct a demographic survey of the region, gather population data and then run descriptive research. The study will help them to uncover purchasing patterns amongst fashion buyers in California, but not necessarily why those patterns exist.

As the research happens in a natural setting, variables can cross-contaminate other variables, making it harder to isolate cause and effect relationships. Therefore, further research will be required if more causal information is needed.

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How is causal research different from the other two methods above?

Well, causal research looks at what variables are involved in a problem and ‘why’ they act a certain way. As the experiment takes place in a controlled setting (thanks to controlled variables) it’s easier to identify cause-and-effect amongst variables.

Furthermore, researchers can carry out causal research at any stage in the process, though it’s usually carried out in the later stages once more is known about a particular topic or situation.

Finally, compared to the other two methods, causal research is more structured, and researchers can combine it with exploratory and descriptive research to assist with research goals.

Summary of three research types

What are the advantages of causal research?

• Improve experiences

By understanding which variables have positive impacts on target variables (like sales revenue or customer loyalty), businesses can improve their processes, return on investment, and the experiences they offer customers and employees.

• Help companies improve internally

By conducting causal research, management can make informed decisions about improving their employee experience and internal operations. For example, understanding which variables led to an increase in staff turnover.

• Repeat experiments to enhance reliability and accuracy of results

When variables are identified, researchers can replicate cause-and-effect with ease, providing them with reliable data and results to draw insights from.

• Test out new theories or ideas

If causal research is able to pinpoint the exact outcome of mixing together different variables, research teams have the ability to test out ideas in the same way to create viable proof of concepts.

• Fix issues quickly

Once an undesirable effect’s cause is identified, researchers and management can take action to reduce the impact of it or remove it entirely, resulting in better outcomes.

What are the disadvantages of causal research?

• Provides information to competitors

If you plan to publish your research, it provides information about your plans to your competitors. For example, they might use your research outcomes to identify what you are up to and enter the market before you.

• Difficult to administer

Causal research is often difficult to administer because it’s not possible to control the effects of extraneous variables.

• Time and money constraints

Budgetary and time constraints can make this type of research expensive to conduct and repeat. Also, if an initial attempt doesn’t provide a cause and effect relationship, the ROI is wasted and could impact the appetite for future repeat experiments.

• Requires additional research to ensure validity

You can’t rely on just the outcomes of causal research as it’s inaccurate. It’s best to conduct other types of research alongside it to confirm its output.

• Trouble establishing cause and effect

Researchers might identify that two variables are connected, but struggle to determine which is the cause and which variable is the effect.

• Risk of contamination

There’s always the risk that people outside your market or area of study could affect the results of your research. For example, if you’re conducting a retail store study, shoppers outside your ‘test parameters’ shop at your store and skew the results.

How can you use causal research effectively?

To better highlight how you can use causal research across functions or markets, here are a few examples:

Market and advertising research

A company might want to know if their new advertising campaign or marketing campaign is having a positive impact. So, their research team can carry out a causal research project to see which variables cause a positive or negative effect on the campaign.

For example, a cold-weather apparel company in a winter ski-resort town may see an increase in sales generated after a targeted campaign to skiers. To see if one caused the other, the research team could set up a duplicate experiment to see if the same campaign would generate sales from non-skiers. If the results reduce or change, then it’s likely that the campaign had a direct effect on skiers to encourage them to purchase products.

Improving customer experiences and loyalty levels

Customers enjoy shopping with brands that align with their own values, and they’re more likely to buy and present the brand positively to other potential shoppers as a result. So, it’s in your best interest to deliver great experiences and retain your customers.

For example, the Harvard Business Review found that an increase in customer retention rates by 5% increased profits by 25% to 95%. But let’s say you want to increase your own, how can you identify which variables contribute to it?Using causal research, you can test hypotheses about which processes, strategies or changes influence customer retention. For example, is it the streamlined checkout? What about the personalized product suggestions? Or maybe it was a new solution that solved their problem? Causal research will help you find out.

Discover how to use analytics to improve customer retention.

Improving problematic employee turnover rates

If your company has a high attrition rate, causal research can help you narrow down the variables or reasons which have the greatest impact on people leaving. This allows you to prioritize your efforts on tackling the issues in the right order, for the best positive outcomes.

For example, through causal research, you might find that employee dissatisfaction due to a lack of communication and transparency from upper management leads to poor morale, which in turn influences employee retention.

To rectify the problem, you could implement a routine feedback loop or session that enables your people to talk to your company’s C-level executives so that they feel heard and understood.

How to conduct causal research first steps to getting started are:

1. Define the purpose of your research

What questions do you have? What do you expect to come out of your research? Think about which variables you need to test out the theory.

2. Pick a random sampling if participants are needed

Using a technology solution to support your sampling, like a database, can help you define who you want your target audience to be, and how random or representative they should be.

3. Set up the controlled experiment

Once you’ve defined which variables you’d like to measure to see if they interact, think about how best to set up the experiment. This could be in-person or in-house via interviews, or it could be done remotely using online surveys.

4. Carry out the experiment

Make sure to keep all irrelevant variables the same, and only change the causal variable (the one that causes the effect) to gather the correct data. Depending on your method, you could be collecting qualitative or quantitative data, so make sure you note your findings across each regularly.

5. Analyze your findings

Either manually or using technology, analyze your data to see if any trends, patterns or correlations emerge. By looking at the data, you’ll be able to see what changes you might need to do next time, or if there are questions that require further research.

6. Verify your findings

Your first attempt gives you the baseline figures to compare the new results to. You can then run another experiment to verify your findings.

7. Do follow-up or supplemental research

You can supplement your original findings by carrying out research that goes deeper into causes or explores the topic in more detail. One of the best ways to do this is to use a survey. See ‘Use surveys to help your experiment’.

Identifying causal relationships between variables

To verify if a causal relationship exists, you have to satisfy the following criteria:

• Nonspurious association

A clear correlation exists between one cause and the effect. In other words, no ‘third’ that relates to both (cause and effect) should exist.

• Temporal sequence

The cause occurs before the effect. For example, increased ad spend on product marketing would contribute to higher product sales.

• Concomitant variation

The variation between the two variables is systematic. For example, if a company doesn’t change its IT policies and technology stack, then changes in employee productivity were not caused by IT policies or technology.

How surveys help your causal research experiments?

There are some surveys that are perfect for assisting researchers with understanding cause and effect. These include:

• Employee Satisfaction Survey – An introductory employee satisfaction survey that provides you with an overview of your current employee experience.
• Manager Feedback Survey – An introductory manager feedback survey geared toward improving your skills as a leader with valuable feedback from your team.
• Net Promoter Score (NPS) Survey – Measure customer loyalty and understand how your customers feel about your product or service using one of the world’s best-recognized metrics.
• Employee Engagement Survey – An entry-level employee engagement survey that provides you with an overview of your current employee experience.
• Customer Satisfaction Survey – Evaluate how satisfied your customers are with your company, including the products and services you provide and how they are treated when they buy from you.
• Employee Exit Interview Survey – Understand why your employees are leaving and how they’ll speak about your company once they’re gone.
• Product Research Survey – Evaluate your consumers’ reaction to a new product or product feature across every stage of the product development journey.
• Brand Awareness Survey – Track the level of brand awareness in your target market, including current and potential future customers.
• Online Purchase Feedback Survey – Find out how well your online shopping experience performs against customer needs and expectations.

That covers the fundamentals of causal research and should give you a foundation for ongoing studies to assess opportunities, problems, and risks across your market, product, customer, and employee segments.

If you want to transform your research, empower your teams and get insights on tap to get ahead of the competition, maybe it’s time to leverage Qualtrics CoreXM.

Qualtrics CoreXM provides a single platform for data collection and analysis across every part of your business — from customer feedback to product concept testing. What’s more, you can integrate it with your existing tools and services thanks to a flexible API.

Qualtrics CoreXM offers you as much or as little power and complexity as you need, so whether you’re running simple surveys or more advanced forms of research, it can deliver every time.

Related resources

Market intelligence 10 min read, marketing insights 11 min read, ethnographic research 11 min read, qualitative vs quantitative research 13 min read, qualitative research questions 11 min read, qualitative research design 12 min read, primary vs secondary research 14 min read, request demo.

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Data representations | Lesson
• Data representations | Worked example
• Center and spread | Lesson
• Center and spread | Worked example
• Random sampling | Lesson
• Random sampling | Worked example
• Scatterplots | Lesson
• Scatterplots | Worked example
• Interpreting linear models | Lesson
• Interpreting linear models | Worked example

Correlation and Causation | Lesson

• Correlation and causation | Worked example
• Probability | Lesson
• Probability | Worked example

What is the difference between correlation and causation?

What skills are tested.

• Describing a relationship between variables
• Identifying statements consistent with the relationship between variables
• Identifying valid conclusions about correlation and causation for data shown in a scatterplot
• Identifying a factor that could explain why a correlation does not imply a causal relationship

How can we determine if variables are correlated?

• Positive correlation : As x ‍   increases, y ‍   tends to increase.
• Negative correlation : As x ‍   increases, y ‍   tends to decrease.
• No correlation : As x ‍   increases, y ‍   tends to stay about the same or have no clear pattern.

Why doesn't correlation mean causation?

• Liam can conclude that sales of ice cream cones and air conditioner are positively correlated.
• Liam can't conclude that selling more ice cream cones causes more air conditioners to be sold. It is likely that the increases in the sales of both ice cream cones and air conditioners are caused by a third factor, an increase in temperature!
• (Choice A)   Causal relationship A Causal relationship
• (Choice B)   No correlation B No correlation
• (Choice C)   Positive correlation C Positive correlation
• (Choice D)   Negative correlation D Negative correlation
• (Choice E)   Cannot be determined from the information provided E Cannot be determined from the information provided
• (Choice A)   The number of absences a student has is not a predictor of their grade point average. A The number of absences a student has is not a predictor of their grade point average.
• (Choice B)   Students with fewer absences tend to have higher grade point averages because they are present for more of their academic classes. B Students with fewer absences tend to have higher grade point averages because they are present for more of their academic classes.
• (Choice C)   There is a linear relationship between the number of absences and grade point average. C There is a linear relationship between the number of absences and grade point average.
• (Choice A)   There is a positive linear correlation between the price of hot dogs and soft drinks. A There is a positive linear correlation between the price of hot dogs and soft drinks.
• (Choice B)   There is a negative linear correlation between the price of hot dogs and soft drinks. B There is a negative linear correlation between the price of hot dogs and soft drinks.
• (Choice C)   There is no correlation between price of hot dogs and soft drinks. C There is no correlation between price of hot dogs and soft drinks.
• (Choice D)   An increase in the price of hot dogs causes an increase in the price of soft drinks. D An increase in the price of hot dogs causes an increase in the price of soft drinks.
• (Choice E)   The ballpark with the most expensive hot dog has the most expensive soft drink. E The ballpark with the most expensive hot dog has the most expensive soft drink.
• (Choice A)   Larger homes have more safety features and amenities, which lead to increased life expectancy. A Larger homes have more safety features and amenities, which lead to increased life expectancy.
• (Choice B)   The ability to afford a larger home and better healthcare is a direct effect of having more wealth. B The ability to afford a larger home and better healthcare is a direct effect of having more wealth.
• (Choice C)   The citizens were not selected at random for the study. C The citizens were not selected at random for the study.
• (Choice D)   There are more people living in small homes than large homes in the city. D There are more people living in small homes than large homes in the city.
• (Choice E)   Some responses may have been lost during the data collection process. E Some responses may have been lost during the data collection process.

Things to remember

• Positive correlation: As x ‍   increases, y ‍   increases.
• Negative correlation: As x ‍   increases, y ‍   decreases.
• No correlation: As x ‍   increases, y ‍   stays about the same or has no clear pattern.
• Sometimes when two variables are correlated, the relationship is coincidental or a third factor is causing them both to change.

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Causal Hypothesis

Ai generator.

In scientific research, understanding causality is key to unraveling the intricacies of various phenomena. A causal hypothesis is a statement that predicts a cause-and-effect relationship between variables in a study. It serves as a guide to study design, data collection, and interpretation of results. This thesis statement segment aims to provide you with clear examples of causal hypotheses across diverse fields, along with a step-by-step guide and useful tips for formulating your own. Let’s delve into the essential components of constructing a compelling causal hypothesis.

What is Causal Hypothesis?

A causal hypothesis is a predictive statement that suggests a potential cause-and-effect relationship between two or more variables. It posits that a change in one variable (the independent or cause variable) will result in a change in another variable (the dependent or effect variable). The primary goal of a causal hypothesis is to determine whether one event or factor directly influences another. This type of Simple hypothesis is commonly tested through experiments where one variable can be manipulated to observe the effect on another variable.

What is an example of a Causal Hypothesis Statement?

Example 1: If a person increases their physical activity (cause), then their overall health will improve (effect).

Explanation: Here, the independent variable is the “increase in physical activity,” while the dependent variable is the “improvement in overall health.” The hypothesis suggests that by manipulating the level of physical activity (e.g., by exercising more), there will be a direct effect on the individual’s health.

Other examples can range from the impact of a change in diet on weight loss, the influence of class size on student performance, or the effect of a new training method on employee productivity. The key element in all causal hypotheses is the proposed direct relationship between cause and effect.

100 Causal Hypothesis Statement Examples

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Causal hypotheses predict cause-and-effect relationships, aiming to understand the influence one variable has on another. Rooted in experimental setups, they’re essential for deriving actionable insights in many fields. Delve into these 100 illustrative examples to understand the essence of causal relationships.

• Dietary Sugar & Weight Gain: Increased sugar intake leads to weight gain.
• Exercise & Mental Health: Regular exercise improves mental well-being.
• Sleep & Productivity: Lack of adequate sleep reduces work productivity.
• Class Size & Learning: Smaller class sizes enhance student understanding.
• Smoking & Lung Disease: Regular smoking causes lung diseases.
• Pesticides & Bee Decline: Use of certain pesticides leads to bee population decline.
• Stress & Hair Loss: Chronic stress accelerates hair loss.
• Music & Plant Growth: Plants grow better when exposed to classical music.
• UV Rays & Skin Aging: Excessive exposure to UV rays speeds up skin aging.
• Reading & Vocabulary: Regular reading improves vocabulary breadth.
• Video Games & Reflexes: Playing video games frequently enhances reflex actions.
• Air Pollution & Respiratory Issues: High levels of air pollution increase respiratory diseases.
• Green Spaces & Happiness: Living near green spaces improves overall happiness.
• Yoga & Blood Pressure: Regular yoga practices lower blood pressure.
• Meditation & Stress Reduction: Daily meditation reduces stress levels.
• Social Media & Anxiety: Excessive social media use increases anxiety in teenagers.
• Alcohol & Liver Damage: Regular heavy drinking leads to liver damage.
• Training & Job Efficiency: Intensive training improves job performance.
• Seat Belts & Accident Survival: Using seat belts increases chances of surviving car accidents.
• Soft Drinks & Bone Density: High consumption of soft drinks decreases bone density.
• Homework & Academic Performance: Regular homework completion improves academic scores.
• Organic Food & Health Benefits: Consuming organic food improves overall health.
• Fiber Intake & Digestion: Increased dietary fiber enhances digestion.
• Therapy & Depression Recovery: Regular therapy sessions improve depression recovery rates.
• Financial Education & Savings: Financial literacy education increases personal saving rates.
• Brushing & Dental Health: Brushing teeth twice a day reduces dental issues.
• Carbon Emission & Global Warming: Higher carbon emissions accelerate global warming.
• Afforestation & Climate Stability: Planting trees stabilizes local climates.
• Ad Exposure & Sales: Increased product advertisement boosts sales.
• Parental Involvement & Academic Success: Higher parental involvement enhances student academic performance.
• Hydration & Skin Health: Regular water intake improves skin elasticity and health.
• Caffeine & Alertness: Consuming caffeine increases alertness levels.
• Antibiotics & Bacterial Resistance: Overuse of antibiotics leads to increased antibiotic-resistant bacteria.
• Pet Ownership & Loneliness: Having pets reduces feelings of loneliness.
• Fish Oil & Cognitive Function: Regular consumption of fish oil improves cognitive functions.
• Noise Pollution & Sleep Quality: High levels of noise pollution degrade sleep quality.
• Exercise & Bone Density: Weight-bearing exercises increase bone density.
• Vaccination & Disease Prevention: Proper vaccination reduces the incidence of related diseases.
• Laughter & Immune System: Regular laughter boosts the immune system.
• Gardening & Stress Reduction: Engaging in gardening activities reduces stress levels.
• Travel & Cultural Awareness: Frequent travel increases cultural awareness and tolerance.
• High Heels & Back Pain: Prolonged wearing of high heels leads to increased back pain.
• Junk Food & Heart Disease: Excessive junk food consumption increases the risk of heart diseases.
• Mindfulness & Anxiety Reduction: Practicing mindfulness lowers anxiety levels.
• Online Learning & Flexibility: Online education offers greater flexibility to learners.
• Urbanization & Wildlife Displacement: Rapid urbanization leads to displacement of local wildlife.
• Vitamin C & Cold Recovery: High doses of vitamin C speed up cold recovery.
• Team Building Activities & Work Cohesion: Regular team-building activities improve workplace cohesion.
• Multitasking & Productivity: Multitasking reduces individual task efficiency.
• Protein Intake & Muscle Growth: Increased protein consumption boosts muscle growth in individuals engaged in strength training.
• Mentoring & Career Progression: Having a mentor accelerates career progression.
• Fast Food & Obesity Rates: High consumption of fast food leads to increased obesity rates.
• Deforestation & Biodiversity Loss: Accelerated deforestation results in significant biodiversity loss.
• Language Learning & Cognitive Flexibility: Learning a second language enhances cognitive flexibility.
• Red Wine & Heart Health: Moderate red wine consumption may benefit heart health.
• Public Speaking Practice & Confidence: Regular public speaking practice boosts confidence.
• Fasting & Metabolism: Intermittent fasting can rev up metabolism.
• Plastic Usage & Ocean Pollution: Excessive use of plastics leads to increased ocean pollution.
• Peer Tutoring & Academic Retention: Peer tutoring improves academic retention rates.
• Mobile Usage & Sleep Patterns: Excessive mobile phone use before bed disrupts sleep patterns.
• Green Spaces & Mental Well-being: Living near green spaces enhances mental well-being.
• Organic Foods & Health Outcomes: Consuming organic foods leads to better health outcomes.
• Art Exposure & Creativity: Regular exposure to art boosts creativity.
• Gaming & Hand-Eye Coordination: Engaging in video games improves hand-eye coordination.
• Prenatal Music & Baby’s Development: Exposing babies to music in the womb enhances their auditory development.
• Dark Chocolate & Mood Enhancement: Consuming dark chocolate can elevate mood.
• Urban Farms & Community Engagement: Establishing urban farms promotes community engagement.
• Reading Fiction & Empathy Levels: Reading fiction regularly increases empathy.
• Aerobic Exercise & Memory: Engaging in aerobic exercises sharpens memory.
• Meditation & Blood Pressure: Regular meditation can reduce blood pressure.
• Classical Music & Plant Growth: Plants exposed to classical music show improved growth.
• Pollution & Respiratory Diseases: Higher pollution levels increase respiratory diseases’ incidence.
• Parental Involvement & Child’s Academic Success: Direct parental involvement in schooling enhances children’s academic success.
• Sugar Intake & Tooth Decay: High sugar intake is directly proportional to tooth decay.
• Physical Books & Reading Comprehension: Reading physical books improves comprehension better than digital mediums.
• Daily Journaling & Self-awareness: Maintaining a daily journal enhances self-awareness.
• Robotics Learning & Problem-solving Skills: Engaging in robotics learning fosters problem-solving skills in students.
• Forest Bathing & Stress Relief: Immersion in forest environments (forest bathing) reduces stress levels.
• Reusable Bags & Environmental Impact: Using reusable bags reduces environmental pollution.
• Affirmations & Self-esteem: Regularly reciting positive affirmations enhances self-esteem.
• Local Produce Consumption & Community Economy: Buying and consuming local produce boosts the local economy.
• Sunlight Exposure & Vitamin D Levels: Regular sunlight exposure enhances Vitamin D levels in the body.
• Group Study & Learning Enhancement: Group studies can enhance learning compared to individual studies.
• Active Commuting & Fitness Levels: Commuting by walking or cycling improves overall fitness.
• Foreign Film Watching & Cultural Understanding: Watching foreign films increases understanding and appreciation of different cultures.
• Craft Activities & Fine Motor Skills: Engaging in craft activities enhances fine motor skills.
• Listening to Podcasts & Knowledge Expansion: Regularly listening to educational podcasts broadens one’s knowledge base.
• Outdoor Play & Child’s Physical Development: Encouraging outdoor play accelerates physical development in children.
• Thrift Shopping & Sustainable Living: Choosing thrift shopping promotes sustainable consumption habits.
• Nature Retreats & Burnout Recovery: Taking nature retreats aids in burnout recovery.
• Virtual Reality Training & Skill Acquisition: Using virtual reality for training accelerates skill acquisition in medical students.
• Pet Ownership & Loneliness Reduction: Owning a pet significantly reduces feelings of loneliness among elderly individuals.
• Intermittent Fasting & Metabolism Boost: Practicing intermittent fasting can lead to an increase in metabolic rate.
• Bilingual Education & Cognitive Flexibility: Being educated in a bilingual environment improves cognitive flexibility in children.
• Urbanization & Loss of Biodiversity: Rapid urbanization contributes to a loss of biodiversity in the surrounding environment.
• Recycled Materials & Carbon Footprint Reduction: Utilizing recycled materials in production processes reduces a company’s overall carbon footprint.
• Artificial Sweeteners & Appetite Increase: Consuming artificial sweeteners might lead to an increase in appetite.
• Green Roofs & Urban Temperature Regulation: Implementing green roofs in urban buildings contributes to moderating city temperatures.
• Remote Work & Employee Productivity: Adopting a remote work model can boost employee productivity and job satisfaction.
• Sensory Play & Child Development: Incorporating sensory play in early childhood education supports holistic child development.

Causal Hypothesis Statement Examples in Research

Research hypothesis often delves into understanding the cause-and-effect relationships between different variables. These causal hypotheses attempt to predict a specific effect if a particular cause is present, making them vital for experimental designs.

• Artificial Intelligence & Job Market: Implementation of artificial intelligence in industries causes a decline in manual jobs.
• Online Learning Platforms & Traditional Classroom Efficiency: The introduction of online learning platforms reduces the efficacy of traditional classroom teaching methods.
• Nano-technology & Medical Treatment Efficacy: Using nano-technology in drug delivery enhances the effectiveness of medical treatments.
• Genetic Editing & Lifespan: Advancements in genetic editing techniques directly influence the lifespan of organisms.
• Quantum Computing & Data Security: The rise of quantum computing threatens the security of traditional encryption methods.
• Space Tourism & Aerospace Advancements: The demand for space tourism propels advancements in aerospace engineering.
• E-commerce & Retail Business Model: The surge in e-commerce platforms leads to a decline in the traditional retail business model.
• VR in Real Estate & Buyer Decisions: Using virtual reality in real estate presentations influences buyer decisions more than traditional methods.
• Biofuels & Greenhouse Gas Emissions: Increasing biofuel production directly reduces greenhouse gas emissions.
• Crowdfunding & Entrepreneurial Success: The availability of crowdfunding platforms boosts the success rate of start-up enterprises.

Causal Hypothesis Statement Examples in Epidemiology

Epidemiology is a study of how and why certain diseases occur in particular populations. Causal hypotheses in this field aim to uncover relationships between health interventions, behaviors, and health outcomes.

• Vaccine Introduction & Disease Eradication: The introduction of new vaccines directly leads to the reduction or eradication of specific diseases.
• Urbanization & Rise in Respiratory Diseases: Increased urbanization causes a surge in respiratory diseases due to pollution.
• Processed Foods & Obesity Epidemic: The consumption of processed foods is directly linked to the rising obesity epidemic.
• Sanitation Measures & Cholera Outbreaks: Implementing proper sanitation measures reduces the incidence of cholera outbreaks.
• Tobacco Consumption & Lung Cancer: Prolonged tobacco consumption is the primary cause of lung cancer among adults.
• Antibiotic Misuse & Antibiotic-Resistant Strains: Misuse of antibiotics leads to the evolution of antibiotic-resistant bacterial strains.
• Alcohol Consumption & Liver Diseases: Excessive and regular alcohol consumption is a leading cause of liver diseases.
• Vitamin D & Rickets in Children: A deficiency in vitamin D is the primary cause of rickets in children.
• Airborne Pollutants & Asthma Attacks: Exposure to airborne pollutants directly triggers asthma attacks in susceptible individuals.
• Sedentary Lifestyle & Cardiovascular Diseases: Leading a sedentary lifestyle is a significant risk factor for cardiovascular diseases.

Causal Hypothesis Statement Examples in Psychology

In psychology, causal hypotheses explore how certain behaviors, conditions, or interventions might influence mental and emotional outcomes. These hypotheses help in deciphering the intricate web of human behavior and cognition.

• Childhood Trauma & Personality Disorders: Experiencing trauma during childhood increases the risk of developing personality disorders in adulthood.
• Positive Reinforcement & Skill Acquisition: The use of positive reinforcement accelerates skill acquisition in children.
• Sleep Deprivation & Cognitive Performance: Lack of adequate sleep impairs cognitive performance in adults.
• Social Isolation & Depression: Prolonged social isolation is a significant cause of depression among teenagers.
• Mindfulness Meditation & Stress Reduction: Regular practice of mindfulness meditation reduces symptoms of stress and anxiety.
• Peer Pressure & Adolescent Risk Taking: Peer pressure significantly increases risk-taking behaviors among adolescents.
• Parenting Styles & Child’s Self-esteem: Authoritarian parenting styles negatively impact a child’s self-esteem.
• Multitasking & Attention Span: Engaging in multitasking frequently leads to a reduced attention span.
• Childhood Bullying & Adult PTSD: Individuals bullied during childhood have a higher likelihood of developing PTSD as adults.
• Digital Screen Time & Child Development: Excessive digital screen time impairs cognitive and social development in children.

Causal Inference Hypothesis Statement Examples

Causal inference is about deducing the cause-effect relationship between two variables after considering potential confounders. These hypotheses aim to find direct relationships even when other influencing factors are present.

• Dietary Habits & Chronic Illnesses: Even when considering genetic factors, unhealthy dietary habits increase the chances of chronic illnesses.
• Exercise & Mental Well-being: When accounting for daily stressors, regular exercise improves mental well-being.
• Job Satisfaction & Employee Turnover: Even when considering market conditions, job satisfaction inversely relates to employee turnover.
• Financial Literacy & Savings Behavior: When considering income levels, financial literacy is directly linked to better savings behavior.
• Online Reviews & Product Sales: Even accounting for advertising spends, positive online reviews boost product sales.
• Prenatal Care & Child Health Outcomes: When considering genetic factors, adequate prenatal care ensures better health outcomes for children.
• Teacher Qualifications & Student Performance: Accounting for socio-economic factors, teacher qualifications directly influence student performance.
• Community Engagement & Crime Rates: When considering economic conditions, higher community engagement leads to lower crime rates.
• Eco-friendly Practices & Brand Loyalty: Accounting for product quality, eco-friendly business practices boost brand loyalty.
• Mental Health Support & Workplace Productivity: Even when considering workload, providing mental health support enhances workplace productivity.

What are the Characteristics of Causal Hypothesis

Causal hypotheses are foundational in many research disciplines, as they predict a cause-and-effect relationship between variables. Their unique characteristics include:

• Cause-and-Effect Relationship: The core of a causal hypothesis is to establish a direct relationship, indicating that one variable (the cause) will bring about a change in another variable (the effect).
• Testability: They are formulated in a manner that allows them to be empirically tested using appropriate experimental or observational methods.
• Specificity: Causal hypotheses should be specific, delineating clear cause and effect variables.
• Directionality: They typically demonstrate a clear direction in which the cause leads to the effect.
• Operational Definitions: They often use operational definitions, which specify the procedures used to measure or manipulate variables.
• Temporal Precedence: The cause (independent variable) always precedes the effect (dependent variable) in time.

What is a causal hypothesis in research?

In research, a causal hypothesis is a statement about the expected relationship between variables, or explanation of an occurrence, that is clear, specific, testable, and falsifiable. It suggests a relationship in which a change in one variable is the direct cause of a change in another variable. For instance, “A higher intake of Vitamin C reduces the risk of common cold.” Here, Vitamin C intake is the independent variable, and the risk of common cold is the dependent variable.

What is the difference between causal and descriptive hypothesis?

• Causal Hypothesis: Predicts a cause-and-effect relationship between two or more variables.
• Descriptive Hypothesis: Describes an occurrence, detailing the characteristics or form of a particular phenomenon.
• Causal: Consuming too much sugar can lead to diabetes.
• Descriptive: 60% of adults in the city exercise at least thrice a week.
• Causal: To establish a causal connection between variables.
• Descriptive: To give an accurate portrayal of the situation or fact.
• Causal: Often involves experiments.
• Descriptive: Often involves surveys or observational studies.

How do you write a Causal Hypothesis? – A Step by Step Guide

• Identify Your Variables: Pinpoint the cause (independent variable) and the effect (dependent variable). For instance, in studying the relationship between smoking and lung health, smoking is the independent variable while lung health is the dependent variable.
• State the Relationship: Clearly define how one variable affects another. Does an increase in the independent variable lead to an increase or decrease in the dependent variable?
• Be Specific: Avoid vague terms. Instead of saying “improved health,” specify the type of improvement like “reduced risk of cardiovascular diseases.”
• Use Operational Definitions: Clearly define any terms or variables in your hypothesis. For instance, define what you mean by “regular exercise” or “high sugar intake.”
• Ensure It’s Testable: Your hypothesis should be structured so that it can be disproven or supported by data.
• Review Existing Literature: Check previous research to ensure that your hypothesis hasn’t already been tested, and to ensure it’s plausible based on existing knowledge.
• Draft Your Hypothesis: Combine all the above steps to write a clear, concise hypothesis. For instance: “Regular exercise (defined as 150 minutes of moderate exercise per week) decreases the risk of cardiovascular diseases.”

Tips for Writing Causal Hypothesis

• Simplicity is Key: The clearer and more concise your hypothesis, the easier it will be to test.
• Avoid Absolutes: Using words like “all” or “always” can be problematic. Few things are universally true.
• Seek Feedback: Before finalizing your hypothesis, get feedback from peers or mentors.
• Stay Objective: Base your hypothesis on existing literature and knowledge, not on personal beliefs or biases.
• Revise as Needed: As you delve deeper into your research, you may find the need to refine your hypothesis for clarity or specificity.
• Falsifiability: Always ensure your hypothesis can be proven wrong. If it can’t be disproven, it can’t be validated either.
• Avoid Circular Reasoning: Ensure that your hypothesis doesn’t assume what it’s trying to prove. For example, “People who are happy have a positive outlook on life” is a circular statement.
• Specify Direction: In causal hypotheses, indicating the direction of the relationship can be beneficial, such as “increases,” “decreases,” or “leads to.”

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What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

• The hypothesis should be clear and precise to consider it to be reliable.
• If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
• The hypothesis must be specific and should have scope for conducting more tests.
• The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

• The resemblance between the phenomenon.
• Observations from past studies, present-day experiences and from the competitors.
• Scientific theories.
• General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

• Simple hypothesis
• Complex hypothesis
• Directional hypothesis
• Non-directional hypothesis
• Null hypothesis
• Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

• Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
• All lilies have the same number of petals is an example of a null hypothesis.
• If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

• Hypothesis helps in making an observation and experiments possible.
• It becomes the start point for the investigation.
• Hypothesis helps in verifying the observations.
• It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Formation of question
• Doing background research
• Creation of hypothesis
• Designing an experiment
• Collection of data
• Result analysis
• Summarizing the experiment
• Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

• Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

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• Review Article
• Published: 26 April 2024

The development of human causal learning and reasoning

• Mariel K. Goddu   ORCID: orcid.org/0000-0003-4969-7948 1 , 2 , 3 &
• Alison Gopnik 4 , 5  

Nature Reviews Psychology volume  3 ,  pages 319–339 ( 2024 ) Cite this article

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• Human behaviour

Causal understanding is a defining characteristic of human cognition. Like many animals, human children learn to control their bodily movements and act effectively in the environment. Like a smaller subset of animals, children intervene: they learn to change the environment in targeted ways. Unlike other animals, children grow into adults with the causal reasoning skills to develop abstract theories, invent sophisticated technologies and imagine alternate pasts, distant futures and fictional worlds. In this Review, we explore the development of human-unique causal learning and reasoning from evolutionary and ontogenetic perspectives. We frame our discussion using an ‘interventionist’ approach. First, we situate causal understanding in relation to cognitive abilities shared with non-human animals. We argue that human causal understanding is distinguished by its depersonalized (objective) and decontextualized (general) representations. Using this framework, we next review empirical findings on early human causal learning and reasoning and consider the naturalistic contexts that support its development. Then we explore connections to related abilities. We conclude with suggestions for ongoing collaboration between developmental, cross-cultural, computational, neural and evolutionary approaches to causal understanding.

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Acknowledgements

The authors acknowledge their funding sources: the Alexander von Humboldt Foundation, the Templeton World Charity Foundation (0434), the John Templeton Foundation (6145), the Defense Advanced Research Projects Agency (047498-002 Machine Common Sense), the Department of Defense Multidisciplinary University Initiative (Self-Learning perception Through Real World Interaction), and the Canadian Institute for Advanced Research Catalyst Award. For helpful discussions, comments, and other forms of support, the authors thank: S. Boardman, E. Bonawitz, B. Brast-McKie, D. Buchsbaum, M. Deigan, J. Engelmann, T. Friend, T. Gerstenberg, S. Kikkert, A. Kratzer, E. Lapidow, B. Leahy, T. Lombrozo, J. Phillips, H. Rakoczy, L. Schulz, D. Sobel, E. Spelke, H. Steward, B. Vetter, M. Waldmann and E. Yiu.

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Relationship between teachers’ workaholic characteristics and emotional exhaustion – the mediating role of work-family conflict and work efficacy and the moderating role of teaching age

• Published: 22 May 2024

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• Wenping Liu   ORCID: orcid.org/0009-0007-2244-7531 1 ,
• Yubiao Wang 1 &
• Hao Yao   ORCID: orcid.org/0000-0002-5794-7129 2  

This paper expands on the previous research on the relationship between workaholic characteristics and individual emotional exhaustion, and studies the influence of workaholic characteristics on emotional exhaustion and its internal mechanism from the new perspectives of utility theory and conservation of resources theory. Based on a questionnaire survey of 3892 rural teachers in China, this paper first constructs a model of the influence of workaholic characteristics on emotional exhaustion, and finds that the two have the stable quadratic relationship. Workaholic characteristics will reduce emotional exhaustion, but when it exceeds the certain level, workaholic characteristics will no longer reduce emotional exhaustion or even aggravate emotional exhaustion, and moderate workaholic characteristics will minimize emotional exhaustion. The increase in teaching age slows down the threshold of the “U-shaped” curve between workaholic characteristics and emotional exhaustion. By constructing a moderation mediation model, it is found that work-family conflict and work efficacy partially mediate the relationship between workaholic characteristics and rural teachers’ emotional exhaustion, and work-family conflict and work-efficacy promote and inhibit the effects of workaholic characteristics on rural teachers’ emotional exhaustion, respectively. Moreover, teaching age negatively moderated the indirect effect of rural teachers’ workaholic characteristics on emotional exhaustion through work-family conflict, and novice teachers in rural areas were more susceptible to the emotional exhaustion caused by work-family conflict.

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In 2001, as part of efforts to improve the overall level of primary education and solve the educational gap between urban and rural areas, China’s State Council announced the plan called “school closure and merger“(chedianbingxiao), which is mainly to adjust the layout of rural schools, close some remote rural schools and “teaching points”, and open large central schools in towns (In China, Town schools belong to rural schools) and counties. Of course, some teaching points have been retained according to the actual situation. In our research, rural teachers came from two types of schools, one is Town schools, and the other is the “Teaching points“(jiaoxuedian).

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Wenping Liu & Yubiao Wang

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Liu, W., Wang, Y. & Yao, H. Relationship between teachers’ workaholic characteristics and emotional exhaustion – the mediating role of work-family conflict and work efficacy and the moderating role of teaching age. Curr Psychol (2024). https://doi.org/10.1007/s12144-024-06090-6

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DOI : https://doi.org/10.1007/s12144-024-06090-6

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