can you ever prove a hypothesis

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Can a scientific theory ever be absolutely proven?

I personally cringe when people talk about scientific theories in the same way we talk about everyday theories.

I was under the impression a scientific theory is similar to a mathematical proof; however a friend of mine disagreed.

He said that you can never be absolutely certain and a scientific theory is still a theory. Just a very well substantiated one. After disagreeing and then looking into it, I think he's right. Even the Wikipedia definition says it's just very accurate but that there is no certainty. Just a closeness to potential certainty.

I then got thinking. Does this mean no matter how advanced we become, we will never become certain of the natural universe and the physics that drives it? Because there will always be something we don't know for certain?

• soft-question
• epistemology

• $\begingroup$ >We will never become certain of the natural universe and the physics that drives it. Mass of the Universe $\sim3.5\cdot10^{54}$ kg Mass of your brain $\sim 1.5$ kg What do you think, is it possible to squeeze information contained in the latter into the former? To me it is really remarkable that we are able to know at least something. $\endgroup$ –  Kostya Commented Jul 3, 2012 at 9:15
• 1 $\begingroup$ I'm sorry to say, but it has been proven now for over 80 years that it is impossible to prove all true statements. en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems $\endgroup$ –  AdamRedwine Commented Jul 3, 2012 at 11:38
• 3 $\begingroup$ @AdamRedwine: I'm not sure how related this is, given that it applies only in certain frameworks and conditations. $\endgroup$ –  Nikolaj-K Commented Jul 3, 2012 at 17:31
• $\begingroup$ Let me add this very brief comment on terminology: "Theory" in everyday language often is meant as "guess", "hunch", "could be that way". Scientifically speaking, those should be called guesses, educated guesses or hypotheses. A theory in science is a rather exhaustive framework of explaining all currently available data pertaining to a certain subject, as in "theory of electrodynamics", "theory of fluid dynamics" etc. Currently, this confusion about what the word "theory" means is most annoying in discussing the "theory of evolution"... $\endgroup$ –  Lagerbaer Commented Jul 3, 2012 at 19:48
• $\begingroup$ Not 100%. You could always argue that for example, the measurement of the 43 arcseconds per century problem in mercury's perhileon in Newtonian Gravity was actually simply because of quantum fluctuations or something, eventhough repeated observations confirmed it. $\endgroup$ –  Abhimanyu Pallavi Sudhir Commented Jul 2, 2013 at 11:08

8 Answers 8

I basically agree with Argus, though I take a slightly different perspective.

Physicists try to explain the world by constructing mathematical models to approximate it. The phrase mathematical model can sound mysterious, but it just means an equation or equations that predict what's going to happen given some initial conditions. For example Newton's laws of motion are a mathematical model, as is general relativity, quantum mechanics, string theory and so on.

Every mathematical model has a domain in which is a good description of the world, and within that domain we regard the model as effectively exact. Outside that domain we know the model fails. For example Newton's laws describe the motion of ideal particles at speeds well below the speed of light. We know that for higher speeds we need a different model i.e. special relativity, but this fails for high mass/energy densities. To handle high mass/energy densities we need general relativity, and so on.

So we describe the world using a range of theories i.e. mathematical models, and we pick the one that we know works for the situation we are considering. In this sense our theories are always approximate.

However within the domain of our model we are completely certain the model works. If you're sitting at a desk in NASA working out how to send a spaceship to Pluto you can be absolutely confident that the trajectory you calculate will work. You would not be worrying about whether some new and unexplained physics might send your spaceship spiralling into the Sun.

• $\begingroup$ +1 very true each mathematical model describes its perticular are of "application to a high enough degree of accuracy to effectively predict "set" situations. $\endgroup$ –  Argus Commented Jul 1, 2012 at 7:13
• $\begingroup$ Cheers guys :) interesting read. $\endgroup$ –  Joseph Commented Jul 1, 2012 at 17:41
• $\begingroup$ " However within the domain of our model we are completely certain the model works " - Can you explain this statement? Is it ment in an absolute sense (justification) or do you interpret " we can " as "it's possible to imagine a world where everyone agrees on this". Or do you mean it as a suggestion, as in "to do it is a good idea, because otherwise you'd worry to much and that's unhealthy". And who is " we " in this sentence? $\endgroup$ –  Nikolaj-K Commented Jul 3, 2012 at 17:19
• 1 $\begingroup$ Within it's domain Newtonian mechanics has been working perfectly for about 400 years so far. Some may say that this doesn't prove anything, to which I'd reply that they really need to get out more. $\endgroup$ –  John Rennie Commented Jul 3, 2012 at 17:23
• $\begingroup$ I doesn't prove anything. (This might however lead in a discussion about the term "prove".) $\endgroup$ –  Nikolaj-K Commented Jul 3, 2012 at 17:27

Simple Answer: Nothing is guaranteed 100%. (In life or physics)

Now to the physics part of the question.

Soft-Answer:

Physics uses positivism and observational proof through the scientific process. No observation is 100% accurate there is uncertainty in all measurement but repetition gives less chance for arbitrary results.

Every theory and for that matter laws in physics are observational representations that best allow prediction of future experiments. Positivism can overcome theological and philosophical discrepancies such as what is the human perception of reality. Is real actually real type questions.

The scientific process is an ever evolving representation of acquired knowledge based on rigorous experimental data.

No theory is set in stone so to speak as new results allow for modification and fine tuning of scientific theory.

• $\begingroup$ Cheers pal. Good writing there. :) do you reckon a super advanced civilization could ever become 100 certain of everything or is there a fundemental issue with that? $\endgroup$ –  Joseph Commented Jul 1, 2012 at 6:02
• 1 $\begingroup$ That is a tricky question as we are 100 percent certain untilled new date proofs us wrong. Fundamentally there is always an arbitrary uncertainty in any "complex" measuring device so I would have to say technically knowing everything all at once would be extremely difficult if not implausible. To be fair ask me again in 100 thousand years I am sure I will have a better answer. $\endgroup$ –  Argus Commented Jul 1, 2012 at 7:17

You can never be certain of anything, except possibly mathematical theorems. This is the conclusion after long debates on epistemology. The ancient Greek skeptics were of the opinion that knowing the uncertainty of everything will give you peace of mind.

The philosopher David Hume pointed out induction can never be proven. Even if we have some proposed "law" describing everything we know so far, there is no guarantee the next observation will completely violate it. The world might not be what we think it is. There could be some malicious demon messing with our minds.

I'll try to answer this with three points about the scientific method and how "certain" we are of the truth in our theories. Keep in mind that scientists are overly dogmatic about pet theories but we should aspire to transparency about how wrong we might be and distrust everything until the evidence, be it scant or ample, is verified.

First, you can gather quite a lot of insight by listening to Richard Feynman's analogy between discovering the laws of nature and learning the rules of chess through observation of a fraction of the board. In particular, there's the part where he talks about a bishop changing it's colour despite ample observations of this never happening. His overall point is that we're never truly sure but we are always inadvertedly gathering evidence that the theory is right.

Secondly, you should read Isaac Asimov's essay The Relativity of Wrong . His point is that while a theory might be "wrong", sometimes they're very wrong ("the Earth is flat") but sometimes less wrong ("the Earth is a sphere"). In some cases, you can quanitify this. For a contemporary example, cosmologists have settled on $\lambda$CDM as the right model of the Universe. The point isn't that $\lambda$CDM is necessarily the whole story but that, if it isn't, then the evidence we've gathered already implies that the whole story can't be much different.

Finally, let's think back to the superluminal neutrino fanfare. It made big news, with the media painting a picture that made it look like the scientific community needed to revolutionize special relativity (SR). But a lot of scientists responded skeptically, even by offering to eat their shorts. So why the skepticism? Surely that flies against the scientific mantra of doubting authority?

Not quite. There were good reasons to doubt the result and anyone who dismissed those results should've defended their position. It was quickly pointed out that, if neutrinos travelled faster than light, we'd detect supernovae early . Also, I think Glashow and others pointed out that we'd see something like Cerenkov radiation from the neutrinos.

But more importantly, SR is, to me, a theory that is close to being "certain". It was and still is tried and tested extensively and it forms the basis of other theories that are themselves successful. So the odds of SR being "wrong" are outrageously small. We have inadvertedly tested it bazillions of times and it's worked perfectly. And the amount by which it can be wrong is very small. At the time, it could've been like the first time a pawn was queened into a bishop, but, to roll out the cliche, extraordinary claims require extraordinary evidence.

• $\begingroup$ "We have inadvertedly tested it bazillions of times and it's worked perfectly." How does this vary, from say, the Aristotle's (and other ancient) views of gravity that IIRC weren't disproven for a thousand years, even though they are trivial to disprove today. $\endgroup$ –  NPSF3000 Commented Dec 19, 2014 at 14:31

The reason you can not prove things in real life, as apposed to in mathematics, is that you can not check your theory for all variables x and t. For example, you can not test that the theory of gravitation holds everywhere in the universe (it will take an almost infinite amount of experiments). And you especially can not prove that it holds at every moment in time, that is backwards in time or forward. You can only test the theory right now.

Check out Clavius' answer at yahoo answers. It is very good: http://answers.yahoo.com/question/index?qid=20081004094805AAzyeZF

No, a physical theory can never be "proven".

There is a classical metaphor to illustrate why, known as the black swan problem or problem of induction.

If in your entire life you have only see white swans, you will formulate the general law (or theory) that all the swans are white . You will then keep seeing only white swans -thousands of them- and think " my theory is great: it has been confirmed by countless observations, and every single observation confirmed it! ".

Then, one day, you will se a black swan, and your theory will suddenly, catastrophically fall apart.

With physics, it is exactly the same. No matter how many experiments corroborate your theory: if only a single experiment gives a result different from the one predicted by your theory, then the theory is wrong : it has been falsified .

The problem of induction and of the foundations of scientific theory has been extensively analyzed by the philosopher Karl Popper , who identified falsifiability as the defining characteristic of every scientific theory.

A theory which can never be falsified (proven wrong) is like religion: not scientific. For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. For example, " God created the Universe " is not a falsifiable statement because it cannot be falsified with observation.

This is a question about philosophy of science and epistemology, so you should expect varying answers with different prespectives.

This is my personal approach to the question.

First let's examine what does it mean to say that a scientific theory is "absolutely proven".

Just as John Rennie pointed out in his answer, a scientific theory is a mathematical model, or another way to put it, a scientific theory consists of a set of axioms which are usually mathematical in nature, and theorems that follow from such set of axioms.

To give you a concrete example, consider Newtonian mechanics, Newton's theory is made up of three axioms: his famous three laws. Add to that the theorems that follow from these axioms, like the work-energy theorem and many others.

Newton's second law is given by: $F=m\dfrac{d^2x}{dt^2}$. To say that Newton's theory is absolutely proven, is tantamout to say that this equation holds true for any arbitrary values(real numbers in this case) of $F,m$ and $x$. The same applies to Newton's first and third law, they should hold for any arbitrary real number.

There is no logically neccessary reason that Newton's second law should hold for all real values. Hence the only way to absolutely prove it, is to test it for all the real values it can take! This is obviously an impossible and insurmountable task to do, and hence it's impossible to absolutely prove a scientific theory.

There's another crucial point to consider, even if you were able to test your theory, for all the values it takes, you have to have gadgets with precision and accuracy of 100%.This is another reason why you cannot prove a theory to be stricly true.

However, There are things in empirical sciences(and mathematics and logic) that you can prove to be absolutely true. You can absolutely prove that assuming Newton's theory implies the work-energy theorem. Or assuming the constancy of speed of light and the principle of relativity impliy relativity of time,space and simultaneity.This is the same as assmuing the axioms of Euclid implies Pythagorean theorem.

To sum up, either in physics or mathematics, You can prove Axiom A implies theorem B , but you cannot stricly prove Axiom A is true , hence you can never absolutely prove a scientific theory is true.

• $\begingroup$ Two points:Mathematical theories start from axioms and prove theorems and are self consistently proven. Physics theories require postulates which are not connected to the mathematics axioms necessarily, but are statements which tie up the mathematics to the observables in physics. example: the postulates of quantum mechanics. Without them the wave mechanics differential equations although self consistent , have no physics meaning. In addition a physics theory can only be validated. Even one falsification will require reexamination of the postulates and the region of validity of the theory. $\endgroup$ –  anna v Commented Aug 10, 2015 at 18:29
• $\begingroup$ @annav I agree with you. $\endgroup$ –  Omar Nagib Commented Aug 10, 2015 at 19:10

Not the answer you're looking for? Browse other questions tagged soft-question epistemology or ask your own question .

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Common Misconceptions About Science I: “Scientific Proof”

Why there is no such thing as a scientific proof..

Posted November 16, 2008 | Reviewed by Ekua Hagan

Misconceptions about the nature and practice of science abound and are sometimes even held by otherwise respectable practicing scientists themselves. I have dispelled some of them (misconceptions, not scientists) in earlier posts (for example, that beauty is in the eye of the beholder , beauty is only skin-deep , and you can’t judge a book by its cover ).

Unfortunately, there are many other misconceptions about science. One of the most common misconceptions concerns the so-called “scientific proofs.” Contrary to popular belief, there is no such thing as a scientific proof.

Proofs exist only in mathematics and logic, not in science. Mathematics and logic are both closed, self-contained systems of propositions, whereas science is empirical and deals with nature as it exists. The primary criterion and standard of evaluation of scientific theory is evidence, not proof. All else equal (such as internal logical consistency and parsimony), scientists prefer theories for which there is more and better evidence to theories for which there is less and worse evidence. Proofs are not the currency of science.

Proofs have two features that do not exist in science: They are final , and they are binary . Once a theorem is proven, it will forever be true and there will be nothing in the future that will threaten its status as a proven theorem (unless a flaw is discovered in the proof). Apart from the discovery of an error, a proven theorem will forever and always be a proven theorem.

In contrast, all scientific knowledge is tentative and provisional , and nothing is final. There is no such thing as final proven knowledge in science. The currently accepted theory of a phenomenon is simply the best explanation for it among all available alternatives . Its status as the accepted theory is contingent on what other theories are available and might suddenly change tomorrow if there appears a better theory or new evidence that might challenge the accepted theory. No knowledge or theory (which embodies scientific knowledge) is final. That, by the way, is why science is so much fun.

Further, proofs, like pregnancy , are binary; a mathematical proposition is either proven (in which case it becomes a theorem) or not (in which case, it remains a conjecture until it is proven). There is nothing in between. A theorem cannot be kind of proven or almost proven. These are the same as unproven.

In contrast, there is no such binary evaluation of scientific theories. Scientific theories are neither absolutely false nor absolutely true. They are always somewhere in between. Some theories are better, more credible, and more accepted than others. There is always more, more credible, and better evidence for some theories than others. It is a matter of more or less, not either/or. For example, experimental evidence is better and more credible than correlational evidence, but even the former cannot prove a theory; it only provides very strong evidence for the theory and against its alternatives.

The knowledge that there is no such thing as a scientific proof should give you a very easy way to tell real scientists from hacks and wannabes. Real scientists never use the words “scientific proofs,” because they know no such thing exists. Anyone who uses the words “proof,” “prove,” and “proven” in their discussion of science is not a real scientist.

The creationists and other critics of evolution are absolutely correct when they point out that evolution is “just a theory” and it is not “proven.” What they neglect to mention is that everything in science is just a theory and is never proven. Unlike the Prime Number Theorem, which will absolutely and forever be true, it is still possible, albeit very, very, very, very, very unlikely, that the theory of evolution by natural and sexual selection may one day turn out to be false. But then again, it is also possible, albeit very, very, very, very, very unlikely, that monkeys will fly out of my ass tomorrow. In my judgment, both events are about equally likely.

Satoshi Kanazawa is an evolutionary psychologist at LSE and the coauthor (with the late Alan S. Miller) of Why Beautiful People Have More Daughters .

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A hypothesis can’t be right unless it can be proven wrong

Charles Rock, PhD, (right) and Jiangwei Yao, PhD, recently reviewed Richard Harris’ book about scientific research, titled "Rigor Mortis: How Sloppy Science Creates Worthless Cures, Crushes Hope, and Wastes Billions." Now, Rock and Yao address specific issues raised in Harris’ book and offer solutions or tips to help avoid the pitfalls identified in the book.

“That (your hypothesis) is not only not right; it is not even wrong.” Wolfgang Pauli (Nobel Prize in Physics, 1945)

A hypothesis is the cornerstone of the scientific method.

It is an educated guess about how the world works that integrates knowledge with observation.

Everyone appreciates that a hypothesis must be testable to have any value, but there is a much stronger requirement that a hypothesis must meet.

A hypothesis is considered scientific only if there is the possibility to disprove the hypothesis.

The proof lies in being able to disprove

A hypothesis or model is called falsifiable if it is possible to conceive of an experimental observation that disproves the idea in question. That is, one of the possible outcomes of the designed experiment must be an answer, that if obtained, would disprove the hypothesis.

Our daily horoscopes are good examples of something that isn’t falsifiable. A scientist cannot disprove that a Piscean may get a surprise phone call from someone he or she hasn’t heard from in a long time. The statement is intentionally vague. Even if our Piscean didn’t get a phone call, the prediction cannot be false because he or she may get a phone call. They may not.

A good scientific hypothesis is the opposite of this. If there is no experimental test to disprove the hypothesis, then it lies outside the realm of science.

Scientists all too often generate hypotheses that cannot be tested by experiments whose results have the potential to show that the idea is false.

Three types of experiments proposed by scientists

• Type 1 experiments are the most powerful. Type 1 experimental outcomes include a possible negative outcome that would falsify, or refute, the working hypothesis. It is one or the other.
• Type 2 experiments are very common, but lack punch. A positive result in a type 2 experiment is consistent with the working hypothesis, but the negative or null result does not address the validity of the hypothesis because there are many explanations for the negative result. These call for extrapolation and semantics.
• Type 3 experiments are those experiments whose results may be consistent with the hypothesis, but are useless because regardless of the outcome, the findings are also consistent with other models. In other words, every result isn’t informative.

Formulate hypotheses in such a way that you can prove or disprove them by direct experiment.

Science advances by conducting the experiments that could potentially disprove our hypotheses.

Increase the efficiency and impact of your science by testing clear hypotheses with well-designed experiments.

For more on the challenges in experimental science , read our review of Richard Harris’  Rigor Mortis: How Sloppy Science Creates Worthless Cures, Crushes Hope, and Wastes Billions.

A researcher’s look at Rigor Mortis: Are motivators and incentives to find a cure hurting scientific research?

St. Jude researchers take a look at Rigor Mortis, Richard Harris’ exposé of how the drive to find results hampers scientific progress.

About the author

Charles Rock, PhD, was a member of the Department of Infectious Diseases and later the Department of Host-Microbe Interactions at St. Jude Children’s Research Hospital until his passing in 2023.  Learn about Dr. Rock's research career .

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scientific hypothesis

Our editors will review what you’ve submitted and determine whether to revise the article.

• National Center for Biotechnology Information - PubMed Central - On the scope of scientific hypotheses
• LiveScience - What is a scientific hypothesis?
• The Royal Society - Open Science - On the scope of scientific hypotheses

scientific hypothesis , an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an “If…then” statement summarizing the idea and in the ability to be supported or refuted through observation and experimentation. The notion of the scientific hypothesis as both falsifiable and testable was advanced in the mid-20th century by Austrian-born British philosopher Karl Popper .

The formulation and testing of a hypothesis is part of the scientific method , the approach scientists use when attempting to understand and test ideas about natural phenomena. The generation of a hypothesis frequently is described as a creative process and is based on existing scientific knowledge, intuition , or experience. Therefore, although scientific hypotheses commonly are described as educated guesses, they actually are more informed than a guess. In addition, scientists generally strive to develop simple hypotheses, since these are easier to test relative to hypotheses that involve many different variables and potential outcomes. Such complex hypotheses may be developed as scientific models ( see scientific modeling ).

Depending on the results of scientific evaluation, a hypothesis typically is either rejected as false or accepted as true. However, because a hypothesis inherently is falsifiable, even hypotheses supported by scientific evidence and accepted as true are susceptible to rejection later, when new evidence has become available. In some instances, rather than rejecting a hypothesis because it has been falsified by new evidence, scientists simply adapt the existing idea to accommodate the new information. In this sense a hypothesis is never incorrect but only incomplete.

The investigation of scientific hypotheses is an important component in the development of scientific theory . Hence, hypotheses differ fundamentally from theories; whereas the former is a specific tentative explanation and serves as the main tool by which scientists gather data, the latter is a broad general explanation that incorporates data from many different scientific investigations undertaken to explore hypotheses.

Countless hypotheses have been developed and tested throughout the history of science . Several examples include the idea that living organisms develop from nonliving matter, which formed the basis of spontaneous generation , a hypothesis that ultimately was disproved (first in 1668, with the experiments of Italian physician Francesco Redi , and later in 1859, with the experiments of French chemist and microbiologist Louis Pasteur ); the concept proposed in the late 19th century that microorganisms cause certain diseases (now known as germ theory ); and the notion that oceanic crust forms along submarine mountain zones and spreads laterally away from them ( seafloor spreading hypothesis ).

What Is a Hypothesis? (Science)

If...,Then...

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A hypothesis (plural hypotheses) is a proposed explanation for an observation. The definition depends on the subject.

In science, a hypothesis is part of the scientific method. It is a prediction or explanation that is tested by an experiment. Observations and experiments may disprove a scientific hypothesis, but can never entirely prove one.

In the study of logic, a hypothesis is an if-then proposition, typically written in the form, "If X , then Y ."

In common usage, a hypothesis is simply a proposed explanation or prediction, which may or may not be tested.

Writing a Hypothesis

Most scientific hypotheses are proposed in the if-then format because it's easy to design an experiment to see whether or not a cause and effect relationship exists between the independent variable and the dependent variable . The hypothesis is written as a prediction of the outcome of the experiment.

Null Hypothesis and Alternative Hypothesis

Statistically, it's easier to show there is no relationship between two variables than to support their connection. So, scientists often propose the null hypothesis . The null hypothesis assumes changing the independent variable will have no effect on the dependent variable.

In contrast, the alternative hypothesis suggests changing the independent variable will have an effect on the dependent variable. Designing an experiment to test this hypothesis can be trickier because there are many ways to state an alternative hypothesis.

For example, consider a possible relationship between getting a good night's sleep and getting good grades. The null hypothesis might be stated: "The number of hours of sleep students get is unrelated to their grades" or "There is no correlation between hours of sleep and grades."

An experiment to test this hypothesis might involve collecting data, recording average hours of sleep for each student and grades. If a student who gets eight hours of sleep generally does better than students who get four hours of sleep or 10 hours of sleep, the hypothesis might be rejected.

But the alternative hypothesis is harder to propose and test. The most general statement would be: "The amount of sleep students get affects their grades." The hypothesis might also be stated as "If you get more sleep, your grades will improve" or "Students who get nine hours of sleep have better grades than those who get more or less sleep."

In an experiment, you can collect the same data, but the statistical analysis is less likely to give you a high confidence limit.

Usually, a scientist starts out with the null hypothesis. From there, it may be possible to propose and test an alternative hypothesis, to narrow down the relationship between the variables.

Example of a Hypothesis

Examples of a hypothesis include:

• If you drop a rock and a feather, (then) they will fall at the same rate.
• Plants need sunlight in order to live. (if sunlight, then life)
• Eating sugar gives you energy. (if sugar, then energy)
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How do scientists know whether to trust their results?

by Salvador Balkus

Collectively, scientists conduct a lot of experiments. Whether they study addiction , air pollution , or animal populations , most basic scientific experiments have one thing in common: data. 

To perform an experiment, scientists first formulate a hypothesis about how something works. Then, they collect data – measurements, sensor information, images, surveys, and the like – that either support their hypothesis or prove it false.

Usually, though, it is impossible to measure all of the data. After all, we cannot track every person with addiction, or measure the particles in every cubic inch of the air – that would be impractical. Instead, scientists take a random sample. They gather data for only a small number of people, or a small set of locations, and use the results to inform our knowledge about the world at large (Figure 1).

However, drawing conclusions from only a sample of the possible data can be risky. Suppose the results show some novel finding – perhaps that a specific drug is less addictive than others. If the finding is based on a random sample of people, then it could be possible that the scientists just happened to select people for whom the drug was less addictive, and that the findings would fail to hold among the general population.  

In this case, how do the scientists know if their hypothesis is supported or if their hypothesis is wrong and the results simply occurred randomly?

To do this, scientists rely on a mathematical calculation called a “ p -value.” Though ubiquitous – p -values have been included in millions of scientific papers – these calculations can also be controversial. And even if you’re not a scientist, the debate around p -values holds crucial implications regarding the public’s trust in science as a whole.

So, what is a p -value?

When a scientist sets up an experiment, they want to test a hypothesis that “some interesting phenomenon” happens. No amount of evidence can ever prove a hypothesis is correct 100% of the time. Instead, scientists first assume that the phenomenon does not actually happen (which, in technical terms, is called the null hypothesis ), and attempt to reject this idea.

Once they gather data, they calculate a p -value : the probability of that data being collected from the experiment simply by chance assuming the null hypothesis – that the phenomenon does not occur. A low p -value suggests the null hypothesis is highly unlikely, lending credence to the researcher’s own hypothesis that the phenomenon does exist. Let’s explore an example.

Imagine you just met a fine lady at a tea shop. The lady claims that by tasting a cup of tea made with milk, her delicate palate can detect whether the milk or the tea was poured into the cup first. You’re skeptical, so you devise an experiment. You prepare 8 cups of tea – 4 with milk added first, and 4 with tea – order them randomly, and ask her to taste each and say how it was prepared. How many cups would she need to classify correctly in order for you to believe her? (Figure 2)

This story was originally recounted in 1935 by a statistician named Ronald Fisher in order to motivate the use of probability in designing experiments. Fisher began by counting the number of possible ways in which a person could label all 8 cups, knowing that 4 were prepared with milk first and 4 with tea. 

As he explains, a person with no distinguishing ability would be expected to, just by chance, classify all 4 cups of each type correctly in only 1 out of 70 experiments, or about 1 percent of the time. Since such an event would be exceedingly rare, if the lady classified all of the cups correctly, you could rule out random guessing and be fairly certain of her claim. 

On the other hand, an unskilled taster would be expected to classify just 3 cups of each type correctly (with one of each incorrect) about 16 times out of 70, or about 20 percent of the time. Since an event with 20 percent probability happens fairly often, if the lady only classified 3 cups of each type correctly, there would not be enough evidence to ascertain if her claim is true or if she was simply a lucky guesser.

Each of these values – the probability of a person with no special tasting ability classifying 3 cups correctly (20%) or 4 cups correctly (1%) – are examples of p -values . In Fisher’s tea experiment, he assumed that the lady did not have the ability to tell if milk was added to the cup first. Then, since she could classify all 8 cups correctly – a highly improbable event under Fisher’s “null hypothesis” – he concluded that she probably did have the ability to tell if milk was added first or second.

Researchers rely on similar logic every day. Though Fisher did not invent the p -value , he did popularize its use in scientific studies and define the common threshold of 1 in 20 ( p < 0.05) as the definition of a “rare” event. The smaller the p -value, the less likely that the results obtained are due to random chance assuming the hypothesized phenomenon does not exist – and the stronger the evidence that the phenomenon under study really occurred.

Why are p -values controversial?

Since Fisher’s time, millions of experiments have used p -values to test whether their models of the world reflect the data they gathered . Today, however, the practice is debated. In 2019, over 800 academics and researchers signed an open letter in Nature to abolish the use of p -values “to decide whether a result refutes or supports a scientific hypothesis.” In addition, select journals have banned the publication of papers containing p -values . 

One major reason for this is the arbitrary definition of “rare.” Though Fisher only mentioned p < 0.05 as an example of rarity, his offhand comment has morphed into a hard threshold that scientists must often meet in order for their studies to be published at all. This can lead to publication bias and frustration from researchers who cannot publish important results that only attain, say, p = 0.06. 

Conversely, some scientists mistake a low p -value to mean that their results are consequential. This is wrong: a low p -value only helps us rule out the possibility of the results occurring due to random chance under a null hypothesis. Results could have low p -value but have limited practical importance (sometimes called “clinically insignificant”).

A commonly-cited example is the Physicians Health Study, which found that taking aspirin reduced subjects’ risk of having a heart attack, albeit only by 0.8%, with p < 0.00001. Though the low p -value ruled out the possibility of aspirin having no effect at all, the effect of taking aspirin was so tiny as to be meaningless for most people – which is why not everyone should take aspirin every day. This idea is related to Fisher’s tea experiment in Figure 3.

Another problem is what some refer to as “ p -hacking .” In the famous “dead salmon study,” which won an IgNobel Prize in 2012, researchers put a dead salmon under an fMRI scan, showed it pictures of people, and found that the salmon actually responded positively!

Of course, this conclusion is nonsense. In fact, the study was written specifically to show how errors arise when calculating many p -values at once. The problem was that, when an fMRI machine scans a human brain (or in this case, a salmon), it measures changes in thousands of tiny sections, called voxels – and a p -value is computed for each. If you run thousands of tests like this, even events with low probability (low p -values under the null hypothesis) are bound to occur eventually by chance. 

This is just one of many types of p -hacking : repeating multiple statistical tests until something “significant” is found. If the insignificant p -values are not reported, this is also considered “cherry-picking” – but even if they are, the presented p -values will be incorrect if the authors fail to correct for the number of tests run (which is not always feasible). The dead salmon study demonstrates how authors can misuse statistical techniques to present misleading results.

Why this controversy is not as bad as it may seem

You might then wonder: isn’t running thousands of experiments exactly what scientists do every day? If doing so is bad, and if p -values are controversial and often misinterpreted , how can we trust scientific papers?

The reason you can rest easy is that scientific evidence requires consensus. Any given phenomenon can have innumerable explanations. Hence, to collectively conduct their work, scientists must propose many hypotheses – and since only one can be correct, most must be wrong . 

But that isn’t a bad thing! Though the media often reports on single articles, one sole study proves little. Accurate knowledge requires replication – repeated experiments that support and refine the theory – as well as disproof of other, incorrect hypotheses. If one poor study happens to publish a false positive or use p -values incorrectly, later studies will correct the error and disprove the previous conclusions.

Yet, such limitations usually are not emphasized in news coverage. That’s why it is important to keep this in mind when reading or listening to news on scientific studies. Does the story report on only a single scientific paper? Does it disprove an existing hypothesis? Importantly, does the paper in question build on years of previous research? Even if an individual paper is trustworthy, it is important to consider questions like these to properly digest scientific news.

Even though a single p -value cannot “prove” a hypothesis, p -values help scientists avoid publishing results that are attributable more to randomness than any relevant phenomenon. They are just one tool out of many that allow scientists to critique their own findings and, in the process, build the types of consensus that really are scientifically important.  

So, if you see low p -values reported from a scientific article, know that the authors took care to ensure the quality of their findings – but also know that the p -value is far from the end of their story.

Salvador Balkus is a PhD student in Biostatistics at the Harvard T.H. Chan School of Public Health.

Cover image by ColiN00B on pixabay .

For More Information:

• Read this article for a more in-depth explanation of p -values and their implications regarding replication of scientific studies. 
• To better understand what p -values do and do not communicate, as well as how they can be misinterpreted, read this .
• Check this out for  a more detailed discussion of Fisher’s “Lady Tasting Tea” experiment.

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2 thoughts on “ How do scientists know whether to trust their results? ”

If “consensus” were a criterion, the earth would still hve been FLAT!

Time to start thinking‽

All very interesting but testing if the lady was correct is hardly important is it? I have just read an article about a man called Jordan McSweeney, who attacked and murdered Zara Aleena. It seems mistakes were made by probation staff. Could science be used to assist people who interview criminals to assist in finding out if they are telling the truth?

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What is a scientific hypothesis?

It's the initial building block in the scientific method.

Hypothesis basics

What makes a hypothesis testable.

• Types of hypotheses
• Hypothesis versus theory

Additional resources

Bibliography.

A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research. 

The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid-20th century by Austrian-British philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).

A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.

A hypothesis is usually written in the form of an if-then statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .

Here are some examples of hypothesis statements:

• If garlic repels fleas, then a dog that is given garlic every day will not get fleas.
• If sugar causes cavities, then people who eat a lot of candy may be more prone to cavities.
• If ultraviolet light can damage the eyes, then maybe this light can cause blindness.

A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."

An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.

Types of scientific hypotheses

In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .

For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."

If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (​​BCcampus, 2015). 

There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a two-tailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a one-tailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.

Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley . 

A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.

Scientific theory vs. scientific hypothesis

The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.

"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts." 

• Read more about writing a hypothesis, from the American Medical Writers Association.
• Find out why a hypothesis isn't always necessary in science, from The American Biology Teacher.
• Learn about null and alternative hypotheses, from Prof. Essa on YouTube .

Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientific-hypothesis

Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.

California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm  

Karl Popper, "Conjectures and Refutations," Routledge, 1963.

Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.‌

University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf  

William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypotheses-explained/  

University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/Lecture-FDR.pdf  

University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19

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• Knowledge Base

Methodology

• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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See an example

Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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An exciting discovery from an incorrect hypothesis

By  Meranda M. Masse Department Communications & Graduate Student (Cavagnero)

A hypothesis can be a scientists’ best-educated guess about how an experiment might turn out or why they got specific results. Sometimes, they’re not far off from the truth. Other times, they’re wrong. Being wrong isn’t always a bad thing. Often, it means that the researchers get to discover something new and exciting. This exact scenario happened when the Burstyn and Buller lab decided to work together on a project.

“You get alternative perspectives… and that’s why collaborations can be so beneficial,” said Brian Weaver , a graduate student in the Burstyn group.

Outside of a healthy diet, proteins are also responsible for many complex chemical reactions in our body’s cells and even in bacteria cells. Sometimes these proteins have metals in them that help to facilitate these reactions. While the Burstyn group aims to understand how these metals can help, the Buller group looks to make new proteins that can perform specific chemical reactions. By combining their knowledge, the Buller and Burstyn group wanted to make bacteria cells that would put cobalt metal into their proteins.

By putting cobalt metal into proteins, bacteria cells can make specific products that would otherwise produce lots of wasteful and potentially hazardous chemicals in a lab. Doing the reactions in cells and not in a lab makes the chemical reactions better for the planet and more efficient.

As Professor Andrew Buller said, “This is how life does chemistry, and the transformations it pulls off are wild!”

Too much cobalt can kill cells, making trying to incorporate the metal into proteins a challenging task. The two groups thought that they could evolve cells to withstand high concentrations of cobalt metal.

Weaver and graduate student Lydia Perkins from the Buller group were paired up and asked to perform these experiments. Interestingly, after evolving these new cells, the pair realized that their initial thoughts were incorrect about how cells can incorporate cobalt into their proteins. Instead of seeing more proteins with cobalt metal in them, the researchers found out that the cells made to survive in high concentrations of cobalt did the opposite.

“When we evolved them, it turned out that they were worse at incorporating cobalt. [The cells were] good at surviving in cobalt, but bad at putting it into [their proteins],” Perkins explained.

When Perkins and Weaver went back to the drawing board, they decided to run some controls. Controls can tell researchers how something they are changing in an experiment compares to their system without that specific change.

Thanks to the control experiments, the two groups soon realized that there was no need to evolve the cells in the first place. As it turns out, at high concentrations of cobalt metal, the cells could survive by putting them into their proteins- which is precisely what the researchers wanted in the first place.

“We had a misconception on how this needed to work. That’s really what Brian and Lydia figured out.” Professor Judith Burstyn commented.

While the two groups’ initial hypothesis was wrong, through careful research and collaboration, they reached their final goal of putting cobalt metal into proteins. Thanks to their work, incorporating cobalt metal into proteins is now accessible to many other researchers- leaving the possibilities for future exploration endless.

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• When scientific hypotheses don’t pan out

One pair of scientists thought they’d discovered a new antiviral protein buried inside skin cells. Another research team saw early hints suggesting that the flu virus might cooperate to boost infections in humans. And a nationwide team of clinicians thought that high doses of certain vitamins might prevent cancer.

These studies don’t have much to do with each other, except that the researchers had all based their hypotheses on convincing earlier data.

And those hypotheses were all wrong.

The hypothesis is a central tenet to scientific research. Scientists ask questions, but a question on its own is often not sufficient to outline the experiments needed to answer it (nor to garner the funding needed to support those experiments).

So researchers construct a hypothesis, their best educated guess as to the answer to that question.

How a hypothesis is formed

Technically speaking, a hypothesis is only a hypothesis if it can be tested. Otherwise, it’s just an idea to discuss at the water cooler.

Researchers are always prepared for the possibility that those tests could disprove their hypotheses — that’s part of the reason they do the studies. But what happens when a beloved idea or dogma is shattered is less technical, less predictable. More human.

In some cases, a disproven hypothesis is devastating, said Swedish Cancer Institute and Fred Hutchinson Cancer Research Center public health researcher Dr. Gary Goodman, who led one of those vitamin studies. In his case, he was part of a group of cancer prevention researchers who ultimately showed that high doses of certain vitamins can increase the risk of lung cancer — an important result, but the opposite of what they thought they would prove in their trials.

But for some, finding a hypothesis to be false is exhilarating and motivating.

Herpes hypothesis leads to surprise cancer-related finding

Dr. Jia Zhu , a Fred Hutch infectious disease scientist, and her research partner (and husband), Fred Hutch and University of Washington infectious disease researcher Dr. Tao Peng, thought they’d found a new antiviral in herpes simplex virus type 2, or HSV-2, in part because they’ve been focused on that virus — and its interaction with human immune cells — for decades now, together with Dr. Larry Corey , virologist and president and director emeritus of Fred Hutch.

A few years ago, Zhu and Peng found that a tiny, mysterious protein called interleukin-17c is massively overproduced by HSV-infected skin cells. Maybe it was an undiscovered antiviral protein, the virologists thought, made by the skin cells in an attempt to protect themselves. They spent more than half a year pursuing that hypothesis, conducting experiment after experiment to see if IL-17c could block the herpes virus from replicating. It didn’t.

Zhu pointed to a microscopic image of a biopsy from a person with HSV, captured more than 10 years ago where she, Corey and their colleagues first discovered that certain T cells, a type of immune cell, cluster in the skin where herpes lesions form. At the top of the colorful image, a layer of skin cells stained blue is studded with orange-colored T cells. Beneath, green nerve endings stretch their branch-like fibers toward the infected skin cells.

“This is my favorite image, but we all focused on the top,” the skin and immune cells, Zhu said. “We never really paid attention to the nerves.”

"You take an approach and then you just have to let the science drive." — Dr. Jia Zhu, infectious disease researcher

Finally, Peng discovered that the nerve fibers themselves carry proteins that can interact with the IL-17c molecule produced in infected skin cells — and that the protein signals the nerves to grow, making it one of only a handful of nerve growth factors identified in humans.

The researchers are excited about their serendipitous finding not just because it’s another piece in the puzzle of this mysterious virus, which infects one in six teens and adults in the U.S. They also hope the protein could fuel new therapies in other settings — such as neuropathy, a type of nerve damage that is a side effect of many cancer chemotherapies.

It’s a finding they never would have anticipated, Zhu said, but that’s often the nature of research.

“You do have a big picture, you know the direction. You take an approach and then you just have to let the science drive,” she said. “If things are unexpected, maybe just explore a little bit more instead of shutting that door.”

Flu hypothesis leads to a new mindset and avenue of research

Sometimes, a mistaken hypothesis has less to do with researchers’ preconceptions and more to do with the way basic research is conducted. Take, for example, the work of Fred Hutch evolutionary biologist Dr. Jesse Bloom , whose laboratory team studies how influenza and other viruses evolve over time. Many of their experiments involve infecting human cells in a petri dish with different strains of the flu virus and seeing what happens.

A few years ago, Bloom and University of Washington doctoral student Katherine Xue made an intriguing discovery using that system: They saw that two variants of influenza H3N2 (the virus that’s wreaking havoc in the current flu season) could cooperate to infect cells better together than either version could alone.

The researchers had only shown that viral collaboration in petri dishes in the lab, but they had reason to think it might be happening in people, too. For one, the same mix of variants was present in public databases of samples taken from infected people — but those samples had also been grown in petri dishes in the lab before their genomic information was captured.

So Xue and Bloom sequenced those variants at their source, the original nasal wash samples collected and stored by the Washington State Public Health Laboratories . They found no such mixture of variants from the samples that hadn’t been grown in the laboratory — so the flu may not cooperate after all, at least not in our bodies. The researchers published their findings last month in the journal mSphere.

Scientists have to ask themselves two questions about any discovery, Bloom said: “Are your findings correct? And are they relevant?”

The team’s first study wasn’t wrong; the viruses do cooperate in cells in the lab. But the second question is usually the tougher one, the researchers said.

“There are a lot of differences, obviously, between viruses growing in a controlled setting in a petri dish versus an actual human,” Xue said.

She and Bloom aren’t too glum about their disproven hypothesis, though. That line of inquiry opened new doors in the lab, Bloom said.

Before Xue’s study, he and his colleagues exclusively studied viruses in petri dishes. Now, more members of his laboratory team are using clinical samples as well — an approach that is made possible by the closer collaborations between basic and clinical research at the Hutch, Bloom said.

Some of their findings in petri dishes aren’t holding true in the clinical samples. But they’re already making interesting findings about how flu evolves in the human body — including the discovery that how flu evolves in single people with unusually long infections can hint at how the virus will evolve globally, years later. They never would have done that study if they hadn’t already been trying to follow up their original, cooperating hypothesis.

“It opened this whole new way of trying to think about this,” Bloom said. “Our mindset has changed a lot.”

Prevention hypothesis flipped on its head

Fred Hutch and Swedish cancer prevention researcher Goodman and his epidemiology colleagues had good reason to think the vitamins they were testing in clinical trials could prevent lung cancer.

All of the data pointed to an association between the vitamins and a reduced risk of lung cancer. But the studies hadn’t shown a causative link — just a correlation. So the researchers set out to do large clinical trials comparing high doses of the vitamins to placebos.

In the CARET trial , which Goodman led and was initiated in 1985, 18,000 people at high risk of lung cancer (primarily smokers) were assigned to take either a placebo, vitamin A, beta-carotene (a vitamin A precursor) or a combination of the two supplements. Two other similar trials started in other parts of the world at around the same time also testing beta-carotene’s effect on lung cancer risk.

In a similar vein, at the same time, a small trial suggested that supplemental selenium decreased the incidence of prostate cancer. So in 2001, the SELECT trial launched through SWOG , a nationwide cancer clinical trial consortium, testing whether selenium or high-dose vitamin E or the combination could prevent prostate cancer. SELECT enrolled 35,000 men; Goodman was the study leader for the Seattle area.

Designing and conducting cancer prevention trials where participants take a drug or some other intervention is a tricky business, Goodman said.

“In prevention, most of the people you treat are healthy and will never get cancer,” he said. “So you have to make sure the agent is very safe.”

Previous studies had all pointed to the vitamins being safe — even beneficial. And the vitamins tested in the trials are all naturally occurring as part of our diets. Nobody thought they could possibly hurt.

But that’s exactly what happened. In the CARET study, participants taking the combination of vitamin A and beta-carotene had higher rates of lung cancer than those taking the placebo; other trials testing those vitamins saw similar results. And in the SELECT trial, those taking vitamin E had higher rates of prostate cancer.

All the trials had close monitoring built in and all were stopped early when the researchers saw that the cancer rates were trending the opposite way that they’d expected.

“It was just devastating when we learned the results,” Goodman said. “Everybody [who worked on the trial] was so hopeful. After all, we’re here to prevent cancer.”

When the CARET study stopped, Goodman and his team hired extra people to answer study participants’ questions and the angry phone calls they assumed they would get. But very few phone calls came in.

“They said they were involved in the study for altruistic reasons, and we got an answer,” he said. “One of the benefits of our study is that we did show that high doses of vitamins can be very harmful.”

That was an important finding, Goodman said, because the prevailing dogma at the time was that high doses of vitamins were good for you. Although these studies disproved that commonly held belief, even today not everyone in the general public buys that message.

Another benefit of that difficult experience: The bar for giving healthy people a supplement or drug with the goal of preventing cancer or other disease is much higher now, Goodman said.

“In prevention, [these studies] really changed people’s perceptions about what kind of evidence you need to have before you can invest the time, money, effort, human resources, people’s lives in an intervention study,” he said. “You really need to have good data suggesting that an intervention will be beneficial.”

rachel-tompa

Rachel Tompa is a former staff writer at Fred Hutchinson Cancer Center. She has a Ph.D. in molecular biology from the University of California, San Francisco and a certificate in science writing from the University of California, Santa Cruz. Follow her on Twitter @Rachel_Tompa .

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What exactly is the scientific method and why do so many people get it wrong?

By Peter Ellerton , The University of Queensland

Claims that the “the science isn’t settled ” with regard to climate change are symptomatic of a large body of ignorance about how science works.

So what is the scientific method, and why do so many people, sometimes including those trained in science, get it so wrong?

The first thing to understand is that there is no one method in science, no one way of doing things. This is intimately connected with how we reason in general.

Science and reasoning

Humans have two primary modes of reasoning: deduction and induction. When we reason deductively, we tease out the implications of information already available to us.

For example, if I tell you that Will is between the ages of Cate and Abby, and that Abby is older than Cate, you can deduce that Will must be older than Cate.

That answer was embedded in the problem, you just had to untangle it from what you already knew. This is how Sudoku puzzles work. Deduction is also the reasoning we use in mathematics.

Inductive reasoning goes beyond the information contained in what we already know and can extend our knowledge into new areas. We induce using generalisations and analogies.

Generalisations include observing regularities in nature and imagining they are everywhere uniform – this is, in part, how we create the so-called laws of nature.

Generalisations also create classes of things, such as “mammals” or “electrons”. We also generalise to define aspects of human behaviour, including psychological tendencies and economic trends.

Analogies make claims of similarities between two things, and extend this to make new knowledge.

For example, if I find a fossilised skull of an extinct animal that has sharp teeth, I might wonder what it ate. I look for animals alive today that have sharp teeth and notice they are carnivores.

Reasoning by analogy, I conclude that the animal was also a carnivore.

Using induction and inferring to the best possible explanation consistent with the evidence, science teaches us more about the world than we could simply deduce.

Science and uncertainty

Most of our theories or models are inductive analogies with the world, or parts of it.

If inputs to my particular theory produce outputs that match those of the real world, I consider it a good analogy, and therefore a good theory. If it doesn’t match, then I must reject it, or refine or redesign the theory to make it more analogous.

If I get many results of the same kind over time and space, I might generalise to a conclusion. But no amount of success can prove me right. Each confirming instance only increases my confidence in my idea. As Albert Einstein famously said :

No amount of experimentation can ever prove me right; a single experiment can prove me wrong.

Einstein’s general and special theories of relativity (which are models and therefore analogies of how he thought the universe works) have been supported by experimental evidence many times under many conditions.

We have great confidence in the theories as good descriptions of reality. But they cannot be proved correct, because proof is a creature that belongs to deduction.

The hypothetico-deductive method

Science also works deductively through the hypothetico-deductive method.

It goes like this. I have a hypothesis or model that predicts that X will occur under certain experimental conditions. Experimentally, X does not occur under those conditions. I can deduce, therefore, that the theory is flawed (assuming, of course, we trust the experimental conditions that produced not-X).

Under these conditions, I have proved that my hypothesis or model is incorrect (or at least incomplete). I reasoned deductively to do so.

But if X does occur, that does not mean I am correct, it just means that the experiment did not show my idea to be false. I now have increased confidence that I am correct, but I can’t be sure.

If one day experimental evidence that was beyond doubt was to go against Einstein’s predictions, we could deductively prove, through the hypothetico-deductive method, that his theories are incorrect or incomplete. But no number of confirming instances can prove he is right.

That an idea can be tested by experiment, that there can be experimental outcomes (in principle) that show the idea is incorrect, is what makes it a scientific one, at least according to the philosopher of science Karl Popper .

As an example of an untestable, and hence unscientific position, take that held by Australian climate denialist and One Nation Senator Malcolm Roberts . Roberts maintains there is no empirical evidence of human-induced climate change.

When presented with authoritative evidence during an episode of the ABC’S Q&A television debating show recently, he claimed that the evidence was corrupted .

Yet his claim that human-induced climate change is not occurring cannot be put to the test as he would not accept any data showing him wrong. He is therefore not acting scientifically. He is indulging in pseudoscience .

Settled does not mean proved

One of the great errors in the public understanding of science is to equate settled with proved. While Einstein’s theories are “settled”, they are not proved. But to plan for them not to work would be utter folly.

As the philosopher John Dewey pointed out in his book Logic: The Theory of Inquiry :

In scientific inquiry, the criterion of what is taken to be settled, or to be knowledge, is [of the science] being so settled that it is available as a resource in further inquiry; not being settled in such a way as not to be subject to revision in further inquiry.

Those who demand the science be “settled” before we take action are seeking deductive certainty where we are working inductively. And there are other sources of confusion.

One is that simple statements about cause and effect are rare since nature is complex. For example, a theory might predict that X will cause Y, but that Y will be mitigated by the presence of Z and not occur at all if Q is above a critical level. To reduce this to the simple statement “X causes Y” is naive.

Another is that even though some broad ideas may be settled, the details remain a source of lively debate. For example, that evolution has occurred is certainly settled by any rational account. But some details of how natural selection operates are still being fleshed out.

To confuse the details of natural selection with the fact of evolution is highly analogous to quibbles about dates and exact temperatures from modelling and researching climate change when it is very clear that the planet is warming in general.

When our theories are successful at predicting outcomes, and form a web of higher level theories that are themselves successful, we have a strong case for grounding our actions in them.

The mark of intelligence is to progress in an uncertain world and the science of climate change, of human health and of the ecology of our planet has given us orders of magnitude more confidence than we need to act with certitude.

Demanding deductive certainty before committing to action does not make us strong, it paralyses us.

Peter Ellerton , Lecturer in Critical Thinking, The University of Queensland

This article was originally published on The Conversation . Read the original article .

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Reject the Null or Accept the Alternative? Semantics of Statistical Hypothesis Testing

If you are conducting a quantitative study for your dissertation, it is likely you have created a set of hypotheses to accompany your research questions. It is also likely that you have constructed your hypotheses in the “null/alternative” format. In this format, each research question has both a null hypothesis and an alternative hypothesis associated with it.

Let’s say, for example, that you were conducting a study with the following research question: “is there a difference in the IQs of arts majors and science majors?” The null hypothesis would state that there is no difference between the variables that you are testing (e.g., “there is no difference in the IQs of arts majors and science majors”). The alternative hypothesis would state that there is a difference (e.g., “there is a difference in the IQs of arts majors and science majors”). Typically, the researcher constructs these hypotheses with the expectation (based on the literature and theories in their field of study) that their findings will contradict the null hypothesis, and in turn support the alternative hypothesis. For instance, in our IQ example we may expect to see a difference between arts majors and science majors. Generally, it is difficult to justify conducting a study if you have no reason to believe that differences or relationships exist between your variables. Thus, studies are set up to provide evidence that the null hypothesis is “wrong,” and that the alternative hypothesis is “correct.”

Discover How We Assist to Edit Your Dissertation Chapters

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Setting up the null and alternative hypotheses is usually a pretty simple task. However, students often run into trouble when they finish their analysis and must present their results using the “null/alternative” language. Confusion may arise over what words to use and how statements should be phrased. For your dissertation, some of this may come down to your reviewers’ preferences. However, below are some basic guidelines you may follow.

First, let’s assume you ran your analysis and your results were significant (e.g., arts majors and science majors had different IQ levels). In this case, it is generally appropriate to say “the null hypothesis was rejected” because you found evidence against the null hypothesis. This statement is often sufficient, but sometimes reviewers want you to go further and also make a statement about the alternative hypothesis. In this case, you could say “the alternative hypothesis was supported.” Personally, I would avoid saying “the alternative hypothesis was accepted ” because this implies that you have proven the alternative hypothesis to be true. Generally, one study cannot “prove” anything, but it can provide evidence for (or against) a hypothesis. Additionally, the concept of challenging or “falsifying” a hypothesis is stronger than “proving” a hypothesis (for more in-depth discussion on this philosophy of science see Popper, 1959). Again, it is worth noting that your reviewers may have different preferences on the exact language to use here.

Now let’s consider the flip side and assume your results were not significant (e.g., there was no significant difference in IQ between arts majors and science majors). Here you could say “the null hypothesis was not rejected” or “failed to reject the null hypothesis” because you did not find evidence against the null hypothesis. You should NOT say “the null hypothesis was accepted .” Your study is not designed to “prove” the null hypothesis (or the alternative hypothesis, for that matter). Rather, your study is designed to challenge or “reject” the null hypothesis. People often compare this idea in statistical hypothesis testing to how verdicts are made in criminal court cases. If the prosecution does not have strong enough evidence that the defendant committed the crime, the defendant is judged as “not guilty” rather than as “innocent.” In other words, the court can provide evidence of guilt, but it cannot prove innocence. In the same way, a statistical test cannot prove the null hypothesis, but it can provide evidence against it. As for the alternative hypothesis, it may be appropriate to say “the alternative hypothesis was not supported” but you should avoid saying “the alternative hypothesis was rejected .” Once again, this is because your study is designed to reject the null hypothesis, not to reject the alternative hypothesis.

These are just some general tips to help guide the writing of your statistical findings. However, always defer to the requirements of your reviewers and your school when in doubt.

Popper, K. (1959). The logic of scientific discovery . London: Hutchinson.

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Understanding Science

How science REALLY works...

• Understanding Science 101
• Misconceptions
• Testing ideas with evidence from the natural world is at the core of science.
• Scientific testing involves figuring out what we would  expect  to observe if an idea were correct and comparing that expectation to what we  actually  observe.
• Scientific arguments are built from an idea and the evidence relevant to that idea.
• Scientific arguments can be built in any order. Sometimes a scientific idea precedes any evidence relevant to it, and other times the evidence helps inspire the idea.

Misconception:  Science proves ideas.

Misconception:  Science can only disprove ideas.

Correction:  Science neither proves nor disproves. It accepts or rejects ideas based on supporting and refuting evidence, but may revise those conclusions if warranted by new evidence or perspectives.  Read more about it.

The core of science: Relating evidence and ideas

In this case, the term  argument  refers not to a disagreement between two people, but to an evidence-based line of reasoning — so scientific arguments are more like the closing argument in a court case (a logical description of what we think and why we think it) than they are like the fights you may have had with siblings. Scientific arguments involve three components: the idea (a  hypothesis  or theory), the  expectations  generated by that idea (frequently called predictions), and the actual observations relevant to those expectations (the evidence). These components are always related in the same logical way:

• What would we expect to see if this idea were true (i.e., what is our expected observation)?
• What do we actually observe?
• Do our expectations match our observations?

PREDICTIONS OR EXPECTATIONS?

When scientists describe their arguments, they frequently talk about their expectations in terms of what a hypothesis or theory predicts: “If it were the case that smoking causes lung cancer, then we’d  predict  that countries with higher rates of smoking would have higher rates of lung cancer.” At first, it might seem confusing to talk about a prediction that doesn’t deal with the future, but that refers to something going on right now or that may have already happened. In fact, this is just another way of discussing the expectations that the hypothesis or theory generates. So when a scientist talks about the  predicted  rates of lung cancer, he or she really means something like “the rates that we’d expect to see if our hypothesis were correct.”

If the idea generates expectations that hold true (are actually observed), then the idea is more likely to be accurate. If the idea generates expectations that don’t hold true (are not observed), then we are less likely to  accept  the idea. For example, consider the idea that cells are the building blocks of life. If that idea were true, we’d expect to see cells in all kinds of living tissues observed under a microscope — that’s our expected observation. In fact, we do observe this (our actual observation), so evidence supports the idea that living things are built from cells.

Though the structure of this argument is consistent (hypothesis, then expectation, then actual observation), its pieces may be assembled in different orders. For example, the first observations of cells were made in the 1600s, but cell theory was not postulated until 200 years later — so in this case, the evidence actually helped inspire the idea. Whether the idea comes first or the evidence comes first, the logic relating them remains the same.

Here, we’ll explore scientific arguments and how to build them. You can investigate:

Putting the pieces together: The hard work of building arguments

• Predicting the past
• Arguments with legs to stand on

Or just click the  Next  button to dive right in!

• Take a sidetrip
• Teaching resources

Scientific arguments rely on testable ideas. To learn what makes an idea testable, review our  Science Checklist .

• Forming hypotheses — scientific explanations — can be difficult for students. It is often easier for students to generate an expectation (what they think will happen or what they expect to observe) based on prior experience than to formulate a potential explanation for that phenomena. You can help students go beyond expectations to generate real, explanatory hypotheses by providing sentence stems for them to fill in: “I expect to observe A because B.” Once students have filled in this sentence you can explain that B is a hypothesis and A is the expectation generated by that hypothesis.
• You can help students learn to distinguish between hypotheses and the expectations generated by them by regularly asking students to analyze lecture material, text, or video. Students should try to figure out which aspects of the content were hypotheses and which were expectations.

Summing up the process

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How we edit science part 1: the scientific method

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We take science seriously at The Conversation and we work hard to report it accurately. This series of five posts is adapted from an internal presentation on how to understand and edit science by our Australian Science & Technology Editor, Tim Dean. We thought you might also find it useful.

Introduction

If I told you that science was a truth-seeking endeavour that uses a single robust method to prove scientific facts about the world, steadily and inexorably driving towards objective truth, would you believe me?

Many would. But you shouldn’t.

The public perception of science is often at odds with how science actually works. Science is often seen to be a separate domain of knowledge, framed to be superior to other forms of knowledge by virtue of its objectivity, which is sometimes referred to as it having a “ view from nowhere ”.

But science is actually far messier than this - and far more interesting. It is not without its limitations and flaws, but it’s still the most effective tool we have to understand the workings of the natural world around us.

In order to report or edit science effectively - or to consume it as a reader - it’s important to understand what science is, how the scientific method (or methods) work, and also some of the common pitfalls in practising science and interpreting its results.

This guide will give a short overview of what science is and how it works, with a more detailed treatment of both these topics in the final post in the series.

What is science?

Science is special, not because it claims to provide us with access to the truth, but because it admits it can’t provide truth .

Other means of producing knowledge, such as pure reason, intuition or revelation, might be appealing because they give the impression of certainty , but when this knowledge is applied to make predictions about the world around us, reality often finds them wanting.

Rather, science consists of a bunch of methods that enable us to accumulate evidence to test our ideas about how the world is, and why it works the way it does. Science works precisely because it enables us to make predictions that are borne out by experience.

Science is not a body of knowledge. Facts are facts, it’s just that some are known with a higher degree of certainty than others. What we often call “scientific facts” are just facts that are backed by the rigours of the scientific method, but they are not intrinsically different from other facts about the world.

What makes science so powerful is that it’s intensely self-critical. In order for a hypothesis to pass muster and enter a textbook, it must survive a battery of tests designed specifically to show that it could be wrong. If it passes, it has cleared a high bar.

The scientific method(s)

Despite what some philosophers have stated , there is a method for conducting science. In fact, there are many. And not all revolve around performing experiments.

One method involves simple observation, description and classification, such as in taxonomy. (Some physicists look down on this – and every other – kind of science, but they’re only greasing a slippery slope .)

However, when most of us think of The Scientific Method, we’re thinking of a particular kind of experimental method for testing hypotheses.

This begins with observing phenomena in the world around us, and then moves on to positing hypotheses for why those phenomena happen the way they do. A hypothesis is just an explanation, usually in the form of a causal mechanism: X causes Y. An example would be: gravitation causes the ball to fall back to the ground.

A scientific theory is just a collection of well-tested hypotheses that hang together to explain a great deal of stuff.

Crucially, a scientific hypothesis needs to be testable and falsifiable .

An untestable hypothesis would be something like “the ball falls to the ground because mischievous invisible unicorns want it to”. If these unicorns are not detectable by any scientific instrument, then the hypothesis that they’re responsible for gravity is not scientific.

An unfalsifiable hypothesis is one where no amount of testing can prove it wrong. An example might be the psychic who claims the experiment to test their powers of ESP failed because the scientific instruments were interfering with their abilities.

(Caveat: there are some hypotheses that are untestable because we choose not to test them. That doesn’t make them unscientific in principle, it’s just that they’ve been denied by an ethics committee or other regulation.)

Experimentation

There are often many hypotheses that could explain any particular phenomenon. Does the rock fall to the ground because an invisible force pulls on the rock? Or is it because the mass of the Earth warps spacetime , and the rock follows the lowest-energy path, thus colliding with the ground? Or is it that all substances have a natural tendency to fall towards the centre of the Universe , which happens to be at the centre of the Earth?

The trick is figuring out which hypothesis is the right one. That’s where experimentation comes in.

A scientist will take their hypothesis and use that to make a prediction, and they will construct an experiment to see if that prediction holds. But any observation that confirms one hypothesis will likely confirm several others as well. If I lift and drop a rock, it supports all three of the hypotheses on gravity above.

Furthermore, you can keep accumulating evidence to confirm a hypothesis, and it will never prove it to be absolutely true. This is because you can’t rule out the possibility of another similar hypothesis being correct, or of making some new observation that shows your hypothesis to be false. But if one day you drop a rock and it shoots off into space, that ought to cast doubt on all of the above hypotheses.

So while you can never prove a hypothesis true simply by making more confirmatory observations, you only one need one solid contrary observation to prove a hypothesis false. This notion is at the core of the hypothetico-deductive model of science.

This is why a great deal of science is focused on testing hypotheses, pushing them to their limits and attempting to break them through experimentation. If the hypothesis survives repeated testing, our confidence in it grows.

So even crazy-sounding theories like general relativity and quantum mechanics can become well accepted, because both enable very precise predictions, and these have been exhaustively tested and come through unscathed.

The next post will cover hypothesis testing in greater detail.

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Why can't we accept the null hypothesis, but we can accept the alternative hypothesis?

I understand it's reasonable only to not reject the null hypothesis. But why can we accept the alternative hypothesis?

What's the difference?

• hypothesis-testing

• 5 $\begingroup$ Rejecting the null hypothesis could be written up as accepting the alternative. Many people would rather not say that. Many people would rather focus on confidence intervals! Or something Bayesian. $\endgroup$ –  Nick Cox Commented Aug 31, 2022 at 18:39
• 6 $\begingroup$ Absence of evidence is not evidence of absence! $\endgroup$ –  Ben Commented Aug 31, 2022 at 18:39
• 4 $\begingroup$ @Ben many people would disagree philosophy.stackexchange.com/questions/92546/… $\endgroup$ –  fblundun Commented Aug 31, 2022 at 21:57
• 3 $\begingroup$ I am sorry I don't know which answer to accept because I can't understand any of them. $\endgroup$ –  user900476 Commented Sep 1, 2022 at 13:31
• 3 $\begingroup$ @user900476 You are in no way obliged to accept any answer as long as none is satisfactory. stackoverflow.com/help/someone-answers You may, however, consider clarifying what would define a better answer. $\endgroup$ –  Bernhard Commented Sep 2, 2022 at 9:25

7 Answers 7

I'll start with a quote for context and to point to a helpful resource that might have an answer for the OP. It's from V. Amrhein, S. Greenland, and B. McShane. Scientists rise up against statistical significance. Nature , 567:305–307, 2019. https://doi.org/10.1038/d41586-019-00857-9

We must learn to embrace uncertainty.

I understand it to mean that there is no need to state that we reject a hypothesis , accept a hypothesis , or don't reject a hypothesis to explain what we've learned from a statistical analysis. The accept/reject language implies certainty; statistics is better at quantifying uncertainty.

Note : I assume the question refers to making a binary reject/accept choice dictated by the significance (P ≤ 0.05) or non-significance (P > 0.05) of a p-value P.

The simplest way to understand hypothesis testing (NHST) — at least for me — is to keep in mind that p-values are probabilities about the data (not about the null and alternative hypotheses): Large p-value means that the data is consistent with the null hypothesis, small p-value means that the data is inconsistent with the null hypothesis. NHST doesn't tell us what hypothesis to reject and/or accept so that we have 100% certainty in our decision: hypothesis testing doesn't prove anything ٭ . The reason is that a p-value is computed by assuming the null hypothesis is true [3].

So rather than wondering if, on calculating P ≤ 0.05, it's correct to declare that you "reject the null hypothesis" (technically correct) or "accept the alternative hypothesis" (technically incorrect), don't make a reject/don't reject determination but report what you've learned from the data: report the p-value or, better yet, your estimate of the quantity of interest and its standard error or confidence interval.

٭ Probability ≠ proof. For illustration, see this story about a small p-value at CERN leading scientists to announce they might have discovered a brand new force of nature: New physics at the Large Hadron Collider? Scientists are excited, but it’s too soon to be sure . Includes a bonus explanation of p-values.

[1] S. Goodman. A dirty dozen: Twelve p-value misconceptions. Seminars in Hematology , 45(3):135–140, 2008. https://doi.org/10.1053/j.seminhematol.2008.04.003

All twelve misconceptions are important to study, understand and avoid. But Misconception #12 is particularly relevant to this question: It's not the case that A scientific conclusion or treatment policy should be based on whether or not the P value is significant.

Steven Goodman explains: "This misconception (...) is equivalent to saying that the magnitude of effect is not relevant, that only evidence relevant to a scientific conclusion is in the experiment at hand, and that both beliefs and actions flow directly from the statistical results."

[2] Using p-values to test a hypothesis in Improving Your Statistical Inferences by Daniël Lakens.

This is my favorite explanation of p-values, their history, theory and misapplications. Has lots of examples from the social sciences.

[3] What is the meaning of p values and t values in statistical tests?

• 1 $\begingroup$ @whuber When did p-values and frequentist statistics started conditioning on the data? If we want to condition on the data, then we goes Bayesian. But I'll edit with my answer with some pointers to papers. $\endgroup$ –  dipetkov Commented Aug 31, 2022 at 19:41
• 2 $\begingroup$ I did not mean "condition" in the sense of assuming a probability distribution for the parameters; only that we are, of course, not making decisions about the hypotheses in vacuo but are basing them on the data. What you write here appears to fly in the face of all the literature on hypothesis testing. Why, after all, would anyone even bother if it weren't for the prospect that the test could tell us something about the state of nature? $\endgroup$ –  whuber ♦ Commented Aug 31, 2022 at 19:45
• 3 $\begingroup$ I haven't complained about any imprecision. As you are gently hinting, I have been imprecise in these comments myself. My original concern what that your statements about interpreting NHSTs looked wrong. $\endgroup$ –  whuber ♦ Commented Aug 31, 2022 at 21:23
• 3 $\begingroup$ For continuous data the probability of observed what we observed is zero, so the P-value is the probability of observing something more extreme than our observed data. So the above answer needs to be more nuanced. $\endgroup$ –  Frank Harrell Commented Sep 1, 2022 at 15:42
• 2 $\begingroup$ What does 'et al.' mean? Could you change that into simple English to make your answer less intimidating. $\endgroup$ –  Sextus Empiricus Commented Sep 1, 2022 at 20:13

Say you have the hypothesis

"on stackexchange there is not yet an answer to my question"

When you randomly sample 1000 questions then you might find zero answers. Based on this, can you 'accept' the null hypothesis?

You can read about this among many older questions and answers, for instance:

• Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?
• Why do we need alternative hypothesis?
• Is it possible to accept the alternative hypothesis?

Also check out the questions about two one-sided tests (TOST) which is about formulating the statement behind a null hypothesis in a way such that it can be a statement that you can potentially 'accept'.

More seriously, a problem with the question is that it is unclear. What does 'accept' actually mean?

And also, it is a loaded question . It asks for something that is not true. Like 'why is it that the earth is flat, but the moon is round?' .

There is no 'acceptance' of an alternative theory. Or at least, when we 'accept' some alternative hypothesis then either:

• Hypothesis testing: the alternative theory is extremely broad and reads as 'something else than the null hypothesis is true'. Whatever this 'something else' means, that is left open. There is no 'acceptance' of a particular theory. See also: https://en.m.wikipedia.org/wiki/Falsifiability
• Expression of significance: or 'acceptance' means that we observed an effect, and consider it as a 'significant' effect. There is no literal 'acceptance' of some theory/hypothesis here. There is just the consideration that we found that the data shows there is some effect and it is significantly different from a case when to there would be zero effect. Whether this means that the alternative theory should be accepted, that is not explicitly stated and should also not be assumed implicitly. The alternative hypothesis (related to the effect) works for the present data, but that is different from being accepted, (it just has not been rejected yet).

In addition to the answers given by highly experienced users here, I'd like to offer a less formal and hopefully more intuitive view.

Briefly, the " null hypothesis " is considered accepted, unless there is some compelling evidence to reject it in favour of an alternative.

It helps to look at it from the decision-making perspective. Tests---not only statistical---help us make decisions. Before performing the test, we have one course of action. After performing the test, we may either keep the course or change it, depending on the test result. The null hypothesis is the default course of action, given no or not enough information.

For example, imagine you are a flying an aeroplane. Without a reason to do otherwise, you'll probably fly it straight towards your destination. But, the whole time you'd be performing "tests", like checking your radar whether there is some unexpected obstacle on your path. If the radar shows no obstacle, you'll keep your course. This is the default decision, which you'd most likely make even if you had to fly without a radar. I mean, what else could you do? Wildly zigzag through the sky?

In this analogy, the null hypothesis is that there is no reason to change the course. You don't "accept" it as a result of the test, because it has already been accepted before you took a look at the radar. Only if you discover an obstacle, you'd reject it in favour of changing the course.

Or, as a more real-world example, imagine developing a new drug for a disease. The default status, before you perform any trials at all, is that the drug is not approved . You may run in vitro , in vivo , and clinical trials to prove that your drug is safe and helpful. If that fails, the drug remains "not approved". Again, there is nothing to " accept ", or at least nothing with practical consequences. Only with compelling evidence of the drug's usefulness its status can change to "approved".

As you can see from the examples, which hypothesis is treated as " null " is somewhat subjective. For example, is "homeopathy works" null , or does it need evidence to be accepted? That depends on your prior beliefs and experience. If you grew up in a homeopathic home, you are likely to consider it to work by default and would't change your mind unless you see strong evidence against it (or maybe ever). But, this can get arbitrarily philosophical / psychological.

• 1 $\begingroup$ (+1: " answers given by highly experienced users " you aren't exacllty a spring chicken on this website yourself...) $\endgroup$ –  usεr11852 Commented Sep 2, 2022 at 14:52
• $\begingroup$ Your plane example seems to have little to do with hypothesis testing and much to do with estimation and optimization. Can you explain how rejecting the null hypothesis of "flying straight" points out the direction in which to fly instead? $\endgroup$ –  dipetkov Commented Sep 2, 2022 at 20:09
• $\begingroup$ @dipetkov It doesn't, much like many statistical tests - think of a two-sided t-test. The direction then needs to be decided based on further information. But, if we failed to reject the null hypothesis, we wouldn't bother collecting further information. $\endgroup$ –  Igor F. Commented Sep 8, 2022 at 7:55
• $\begingroup$ Hm. While in a plane in the middle of the sky? I'll probably bother collecting further information. By the way, I like your example because it illustrates (it seems to me) that usually we'd like to learn more than what NHST can give us. $\endgroup$ –  dipetkov Commented Sep 8, 2022 at 8:29
• $\begingroup$ Furthermore, "wouldn't bother collecting further information" means that you've accepted the null hypothesis. Not rejecting the null hypothesis means that you acknowledge other hypotheses are still in play. That would correspond to "keep going straight for now while collecting further information". In practice the more natural formulation is to ask: "What's the optimal direction to be flying in right now?" $\endgroup$ –  dipetkov Commented Sep 8, 2022 at 9:54

We should not accept the research/alternative hypothesis.

The main value of a null hypothesis statistical test is to help the researcher adopt a degree of self-skepticism about their research hypothesis. The null hypothesis is the hypothesis we need to nullify in order to proceed with promulgation of our research hypothesis. It doesn't mean the alternative hypothesis is right, just that it hasn't failed a test - we have managed to get over a (usually fairly low) hurdle, nothing more. I view this a little like naive falsificationism - we can't prove a theory, only disprove it†, so all we can say is that a theory has survived an attempt to refute it. IIRC Popper says that the test "corroborates" a theory, but this is a long way short of showing it is true (or accepting it).

A good example of this is the classic XKCD cartoon (see this question ):

Is it reasonable for the frequentist to "accept" the alternative hypothesis that the sun has gone nova? No!!! In this case, the most obvious reason is that the analysis doesn't consider the prior probabilities of the two hypotheses, which a frequentist would do by setting a much more stringent significance level. But also there may be explanations for the neutrinos that have nothing to do with the sun going nova (perhaps I have just come back from a visit to the Cretaceous to see the dinosaurs, and you've detected my return to this timeline). So rejecting the null hypothesis doesn't mean the alternative hypothesis is true.

A frequentist analysis fundamentally cannot assign a probability to the truth of a hypothesis, so it doesn't give much of a basis for accepting it. The "we reject the null hypothesis" is basically a an incantation in a ritual. It doesn't literally mean that we are discarding the null hypothesis as we are confident that it is false. It is just a convention that we proceed with the alternative hypothesis if we can "reject" the null hypothesis. There is no mathematical requirement that the null hypothesis is wrong. This isn't necessarily a bad thing, it is just best to take it as technical jargon and not read too much into the actual words.

Unfortunately the semantics of Null Hypothesis Statistical Tests are rather subtle, and often not a direct answer to the question we actually want to pose, so I would recommend just saying "we reject the null hypothesis" or "we fail to reject the null hypothesis" and leave it at that. Those that understand the semantics will draw the appropriate conclusion. Those who don't understand the semantics won't be mislead into thinking that the alternative hypothesis has been shown to be true (by accepting it).

† Sadly, we can't really disprove them either .

• 1 $\begingroup$ +1 I think this is the best answer. Hopefully the OP will revisit the question and let us know whether he/she/they understood it. $\endgroup$ –  dipetkov Commented Sep 7, 2022 at 7:22

The answer depends on whether you are using a pre-defined critical value (or p-value threshold like p<0.05) in a hypothesis test that yields a decision (a Neyman–Pearsonian hypothesis test), or whether you are using the magnitude of the actual p-value as an index of the evidence in the data (a [neo-]Fisherian significance test).

If you are doing a hypothesis test then you are working with a set of rules that grant you a pre-set confidence of long-run performance of the test procedure. The way that the rules can give confidence about long-run test performance is by specifying what decision applies depending on the data, and the decision relates to the acceptance or non-acceptance (yes, that is rejection as far as I am concerned) of the null hypothesis. Rejection of the statistical null hypothesis can be thought of as acceptance of another hypothesis, but that other hypothesis can be nothing more than a set of all not-the-null hypotheses that exist within the statistical model. Accepting that not-the-null hypothesis is not very informative and so it is not unreasonable to simply say that the test rejects the null but does not accept anything else.

There is (sometimes) a specific 'alternative' hypothesis specified for a hypothesis test: the hypothetical effect size plugged into the pre-experiment power analysis used to set the sample size. That 'alternative' hypothesis IS NOT tested by the hypothesis test and has very little meaning once the data are available.

If you are doing a significance test then a small p-value implies that the data are inconsistent with the statistical model's expectations regarding probable observations where the null hypothesis is true. The analyst can then use that evidence to make a scientific inference. The scientific inference might well include an interim rejection of the statistical null hypothesis and acceptance of a specific 'alternative' hypothesis of scientific interest. It depends on the information available and the scientific objectives, and it is a process that is very rarely considered in statistical instruction.

See this open access chapter for much more detail: https://link.springer.com/chapter/10.1007/164_2019_286

• $\begingroup$ Thank you for the reference! Could you please clarify this: The "pre-set confidence of long-run performance" is assuming the null hypothesis is true, right? But if there is a possibility the null hypothesis is false, can we really say anything? $\endgroup$ –  Mankka Commented Sep 1, 2022 at 8:27
• $\begingroup$ @Mankka The pre-set confidence is regarding the long run false positive error rate. Can we say anything? Well, within the Neyman–Pearsonian framework you cannot say anything about the particular hypothesis of concern because that framework deals with only the global error rates. The Fisherian significance test does say things about the particular experiment. That's the difference. $\endgroup$ –  Michael Lew Commented Sep 1, 2022 at 20:04

Within the Bayesian framework you can "accept the null hypothesis" in the sense that the posterior probability of a point null hypothesis can tend to one with increasing sample size. This requires that the null hypothesis is exactly true and that you're willing to represent this in your prior by a point mass. Lindley (1957, p. 188) gives two examples where this is arguably reasonable: testing for linkage in genetics, and testing someone for telepathic powers. In addition, your prior on the parameter of interest must be proper under the alternative hypothesis. See for example this answer .

"Absence of evidence is not evidence of absence." Carl Sagan.

The null hypothesis specifies no effect, that is absence of effect. You reject the null if the results are statistically significant, that is, when you have evidence for rejecting the null. If the results are not statistically significant, what you have is absence of evidence.

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What Is a Hypothesis and How Do I Write One?

General Education

Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

• Defining the term “hypothesis” 
• Providing hypothesis examples 
• Giving you tips for how to write your own hypothesis

So let’s get started!

What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Asking questions
• Forming a hypothesis
• Analyze the data
• Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party. 
• If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

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Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Can you ever prove that a hypothesis is correct?

Table of Contents

• 1 Can you ever prove that a hypothesis is correct?
• 2 What is the conclusion of hypothesis?
• 3 What does it take to prove a hypothesis?
• 4 How to prove or disprove a hypothesis?

In science, you can never prove your hypothesis. You can only prove your hypothesis to be wrong. This is also true of any scientific theory.

What is the conclusion of hypothesis?

The conclusion is the final decision of the hypothesis test. The conclusion must always be clearly stated, communicating the decision based on the components of the test. It is important to realize that we never prove or accept the null hypothesis.

Why can we never prove that a hypothesis is true?

What does it take to prove a hypothesis?

How to prove or disprove a hypothesis.

• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test.
• Decide whether the null hypothesis is supported or refuted.
• Present the findings in your results and discussion section.

Can data prove a hypothesis to be true?

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