types of probability in critical thinking

Pursuing Truth: A Guide to Critical Thinking

Chapter 10 probability.

Students tend to find these two chapters on probability the most difficult material in the course. It looks hard, but it’s really not as complicated as it looks. It is important to understand how probabilities work in order to reason well. We rarely have conclusive evidence for or against any claim. Imagine that you’re on a jury trial, you have been tasked with determining the probability of the defendant’s guilt given the evidence. To do this well requires that a person have a basic understanding of how probability works.

Given the example about serving on a jury, it’s more than a little disturbing that our intuitions about probabilities are extremely flawed. Here’s a classic example called the Monty Hall Problem: In the game show Let’s Make a Deal , the host, Monty Hall, would select a person to play for the big prize. The contestant would have a choice of three doors. After choosing a door, the host, who knows which door the prize is behind, would open one of the other doors and show the contestant that that door did not reveal the prize. The contestant would then be offered the choice to stick with his original choice or to switch to the third door.

So, you are the contestant. You choose door number 1. Let’s say that Monty opens door 2 and shows you that it has nothing behind it. What should you do? Stick with 1 or switch to 3? You should do what will increase the probability of your winning. Which has the higher probability? Most people will answer that, since there are only two doors, neither has a higher probability than the other. So, the common answer goes, the odds of your winning are simply 50/50.

The correct answer, though, is that you should switch. If you switch, the probability of winning doubles. Is this intuitive? Absolutely not.

10.1 Calculating Probabilities

First, a few preliminaries. Probabilities are numbers between 0 and 1. Unfortunately, it will be necessary to be able to add, multiply, and divide fractions. If you can’t remember how, look at the review in section 13.6 of the text.

We won’t worry about the morality of gambling, but it’s easiest to learn basic probability in the context of cards, dice, and coin tosses. Basic probability questions are often about cards and dice. So, a few facts to keep in mind:

• Each die has six sides.
• A standard deck of cards has 52 cards, divided into 4 suits (clubs, diamonds, hearts, and spades). Each suit has an Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. We’ll never have Jokers in our imaginary decks.
• \(\Pr(S) = n\) means that the probability that the sentence S is true is equal to n.
• Probabilities range from zero to one, inclusive. The answer to a probability problem will never be less than zero nor greater than one.

10.2 Calculating Simple Events

Examples of simple events include tossing heads with one toss of a single coin, getting a six with a roll of a single die, and drawing a heart on one draw from a standard deck of cards. The rule for calculating the probability of a simple event is this:

\[ \Pr(A)=\frac{\textrm{favorable outcomes}}{\textrm{total possible outcomes}} \]

That’s easy enough. We just have to determine how many possible ways this scenario could work out, and how many of those ways get us the outcome that we’re looking for.

10.2.1 Examples

What is the probability of tossing heads with a single coin? If we toss a coin once, there are only two possible outcomes (to keep things simple, we rule out the very, very slim possibility that it lands and stays on edge). Of those two outcomes. only one is heads. So, the probability of tossing heads is equal to 1/2. In probability notation, \(\Pr(H) = 1/2\)

What is the probability of rolling two on one roll with a single die? There are six possible outcomes, only one is a two. \(\Pr(2) = 1/6\)

What is the probability of drawing the Ace of Spades on one draw from a deck of cards? There is one favorable outcome out of 52 total possible: \(\Pr(A\spadesuit) = 1/52\)

What is the probability of drawing an Ace on a single draw? Now there are four favorable outcomes in the 52 total possible: \(\Pr(A) = 4/52 = 1/13\)

What is the probability of drawing a Heart on a single draw? Since there are thirteen Hearts, there are 13 favorable outcomes, but still only 52 cards. \(\Pr(A) = 13/52 = 1/4\)

10.3 Calculating Complex Events

Complex probabilities are probabilities of negations, conjunctions, or disjunctions. A negation is a “not” sentence. The sentence “I will not go to the movies tonight” is the negation of the sentence “I will go to the movies tonight.” A conjunction is an “and” sentence. An example is the sentence “I will go to dinner and I will go to the movies.” A disjunction is an “or” sentence, as in “I will go to dinner or I will go to the movies.” Unless specified otherwise, disjunctions are always inclusive disjunctions. So, “I will go to dinner or I will go to the movies” means that I will do one, or the other, or both.

There are also some symbols that you need to know. “Not” is symbolized by “ \(\neg\) ” and “and” is symbolized by “&”

• The probability of \(\neg P\) is the probability that P is not true.
• The probability of \(P\&Q\) is the probability that both P and Q are true.
• The probablity of \(P \textrm{ or } Q\) the probability that either P or Q or both are true.

10.3.1 Necessities and Impossibilities

\[ \textrm{If S cannot be true, then} \Pr(S) = 0 \]

\[ \textrm{If S must be true, then} \Pr(S) = 1 \]

What is the probability of rolling a 7 with one die? Since it is impossible to roll more than a six with one die, \(\Pr(7) = 0\) .

What is the probability of rolling at least a 1 with one die? No matter what you roll, you will get at least a 1, so \(\Pr (\textrm{at least 1}) = 1\) .

10.3.2 Negations

Now, let’s pause and think for a moment. Remember that the probability of an event that must occur is equal to one. For any event, it must be the case that some outcome occurs. For example, if you toss a coin, you have to get either heads or tails. So, if you add up the probabilities of all the possible outcomes for an event, they have to add up to 1. Now, let’s imagine an event that has three possible outcomes, A, B, and C. By our reasoning, \(\Pr(A) + \Pr(B) + \Pr(C) = 1\) . That is, we can think of the probability of an event as represented by a big pie. Each possible outcome is a piece of the pie. The size of the whole pie is 1, so when we add up the areas of each the pieces, they have to total 1. Now, let’s I want to know the probability of \(\neg A\) . The probability of A is just the size of A in the pie. The probability of \(\neg A\) then is the size of the remainder of the pie, once we take out A. Since the size of all of the pieces add up to 1, the probability of A not occuring is equal to \(1 - \Pr(A)\) . Thus, we get the negation rule:

\[ \Pr(\neg S) = 1-\Pr(S) \] For example, what is the probability of not rolling a 6 on one roll of a die? It must be equal to 1 minus the probability of rolling a six. Since there a six sides, the probability of rolling a six equals 1/6. So, \(\Pr(\neg 6) = 1 - 1/6 = 5/6\)

What is the probability of not drawing the King of Hearts? \(1 - Pr(K\heartsuit) = 1 − 1/52 = 51/52\)

10.3.3 Compatibility

Two statements are compatible if they can both be true, and two events are compatible if they can both occur. There are certain events such that one’s occurring automatically rules out the other’s occurring. For example, if I get heads on one coin toss, that means that I didn’t get tails. There’s no way for both of those to occur on the same toss. They are incompatible events. Other events are compatible. Let’s say I draw one card from a deck. Can I get both a King and a Heart? Yes, if I get the King of Hearts. So, getting a King and getting a Heart on the same draw are compatible events.

So, compatible or incompatible?

• Tossing heads on one coin toss and tossing tails on the same toss. Incompatible
• Tossing heads on one toss and tossing tails on the next. Compatible.
• Drawing the ace of spades on both of two draws, if
• The first card is put back into the deck (with replacement). Compatible
• The first card is not put back into the deck (without replacement). Incompatible

10.3.4 Incompatible Disjunctions

If A and B are incompatible, then \(\Pr(A \textrm{ or } B) = \Pr(A) + \Pr(B)\)

What is the probability of getting either heads or tails on one coin toss? The two events are incompatible, you can’t get both, so \(\Pr(H \textrm{ or } T) = \Pr(H) + \Pr(T) = 1/2 + 1/2 = 1\) . Of course it equals one, since you must get one or the other.

What is the probability of getting either a king or a queen on one draw from a deck? They are incompatible, you can’t get both, so \(\Pr(K \textrm{ or } Q) = \Pr(K) + \Pr(Q) = 1/13 +1/13 = 2/13\) .

What is the probability of getting the Ace of Spades or a heart on one draw? Incompatible, so \(\Pr(A\spadesuit \textrm{ or } \heartsuit) = \Pr(A\spadesuit) + \Pr(\heartsuit) = 1/52 + 13/52 = 14/52 = 7/26\) .

10.3.5 Compatible Disjunctions

What about compatible events? First, let’s see why that formula will not work. What is the probability of getting heads at least once on two coin tosses? If we use the formula for incompatible events, we have \(\Pr (H1 \textrm{ or } H2) = \Pr(H1) + \Pr (H2) = 1/2 + 1/2 = 1\) . This cannot be right! Why not? If it has a probability of one, it must occur, but we know it’s possible to get tails on both tosses. In fact, we know the answer should be 3/4. (I’ll let you figure out why. Think in terms of favorable and total possible.)

So what went wrong with the formula? Essentially, we counted the same thing twice. If we toss a coin twice, there are four possible outcomes: HH, HT, TH, and TT. Out of those, there are two ways to get H on toss 1 and two ways to get H on toss 2. Adding those, it looks like we have four favorable outcomes. The problem is that we have counted one of those favorable outcomes (HH) twice, so we need to #tract one of them.

That gives us the rule for compatible disjunctions:

\[ \textrm{If A and B are compatible, then } \Pr (A \textrm{ or } B) = \Pr(A) + \Pr(B) − \Pr(A \& B) \]

The problem now is that \(\Pr(A \& B)\) is the probability of a conjunction. So, before we can calculate compatible disjunctions, we need to learn to calculate the probabilities of conjunctions.

10.3.6 Independent Conjunctions

To calculate disjunctions, we have to determine whether they are compatible or incompatible. For conjunctions, we’re concerned about dependence and independence. Two statements are independent if the truth value of one has no bearing on the truth value of the other. Two events are independent if the occurrence of one has no bearing on the truth value of the other.

For example, tossing heads on one toss and tossing tails on the same toss are dependent events. If the first happens, the probability of the second becomes zero. Tossing heads on one toss and then tossing tails on the next toss are independent events. he second has a probability of 1/2 whether the first occurs or not. Card draws are independent if you put the cards back as you draw them (called with replacement). Card draws are dependent if the cards are not placed back in the deck (without replacement).

\[ \textrm{If A and B are independent, then } \Pr(A \& B) = \Pr(A) \times \Pr(B) \]

Here are some examples. What is the probability of getting heads on two consecutive tosses? That means getting heads on the first toss and heads on the second toss. The two are independent events, so \(\Pr(H1 \& H2) = \Pr(H1) \times \Pr(H2) = 1/2 \times 1/2 = 1/4\) .

What’s the probability of getting a king on two consecutive draws with replacement? Again, these are independent events. \(\Pr(K1 \& K2) = \Pr(K1) \times \Pr(K2) =1/13 \times 1/13 = 1/169\) .

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10.7: Decision Making and Probability

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• Jim Marteney
• Los Angeles Valley College via ASCCC Open Educational Resources Initiative (OERI)

Other than a reflex reaction, human decision-making is not some random act. We make decisions based on the probabilities of the outcome. The following three quotes provide an overall view of how probability affects our decision-making.

Probability is associated with a high degree of likelihood that a conclusion is valid. In critical thinking, probability is how likely a target audience believes something will become reality .

--Austin J. Freeley Argumentation and Debate 1

At any given moment, we make our estimate of probabilities on the basis of the evidence available to us at that time. And, we can never reach more than a highly probable conclusion, for ALL the facts can never be known.

--Lionel Ruby and Robert Yarber The Art of Making Sense 1978 2

People make decisions! To be sure, people sometimes make stupid, uninformed decision. They make highly informed decisions that sometimes turn out badly. They can learn to do a better job of making decisions.

--Richard Reike and Malcom Sillars Argumentation and Decision-Making Process 3

All three of these quotes refer to the key idea that we make decisions based on the probability of the outcome from the limited information provided. Because of this, we can never be absolutely sure of the outcome of that decision. Therefore, we operate within a range of possibilities that our decision is the correct decision. We look at the probabilities of the outcomes to each decision we make.

No two people will view probability, or the risk involved, the same way. If you are speeding along the highway at 15 miles per hour over the speed limit, what is the probability that you will get a ticket? You might decide that it is only 20% so you continue at that speed. Someone else may decide that 20% is too big a risk to take and slow down. But assume you hear on your navigation app that there may be a police officer up ahead. You believe that the probability of getting a ticket is now closer to 90%. Now you decide to slow down.

Both courts of law and science operate using probability. Neither has to prove their claim, legal charges, or hypothesis with 100% certainty. Both deal in the probability of the decision claim being made. The claim is accepted when the probability reaches the “Threshold” of the person or persons making the decision

• Austin J Freeley, Argumentation and Debate . (Belmont: Wadsworth Publishing Co., 1993)
• Lionel Ruby and Robert Yarber. The Art of Making Sense . (Taipei: Chuang Yuan Publisher, 1978)
• Richard D. Rieke and Malcolm Sillars. Argumentation and Critical Decision Making . (New York: HaperCollins Rhetoric and Society Series, 1993)

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1.3: Truth and Its Role in Argumentation - Certainty, Probability, and Monty Hall

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• Golden West College via NGE Far Press

Only certain sorts of sentences can be used in arguments. We call these sentences propositions , statements or claims .

Statements or claims have the following characteristics:

• They are either true or false.
• They are declarative (that is to say, they are not questions or commands; they are sentences that describe how things are, were, will be, would be, could be or should be.)
• They are clearly written or stated such that there is no ambiguity as to their meaning (i.e. they don’t have two or more highly distinct interpretations, as in sentences like “I saw the waiter with the glasses”) and they are not so vague as to make it impossible to say under what conditions they would be true.
• There are lots of ways for a sentence to fail to be a claim, just as there are a lot of way for a sentence to fail to be a question, or description of a dog, or a command.

Example \(\PageIndex{1}\)

Which of the following are claims:

• All dogs have four legs.
• John F. Kennedy was the 35 th president of the United States.
• Don’t go into Central Park at night.
• Why do people always talk on their cell phones on the J train?
• Barack Obama is very tall.
• There is life on other planets.
• Is a claim. It’s false (there are dogs that have lost a leg, thus three-legged dogs.) The fact that it’s false means that it must be a claim . ONLY claims can be false.
• Is a claim. It’s true. The fact that it’s true means that it must be a claim . ONLY claims can be true.
• Not a claim. It is a command; it is neither true nor false (though it might be good advice.)
• Not a claim. It is a question. Questions are never true or false, though sometimes they imply claims.
• Not a claim. “Very tall” is too vague. We have no standard, agreed upon method for determining if someone is “very tall.” By Danish standards (where the average male height is 5’11”) Obama is probably not “very” tall. By Vietnamese standards (where the average male is 5’4”) Obama might well be considered “very” tall. We could turn this sentence into a claim by changing it to “President Obama is 6’2” tall.”
• This is a claim, but we don’t know if it’s true or not. Still, it’s clearly either true or false, so it must be a claim.

Subjective and Objective claims

Claims are either subjective or objective . These words have a special, technical sense in philosophy. A claim is subjective if it is about thoughts, feelings, or other internal states of the mind. A claim is objective if it is about something that is not dependent on a state of the mind. It’s important to keep in mind that you might have used “subjective” and “objective” differently from this, and like all words these have multiple senses. For our purposes, though, we’ll be using subjective and objective only of claims, because only claims are true or false, and here subjective and objective describe something about the truth conditions for a claim.

Whereas, for example, “I'm itchy,” is a subjective claim. “I feel hot,” “John is tired,” “Anita loves Keyshawn,” “Thomas believes in God,” and “The Black Keys are my favorite band,” are all subjective claims. This is because their truth or falsity depends upon what someone thinks or feels, or, we can say, the truth conditions for these claims are found in someone’s mental content. If I say, “I feel nauseated,” that claim is true if, and only if, I actually have the feeling of nausea, and false if, and only if, I do not have that feeling. So if I’m trying to get out of doing something, I might say “I feel nauseated” when I had no such feeling, that is to say, when the truth condition does not exist.

The following claims are objective: “Dan is six feet tall,” “The Empire state building is made of cheese,” “New York is the largest city in the United States,” and “God exists.” In each of these cases, though I might have a subjective belief about the claim, the actual truth condition is external to my thoughts and feelings.

Note that the second claim is a false objective claim. The Empire State Building is not made of cheese. But the truth or falsity of the claim is independent of what anyone thinks or feels. It's a fact about the world outside of our minds. Similarly, “God exists” is an objective claim. Some people believe it to be true, some people believe it to be false, but their beliefs do not make the claim true or false any more than one's belief that New York is the largest city in the world would make that claim true. God exists, or fails to exist, whether or not we believe or think that God exists. However, if I said, “I believe that God exists,” that would be a subjective claim. In fact, any objective claim can be turned into a subjective claim by prefixing the words “I think that…” or “I believe that…” to it. That’s because the truth conditions for “I believe there is butter in the refrigerator” are found in my (and only my) beliefs, regardless of whether there is butter in the refrigerator, whereas the claim “there is butter in the refrigerator” is true if, and only if, there is butter in the refrigerator, regardless of what I believe.

Notably, truth is a very complex philosophical topic, and there are interesting disputes about its nature. But at the basic level, pretty much everyone working on the topic agrees that the claim “there is a dog on my bed,” is true if and only if there is a dog on my bed. That is, there is general agreement about the need for truth conditions (which, minimally, means that there is always some difference between a true claim and a false claim.) For our purposes, then, we’ll divide claims up as subjective or objective depending on the nature of their truth conditions.

For the following claims, say if they are subjective or objective:

• There are over 1200 species of beetles in the world today.
• The Yankees will win the World Series in 2034.
• Alissa's head hurts.
• I'm tired of hearing about the economy.
• There is no God but Allah and Mohammed is his prophet.
• There are over 9 billion people living in Brooklyn.

Answers: 1 is an objective claim. 2 is also objective: though it refers to a future event, it's not the case that our thoughts or feelings can make it true or false; we just have to wait to see if it's true or false. Its truth conditions will be independent of thought or feeling. Some hold that it is temporarily neither true nor false; most philosophers, though, hold that claims about the future are true or false but that the truth conditions are simply placed at a different point in time from the claim’s utterance. 3 is subjective: it refers to a feeling that Alissa has. 4 is subjective; it refers to a feeling or thought had by the speaker. 5 is objective: many people believe it to be true, many others do not, but it's true if and only if there is, in fact, one God, that God's name is Allah, and Mohammed is the prophet of that God. My thoughts or feelings on this cannot alter its truth value. 6 is objective: there are not, in fact, 9 billion people living in Brooklyn, and we can ascertain that by counting, looking at the census, or just noting the impossibility of getting 9 billion people into the existing housing in Brooklyn.

Note: we distinguish subjective from objective claims to aid in argumentation and conversation.

Generally, we have to be very careful about giving subjective premises for an objective conclusion. “I feel like God exists” or “I feel like Sarmatians are sneaky people” are probably not good premises for the conclusions “God exists” or “Sarmatians are sneaky people.

It’s also important to understand that, if someone makes an objective claim, we can’t respond with “that’s true for you but not for me.” Objective claims, by their nature, are not true relative to some person. An objective claim can be false , but it can’t be simply relative to a person’s beliefs—if it is, it’s not an objective claim. Further, just because a claim is controversial does not make it subjective! Most of the truly controversial claims are objective. We don’t develop a lot of controversy over claims like “I feel tired,” but there is a great deal of debate over claims like “There is only one God and He is the creator of the world.”

Finally, when someone makes a subjective claim but states it as though it were an objective claim, this can cause needless disagreement. If Tammy says “Beyonce is the best singer in the world,” she probably just means that Beyonce is her favorite singer. If Lamar responds with “no way, Taylor Swift is the best singer!” they could be on the verge of a pointless disagreement. There is no standard for “best singer in the world,” so there’s no settling this by argument. Instead, recognizing that Tammy was actually making a subjective claim, Lamar might ask, “really, what do you like about Beyonce’s singing?”

Probability, Certainty, and Monty Hall 7

People often say they know things “for certain,” but they’re certainly wrong. Certainty has a connotation that means there is no doubt: you are absolutely, 100% positive that your claim is true. Skepticism is a theory that claims certainty and truth are impossibilities, and while we can have very good justified beliefs and claims backed by solid reasoning and evidence, nothing is ever certain. If you’re not a skeptic, then finding certainty is possible, but very hard. What do you think you would know for certain? In this class, the closest we will get to uncontroversial certainty certain logical deductions, like inferences and proofs. Proofs are aimed at telling us something for certain, while inferences are simply following something simple we know and figuring out what else it tells us. For example, if I say that “No bananas are underwear” (and we assume it’s true), then we also know that “No underwear are bananas.” Or if I say that “If you eat a banana, then you will sit on its peel, and you ate a banana…” what else could I say? That you’re sitting on its peel. If we assume that the first two claims (about eating bananas and sitting on peels) are true, then the conclusion must follow certainly. We’ll cover these concepts more later on the course, but for now, keep in mind that almost nothing is technically certain. If we’re not certain about things, then what can we say? Just that they’re more or less likely. And that’s where probability comes in to help us.

Probability is how likely something is to happen.

Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.

Tossing a Coin

When a coin is tossed, there are two possible outcomes:

• heads (H) or

We say that the probability of the coin landing H is ½

And the probability of the coin landing T is ½

Throwing Dice

When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

The probability of any one of them is 1 in 6

In general:

Probability of an event happening = Number of ways it can happen divided by Total number of outcomes

Example: the chances of rolling a "4" with a die

Number of ways it can happen: 1 (there is only 1 face with a "4" on it)

Total number of outcomes: 6 (there are 6 faces altogether)

So the probability = 1 in 6

Example: there are 5 marbles in a bag: 4 are blue, and 1 is red. What is the probability that a blue marble gets picked?

Number of ways it can happen: 4 (there are 4 blues)

Total number of outcomes: 5 (there are 5 marbles in total)

So the probability = 4 in 5 = 0.8 (or 80%)

Probability is Just a Guide

Probability does not tell us exactly what will happen, it is just a guide

Example: toss a coin 100 times, how many Heads will come up?

Probability says that heads have a ½ chance, so we can expect 50 Heads.

But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.

Some words have special meaning in Probability:

Experiment or Trial: an action where the result is uncertain.

Tossing a coin, throwing dice, seeing what pizza people choose are all examples of experiments.

Example: choosing a card from a deck

There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards: {Ace of Hearts, 2 of Hearts, etc... }

Sample Point: just one of the possible outcomes

Example: Deck of Cards

• the 5 of Clubs is a sample point
• the King of Hearts is a sample point

"King" is not a sample point. As there are 4 Kings that is 4 different sample points.

Event: a single result of an experiment

Example Events:

• Getting a Tail when tossing a coin is an event
• Rolling a "5" is an event.

An event can include one or more possible outcomes:

• Choosing a "King" from a deck of cards (any of the 4 Kings) is an event
• Rolling an "even number" (2, 4 or 6) is also an event
• The Sample Space is all possible outcomes.
• A Sample Point is just one possible outcome.
• And an Event can be one or more of the possible outcomes.

Hey, let's use those words, so you get used to them:

Example: Alex wants to see how many times a "double" comes up when throwing 2 dice.

Each time Alex throws the 2 dice is an Experiment.

It is an Experiment because the result is uncertain.

The Event Alex is looking for is a "double", where both dice have the same number. It is made up of these 6 Sample Points:

{1,1} {2,2} {3,3} {4,4} {5,5} and {6,6}

The Sample Space is all possible outcomes (36 Sample Points):

{1,1} {1,2} {1,3} {1,4} ... {6,3} {6,4} {6,5} {6,6}

These are Alex's Results:

After 100 Experiments, Alex has 19 "double" Events ... is that close to what you would expect?

While we think we have a good understanding of how chance and probability work, our instincts often mislead us. A prime example of problems we have in understanding and identifying probabilities and certainties is “The Monty Hall problem.”

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Is it to your advantage to switch? Does it matter? Think about what you would do and why. Try it out yourself in a little experiment where you use cards to represent the goats and car. Pretend to be the contestant and host by picking a door and then either switching or staying with your door. Try sticking with your pick the first 10 times and then switching the next 10 times (remember that Monty Hall will ALWAYS show you a goat when he reveals a door). Was there any difference in outcome? Why do you think you got these results? You can look online for further discussions of this “puzzle.”

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Probability and its Paradoxes for Critical Thinking

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Critical Thinking

Critical thinking is a widely accepted educational goal. Its definition is contested, but the competing definitions can be understood as differing conceptions of the same basic concept: careful thinking directed to a goal. Conceptions differ with respect to the scope of such thinking, the type of goal, the criteria and norms for thinking carefully, and the thinking components on which they focus. Its adoption as an educational goal has been recommended on the basis of respect for students’ autonomy and preparing students for success in life and for democratic citizenship. “Critical thinkers” have the dispositions and abilities that lead them to think critically when appropriate. The abilities can be identified directly; the dispositions indirectly, by considering what factors contribute to or impede exercise of the abilities. Standardized tests have been developed to assess the degree to which a person possesses such dispositions and abilities. Educational intervention has been shown experimentally to improve them, particularly when it includes dialogue, anchored instruction, and mentoring. Controversies have arisen over the generalizability of critical thinking across domains, over alleged bias in critical thinking theories and instruction, and over the relationship of critical thinking to other types of thinking.

2.1 Dewey’s Three Main Examples

2.2 dewey’s other examples, 2.3 further examples, 2.4 non-examples, 3. the definition of critical thinking, 4. its value, 5. the process of thinking critically, 6. components of the process, 7. contributory dispositions and abilities, 8.1 initiating dispositions, 8.2 internal dispositions, 9. critical thinking abilities, 10. required knowledge, 11. educational methods, 12.1 the generalizability of critical thinking, 12.2 bias in critical thinking theory and pedagogy, 12.3 relationship of critical thinking to other types of thinking, other internet resources, related entries.

Use of the term ‘critical thinking’ to describe an educational goal goes back to the American philosopher John Dewey (1910), who more commonly called it ‘reflective thinking’. He defined it as

active, persistent and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it, and the further conclusions to which it tends. (Dewey 1910: 6; 1933: 9)

and identified a habit of such consideration with a scientific attitude of mind. His lengthy quotations of Francis Bacon, John Locke, and John Stuart Mill indicate that he was not the first person to propose development of a scientific attitude of mind as an educational goal.

In the 1930s, many of the schools that participated in the Eight-Year Study of the Progressive Education Association (Aikin 1942) adopted critical thinking as an educational goal, for whose achievement the study’s Evaluation Staff developed tests (Smith, Tyler, & Evaluation Staff 1942). Glaser (1941) showed experimentally that it was possible to improve the critical thinking of high school students. Bloom’s influential taxonomy of cognitive educational objectives (Bloom et al. 1956) incorporated critical thinking abilities. Ennis (1962) proposed 12 aspects of critical thinking as a basis for research on the teaching and evaluation of critical thinking ability.

Since 1980, an annual international conference in California on critical thinking and educational reform has attracted tens of thousands of educators from all levels of education and from many parts of the world. Also since 1980, the state university system in California has required all undergraduate students to take a critical thinking course. Since 1983, the Association for Informal Logic and Critical Thinking has sponsored sessions in conjunction with the divisional meetings of the American Philosophical Association (APA). In 1987, the APA’s Committee on Pre-College Philosophy commissioned a consensus statement on critical thinking for purposes of educational assessment and instruction (Facione 1990a). Researchers have developed standardized tests of critical thinking abilities and dispositions; for details, see the Supplement on Assessment . Educational jurisdictions around the world now include critical thinking in guidelines for curriculum and assessment.

For details on this history, see the Supplement on History .

2. Examples and Non-Examples

Before considering the definition of critical thinking, it will be helpful to have in mind some examples of critical thinking, as well as some examples of kinds of thinking that would apparently not count as critical thinking.

Dewey (1910: 68–71; 1933: 91–94) takes as paradigms of reflective thinking three class papers of students in which they describe their thinking. The examples range from the everyday to the scientific.

Transit : “The other day, when I was down town on 16th Street, a clock caught my eye. I saw that the hands pointed to 12:20. This suggested that I had an engagement at 124th Street, at one o’clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o’clock.” (Dewey 1910: 68–69; 1933: 91–92)

Ferryboat : “Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river is a long white pole, having a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere on the boat two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

“I then tried to imagine all possible purposes of the pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

“In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot’s position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly.” (Dewey 1910: 69–70; 1933: 92–93)

Bubbles : “In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat, or by decrease of pressure, or both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside. But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse” (Dewey 1910: 70–71; 1933: 93–94).

Dewey (1910, 1933) sprinkles his book with other examples of critical thinking. We will refer to the following.

Weather : A man on a walk notices that it has suddenly become cool, thinks that it is probably going to rain, looks up and sees a dark cloud obscuring the sun, and quickens his steps (1910: 6–10; 1933: 9–13).

Disorder : A man finds his rooms on his return to them in disorder with his belongings thrown about, thinks at first of burglary as an explanation, then thinks of mischievous children as being an alternative explanation, then looks to see whether valuables are missing, and discovers that they are (1910: 82–83; 1933: 166–168).

Typhoid : A physician diagnosing a patient whose conspicuous symptoms suggest typhoid avoids drawing a conclusion until more data are gathered by questioning the patient and by making tests (1910: 85–86; 1933: 170).

Blur : A moving blur catches our eye in the distance, we ask ourselves whether it is a cloud of whirling dust or a tree moving its branches or a man signaling to us, we think of other traits that should be found on each of those possibilities, and we look and see if those traits are found (1910: 102, 108; 1933: 121, 133).

Suction pump : In thinking about the suction pump, the scientist first notes that it will draw water only to a maximum height of 33 feet at sea level and to a lesser maximum height at higher elevations, selects for attention the differing atmospheric pressure at these elevations, sets up experiments in which the air is removed from a vessel containing water (when suction no longer works) and in which the weight of air at various levels is calculated, compares the results of reasoning about the height to which a given weight of air will allow a suction pump to raise water with the observed maximum height at different elevations, and finally assimilates the suction pump to such apparently different phenomena as the siphon and the rising of a balloon (1910: 150–153; 1933: 195–198).

Diamond : A passenger in a car driving in a diamond lane reserved for vehicles with at least one passenger notices that the diamond marks on the pavement are far apart in some places and close together in others. Why? The driver suggests that the reason may be that the diamond marks are not needed where there is a solid double line separating the diamond lane from the adjoining lane, but are needed when there is a dotted single line permitting crossing into the diamond lane. Further observation confirms that the diamonds are close together when a dotted line separates the diamond lane from its neighbour, but otherwise far apart.

Rash : A woman suddenly develops a very itchy red rash on her throat and upper chest. She recently noticed a mark on the back of her right hand, but was not sure whether the mark was a rash or a scrape. She lies down in bed and thinks about what might be causing the rash and what to do about it. About two weeks before, she began taking blood pressure medication that contained a sulfa drug, and the pharmacist had warned her, in view of a previous allergic reaction to a medication containing a sulfa drug, to be on the alert for an allergic reaction; however, she had been taking the medication for two weeks with no such effect. The day before, she began using a new cream on her neck and upper chest; against the new cream as the cause was mark on the back of her hand, which had not been exposed to the cream. She began taking probiotics about a month before. She also recently started new eye drops, but she supposed that manufacturers of eye drops would be careful not to include allergy-causing components in the medication. The rash might be a heat rash, since she recently was sweating profusely from her upper body. Since she is about to go away on a short vacation, where she would not have access to her usual physician, she decides to keep taking the probiotics and using the new eye drops but to discontinue the blood pressure medication and to switch back to the old cream for her neck and upper chest. She forms a plan to consult her regular physician on her return about the blood pressure medication.

Candidate : Although Dewey included no examples of thinking directed at appraising the arguments of others, such thinking has come to be considered a kind of critical thinking. We find an example of such thinking in the performance task on the Collegiate Learning Assessment (CLA+), which its sponsoring organization describes as

a performance-based assessment that provides a measure of an institution’s contribution to the development of critical-thinking and written communication skills of its students. (Council for Aid to Education 2017)

A sample task posted on its website requires the test-taker to write a report for public distribution evaluating a fictional candidate’s policy proposals and their supporting arguments, using supplied background documents, with a recommendation on whether to endorse the candidate.

Immediate acceptance of an idea that suggests itself as a solution to a problem (e.g., a possible explanation of an event or phenomenon, an action that seems likely to produce a desired result) is “uncritical thinking, the minimum of reflection” (Dewey 1910: 13). On-going suspension of judgment in the light of doubt about a possible solution is not critical thinking (Dewey 1910: 108). Critique driven by a dogmatically held political or religious ideology is not critical thinking; thus Paulo Freire (1968 [1970]) is using the term (e.g., at 1970: 71, 81, 100, 146) in a more politically freighted sense that includes not only reflection but also revolutionary action against oppression. Derivation of a conclusion from given data using an algorithm is not critical thinking.

What is critical thinking? There are many definitions. Ennis (2016) lists 14 philosophically oriented scholarly definitions and three dictionary definitions. Following Rawls (1971), who distinguished his conception of justice from a utilitarian conception but regarded them as rival conceptions of the same concept, Ennis maintains that the 17 definitions are different conceptions of the same concept. Rawls articulated the shared concept of justice as

a characteristic set of principles for assigning basic rights and duties and for determining… the proper distribution of the benefits and burdens of social cooperation. (Rawls 1971: 5)

Bailin et al. (1999b) claim that, if one considers what sorts of thinking an educator would take not to be critical thinking and what sorts to be critical thinking, one can conclude that educators typically understand critical thinking to have at least three features.

• It is done for the purpose of making up one’s mind about what to believe or do.
• The person engaging in the thinking is trying to fulfill standards of adequacy and accuracy appropriate to the thinking.
• The thinking fulfills the relevant standards to some threshold level.

One could sum up the core concept that involves these three features by saying that critical thinking is careful goal-directed thinking. This core concept seems to apply to all the examples of critical thinking described in the previous section. As for the non-examples, their exclusion depends on construing careful thinking as excluding jumping immediately to conclusions, suspending judgment no matter how strong the evidence, reasoning from an unquestioned ideological or religious perspective, and routinely using an algorithm to answer a question.

If the core of critical thinking is careful goal-directed thinking, conceptions of it can vary according to its presumed scope, its presumed goal, one’s criteria and threshold for being careful, and the thinking component on which one focuses. As to its scope, some conceptions (e.g., Dewey 1910, 1933) restrict it to constructive thinking on the basis of one’s own observations and experiments, others (e.g., Ennis 1962; Fisher & Scriven 1997; Johnson 1992) to appraisal of the products of such thinking. Ennis (1991) and Bailin et al. (1999b) take it to cover both construction and appraisal. As to its goal, some conceptions restrict it to forming a judgment (Dewey 1910, 1933; Lipman 1987; Facione 1990a). Others allow for actions as well as beliefs as the end point of a process of critical thinking (Ennis 1991; Bailin et al. 1999b). As to the criteria and threshold for being careful, definitions vary in the term used to indicate that critical thinking satisfies certain norms: “intellectually disciplined” (Scriven & Paul 1987), “reasonable” (Ennis 1991), “skillful” (Lipman 1987), “skilled” (Fisher & Scriven 1997), “careful” (Bailin & Battersby 2009). Some definitions specify these norms, referring variously to “consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends” (Dewey 1910, 1933); “the methods of logical inquiry and reasoning” (Glaser 1941); “conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication” (Scriven & Paul 1987); the requirement that “it is sensitive to context, relies on criteria, and is self-correcting” (Lipman 1987); “evidential, conceptual, methodological, criteriological, or contextual considerations” (Facione 1990a); and “plus-minus considerations of the product in terms of appropriate standards (or criteria)” (Johnson 1992). Stanovich and Stanovich (2010) propose to ground the concept of critical thinking in the concept of rationality, which they understand as combining epistemic rationality (fitting one’s beliefs to the world) and instrumental rationality (optimizing goal fulfillment); a critical thinker, in their view, is someone with “a propensity to override suboptimal responses from the autonomous mind” (2010: 227). These variant specifications of norms for critical thinking are not necessarily incompatible with one another, and in any case presuppose the core notion of thinking carefully. As to the thinking component singled out, some definitions focus on suspension of judgment during the thinking (Dewey 1910; McPeck 1981), others on inquiry while judgment is suspended (Bailin & Battersby 2009, 2021), others on the resulting judgment (Facione 1990a), and still others on responsiveness to reasons (Siegel 1988). Kuhn (2019) takes critical thinking to be more a dialogic practice of advancing and responding to arguments than an individual ability.

In educational contexts, a definition of critical thinking is a “programmatic definition” (Scheffler 1960: 19). It expresses a practical program for achieving an educational goal. For this purpose, a one-sentence formulaic definition is much less useful than articulation of a critical thinking process, with criteria and standards for the kinds of thinking that the process may involve. The real educational goal is recognition, adoption and implementation by students of those criteria and standards. That adoption and implementation in turn consists in acquiring the knowledge, abilities and dispositions of a critical thinker.

Conceptions of critical thinking generally do not include moral integrity as part of the concept. Dewey, for example, took critical thinking to be the ultimate intellectual goal of education, but distinguished it from the development of social cooperation among school children, which he took to be the central moral goal. Ennis (1996, 2011) added to his previous list of critical thinking dispositions a group of dispositions to care about the dignity and worth of every person, which he described as a “correlative” (1996) disposition without which critical thinking would be less valuable and perhaps harmful. An educational program that aimed at developing critical thinking but not the correlative disposition to care about the dignity and worth of every person, he asserted, “would be deficient and perhaps dangerous” (Ennis 1996: 172).

Dewey thought that education for reflective thinking would be of value to both the individual and society; recognition in educational practice of the kinship to the scientific attitude of children’s native curiosity, fertile imagination and love of experimental inquiry “would make for individual happiness and the reduction of social waste” (Dewey 1910: iii). Schools participating in the Eight-Year Study took development of the habit of reflective thinking and skill in solving problems as a means to leading young people to understand, appreciate and live the democratic way of life characteristic of the United States (Aikin 1942: 17–18, 81). Harvey Siegel (1988: 55–61) has offered four considerations in support of adopting critical thinking as an educational ideal. (1) Respect for persons requires that schools and teachers honour students’ demands for reasons and explanations, deal with students honestly, and recognize the need to confront students’ independent judgment; these requirements concern the manner in which teachers treat students. (2) Education has the task of preparing children to be successful adults, a task that requires development of their self-sufficiency. (3) Education should initiate children into the rational traditions in such fields as history, science and mathematics. (4) Education should prepare children to become democratic citizens, which requires reasoned procedures and critical talents and attitudes. To supplement these considerations, Siegel (1988: 62–90) responds to two objections: the ideology objection that adoption of any educational ideal requires a prior ideological commitment and the indoctrination objection that cultivation of critical thinking cannot escape being a form of indoctrination.

Despite the diversity of our 11 examples, one can recognize a common pattern. Dewey analyzed it as consisting of five phases:

• suggestions , in which the mind leaps forward to a possible solution;
• an intellectualization of the difficulty or perplexity into a problem to be solved, a question for which the answer must be sought;
• the use of one suggestion after another as a leading idea, or hypothesis , to initiate and guide observation and other operations in collection of factual material;
• the mental elaboration of the idea or supposition as an idea or supposition ( reasoning , in the sense on which reasoning is a part, not the whole, of inference); and
• testing the hypothesis by overt or imaginative action. (Dewey 1933: 106–107; italics in original)

The process of reflective thinking consisting of these phases would be preceded by a perplexed, troubled or confused situation and followed by a cleared-up, unified, resolved situation (Dewey 1933: 106). The term ‘phases’ replaced the term ‘steps’ (Dewey 1910: 72), thus removing the earlier suggestion of an invariant sequence. Variants of the above analysis appeared in (Dewey 1916: 177) and (Dewey 1938: 101–119).

The variant formulations indicate the difficulty of giving a single logical analysis of such a varied process. The process of critical thinking may have a spiral pattern, with the problem being redefined in the light of obstacles to solving it as originally formulated. For example, the person in Transit might have concluded that getting to the appointment at the scheduled time was impossible and have reformulated the problem as that of rescheduling the appointment for a mutually convenient time. Further, defining a problem does not always follow after or lead immediately to an idea of a suggested solution. Nor should it do so, as Dewey himself recognized in describing the physician in Typhoid as avoiding any strong preference for this or that conclusion before getting further information (Dewey 1910: 85; 1933: 170). People with a hypothesis in mind, even one to which they have a very weak commitment, have a so-called “confirmation bias” (Nickerson 1998): they are likely to pay attention to evidence that confirms the hypothesis and to ignore evidence that counts against it or for some competing hypothesis. Detectives, intelligence agencies, and investigators of airplane accidents are well advised to gather relevant evidence systematically and to postpone even tentative adoption of an explanatory hypothesis until the collected evidence rules out with the appropriate degree of certainty all but one explanation. Dewey’s analysis of the critical thinking process can be faulted as well for requiring acceptance or rejection of a possible solution to a defined problem, with no allowance for deciding in the light of the available evidence to suspend judgment. Further, given the great variety of kinds of problems for which reflection is appropriate, there is likely to be variation in its component events. Perhaps the best way to conceptualize the critical thinking process is as a checklist whose component events can occur in a variety of orders, selectively, and more than once. These component events might include (1) noticing a difficulty, (2) defining the problem, (3) dividing the problem into manageable sub-problems, (4) formulating a variety of possible solutions to the problem or sub-problem, (5) determining what evidence is relevant to deciding among possible solutions to the problem or sub-problem, (6) devising a plan of systematic observation or experiment that will uncover the relevant evidence, (7) carrying out the plan of systematic observation or experimentation, (8) noting the results of the systematic observation or experiment, (9) gathering relevant testimony and information from others, (10) judging the credibility of testimony and information gathered from others, (11) drawing conclusions from gathered evidence and accepted testimony, and (12) accepting a solution that the evidence adequately supports (cf. Hitchcock 2017: 485).

Checklist conceptions of the process of critical thinking are open to the objection that they are too mechanical and procedural to fit the multi-dimensional and emotionally charged issues for which critical thinking is urgently needed (Paul 1984). For such issues, a more dialectical process is advocated, in which competing relevant world views are identified, their implications explored, and some sort of creative synthesis attempted.

If one considers the critical thinking process illustrated by the 11 examples, one can identify distinct kinds of mental acts and mental states that form part of it. To distinguish, label and briefly characterize these components is a useful preliminary to identifying abilities, skills, dispositions, attitudes, habits and the like that contribute causally to thinking critically. Identifying such abilities and habits is in turn a useful preliminary to setting educational goals. Setting the goals is in its turn a useful preliminary to designing strategies for helping learners to achieve the goals and to designing ways of measuring the extent to which learners have done so. Such measures provide both feedback to learners on their achievement and a basis for experimental research on the effectiveness of various strategies for educating people to think critically. Let us begin, then, by distinguishing the kinds of mental acts and mental events that can occur in a critical thinking process.

• Observing : One notices something in one’s immediate environment (sudden cooling of temperature in Weather , bubbles forming outside a glass and then going inside in Bubbles , a moving blur in the distance in Blur , a rash in Rash ). Or one notes the results of an experiment or systematic observation (valuables missing in Disorder , no suction without air pressure in Suction pump )
• Feeling : One feels puzzled or uncertain about something (how to get to an appointment on time in Transit , why the diamonds vary in spacing in Diamond ). One wants to resolve this perplexity. One feels satisfaction once one has worked out an answer (to take the subway express in Transit , diamonds closer when needed as a warning in Diamond ).
• Wondering : One formulates a question to be addressed (why bubbles form outside a tumbler taken from hot water in Bubbles , how suction pumps work in Suction pump , what caused the rash in Rash ).
• Imagining : One thinks of possible answers (bus or subway or elevated in Transit , flagpole or ornament or wireless communication aid or direction indicator in Ferryboat , allergic reaction or heat rash in Rash ).
• Inferring : One works out what would be the case if a possible answer were assumed (valuables missing if there has been a burglary in Disorder , earlier start to the rash if it is an allergic reaction to a sulfa drug in Rash ). Or one draws a conclusion once sufficient relevant evidence is gathered (take the subway in Transit , burglary in Disorder , discontinue blood pressure medication and new cream in Rash ).
• Knowledge : One uses stored knowledge of the subject-matter to generate possible answers or to infer what would be expected on the assumption of a particular answer (knowledge of a city’s public transit system in Transit , of the requirements for a flagpole in Ferryboat , of Boyle’s law in Bubbles , of allergic reactions in Rash ).
• Experimenting : One designs and carries out an experiment or a systematic observation to find out whether the results deduced from a possible answer will occur (looking at the location of the flagpole in relation to the pilot’s position in Ferryboat , putting an ice cube on top of a tumbler taken from hot water in Bubbles , measuring the height to which a suction pump will draw water at different elevations in Suction pump , noticing the spacing of diamonds when movement to or from a diamond lane is allowed in Diamond ).
• Consulting : One finds a source of information, gets the information from the source, and makes a judgment on whether to accept it. None of our 11 examples include searching for sources of information. In this respect they are unrepresentative, since most people nowadays have almost instant access to information relevant to answering any question, including many of those illustrated by the examples. However, Candidate includes the activities of extracting information from sources and evaluating its credibility.
• Identifying and analyzing arguments : One notices an argument and works out its structure and content as a preliminary to evaluating its strength. This activity is central to Candidate . It is an important part of a critical thinking process in which one surveys arguments for various positions on an issue.
• Judging : One makes a judgment on the basis of accumulated evidence and reasoning, such as the judgment in Ferryboat that the purpose of the pole is to provide direction to the pilot.
• Deciding : One makes a decision on what to do or on what policy to adopt, as in the decision in Transit to take the subway.

By definition, a person who does something voluntarily is both willing and able to do that thing at that time. Both the willingness and the ability contribute causally to the person’s action, in the sense that the voluntary action would not occur if either (or both) of these were lacking. For example, suppose that one is standing with one’s arms at one’s sides and one voluntarily lifts one’s right arm to an extended horizontal position. One would not do so if one were unable to lift one’s arm, if for example one’s right side was paralyzed as the result of a stroke. Nor would one do so if one were unwilling to lift one’s arm, if for example one were participating in a street demonstration at which a white supremacist was urging the crowd to lift their right arm in a Nazi salute and one were unwilling to express support in this way for the racist Nazi ideology. The same analysis applies to a voluntary mental process of thinking critically. It requires both willingness and ability to think critically, including willingness and ability to perform each of the mental acts that compose the process and to coordinate those acts in a sequence that is directed at resolving the initiating perplexity.

Consider willingness first. We can identify causal contributors to willingness to think critically by considering factors that would cause a person who was able to think critically about an issue nevertheless not to do so (Hamby 2014). For each factor, the opposite condition thus contributes causally to willingness to think critically on a particular occasion. For example, people who habitually jump to conclusions without considering alternatives will not think critically about issues that arise, even if they have the required abilities. The contrary condition of willingness to suspend judgment is thus a causal contributor to thinking critically.

Now consider ability. In contrast to the ability to move one’s arm, which can be completely absent because a stroke has left the arm paralyzed, the ability to think critically is a developed ability, whose absence is not a complete absence of ability to think but absence of ability to think well. We can identify the ability to think well directly, in terms of the norms and standards for good thinking. In general, to be able do well the thinking activities that can be components of a critical thinking process, one needs to know the concepts and principles that characterize their good performance, to recognize in particular cases that the concepts and principles apply, and to apply them. The knowledge, recognition and application may be procedural rather than declarative. It may be domain-specific rather than widely applicable, and in either case may need subject-matter knowledge, sometimes of a deep kind.

Reflections of the sort illustrated by the previous two paragraphs have led scholars to identify the knowledge, abilities and dispositions of a “critical thinker”, i.e., someone who thinks critically whenever it is appropriate to do so. We turn now to these three types of causal contributors to thinking critically. We start with dispositions, since arguably these are the most powerful contributors to being a critical thinker, can be fostered at an early stage of a child’s development, and are susceptible to general improvement (Glaser 1941: 175)

8. Critical Thinking Dispositions

Educational researchers use the term ‘dispositions’ broadly for the habits of mind and attitudes that contribute causally to being a critical thinker. Some writers (e.g., Paul & Elder 2006; Hamby 2014; Bailin & Battersby 2016a) propose to use the term ‘virtues’ for this dimension of a critical thinker. The virtues in question, although they are virtues of character, concern the person’s ways of thinking rather than the person’s ways of behaving towards others. They are not moral virtues but intellectual virtues, of the sort articulated by Zagzebski (1996) and discussed by Turri, Alfano, and Greco (2017).

On a realistic conception, thinking dispositions or intellectual virtues are real properties of thinkers. They are general tendencies, propensities, or inclinations to think in particular ways in particular circumstances, and can be genuinely explanatory (Siegel 1999). Sceptics argue that there is no evidence for a specific mental basis for the habits of mind that contribute to thinking critically, and that it is pedagogically misleading to posit such a basis (Bailin et al. 1999a). Whatever their status, critical thinking dispositions need motivation for their initial formation in a child—motivation that may be external or internal. As children develop, the force of habit will gradually become important in sustaining the disposition (Nieto & Valenzuela 2012). Mere force of habit, however, is unlikely to sustain critical thinking dispositions. Critical thinkers must value and enjoy using their knowledge and abilities to think things through for themselves. They must be committed to, and lovers of, inquiry.

A person may have a critical thinking disposition with respect to only some kinds of issues. For example, one could be open-minded about scientific issues but not about religious issues. Similarly, one could be confident in one’s ability to reason about the theological implications of the existence of evil in the world but not in one’s ability to reason about the best design for a guided ballistic missile.

Facione (1990a: 25) divides “affective dispositions” of critical thinking into approaches to life and living in general and approaches to specific issues, questions or problems. Adapting this distinction, one can usefully divide critical thinking dispositions into initiating dispositions (those that contribute causally to starting to think critically about an issue) and internal dispositions (those that contribute causally to doing a good job of thinking critically once one has started). The two categories are not mutually exclusive. For example, open-mindedness, in the sense of willingness to consider alternative points of view to one’s own, is both an initiating and an internal disposition.

Using the strategy of considering factors that would block people with the ability to think critically from doing so, we can identify as initiating dispositions for thinking critically attentiveness, a habit of inquiry, self-confidence, courage, open-mindedness, willingness to suspend judgment, trust in reason, wanting evidence for one’s beliefs, and seeking the truth. We consider briefly what each of these dispositions amounts to, in each case citing sources that acknowledge them.

• Attentiveness : One will not think critically if one fails to recognize an issue that needs to be thought through. For example, the pedestrian in Weather would not have looked up if he had not noticed that the air was suddenly cooler. To be a critical thinker, then, one needs to be habitually attentive to one’s surroundings, noticing not only what one senses but also sources of perplexity in messages received and in one’s own beliefs and attitudes (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Habit of inquiry : Inquiry is effortful, and one needs an internal push to engage in it. For example, the student in Bubbles could easily have stopped at idle wondering about the cause of the bubbles rather than reasoning to a hypothesis, then designing and executing an experiment to test it. Thus willingness to think critically needs mental energy and initiative. What can supply that energy? Love of inquiry, or perhaps just a habit of inquiry. Hamby (2015) has argued that willingness to inquire is the central critical thinking virtue, one that encompasses all the others. It is recognized as a critical thinking disposition by Dewey (1910: 29; 1933: 35), Glaser (1941: 5), Ennis (1987: 12; 1991: 8), Facione (1990a: 25), Bailin et al. (1999b: 294), Halpern (1998: 452), and Facione, Facione, & Giancarlo (2001).
• Self-confidence : Lack of confidence in one’s abilities can block critical thinking. For example, if the woman in Rash lacked confidence in her ability to figure things out for herself, she might just have assumed that the rash on her chest was the allergic reaction to her medication against which the pharmacist had warned her. Thus willingness to think critically requires confidence in one’s ability to inquire (Facione 1990a: 25; Facione, Facione, & Giancarlo 2001).
• Courage : Fear of thinking for oneself can stop one from doing it. Thus willingness to think critically requires intellectual courage (Paul & Elder 2006: 16).
• Open-mindedness : A dogmatic attitude will impede thinking critically. For example, a person who adheres rigidly to a “pro-choice” position on the issue of the legal status of induced abortion is likely to be unwilling to consider seriously the issue of when in its development an unborn child acquires a moral right to life. Thus willingness to think critically requires open-mindedness, in the sense of a willingness to examine questions to which one already accepts an answer but which further evidence or reasoning might cause one to answer differently (Dewey 1933; Facione 1990a; Ennis 1991; Bailin et al. 1999b; Halpern 1998, Facione, Facione, & Giancarlo 2001). Paul (1981) emphasizes open-mindedness about alternative world-views, and recommends a dialectical approach to integrating such views as central to what he calls “strong sense” critical thinking. In three studies, Haran, Ritov, & Mellers (2013) found that actively open-minded thinking, including “the tendency to weigh new evidence against a favored belief, to spend sufficient time on a problem before giving up, and to consider carefully the opinions of others in forming one’s own”, led study participants to acquire information and thus to make accurate estimations.
• Willingness to suspend judgment : Premature closure on an initial solution will block critical thinking. Thus willingness to think critically requires a willingness to suspend judgment while alternatives are explored (Facione 1990a; Ennis 1991; Halpern 1998).
• Trust in reason : Since distrust in the processes of reasoned inquiry will dissuade one from engaging in it, trust in them is an initiating critical thinking disposition (Facione 1990a, 25; Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001; Paul & Elder 2006). In reaction to an allegedly exclusive emphasis on reason in critical thinking theory and pedagogy, Thayer-Bacon (2000) argues that intuition, imagination, and emotion have important roles to play in an adequate conception of critical thinking that she calls “constructive thinking”. From her point of view, critical thinking requires trust not only in reason but also in intuition, imagination, and emotion.
• Seeking the truth : If one does not care about the truth but is content to stick with one’s initial bias on an issue, then one will not think critically about it. Seeking the truth is thus an initiating critical thinking disposition (Bailin et al. 1999b: 294; Facione, Facione, & Giancarlo 2001). A disposition to seek the truth is implicit in more specific critical thinking dispositions, such as trying to be well-informed, considering seriously points of view other than one’s own, looking for alternatives, suspending judgment when the evidence is insufficient, and adopting a position when the evidence supporting it is sufficient.

Some of the initiating dispositions, such as open-mindedness and willingness to suspend judgment, are also internal critical thinking dispositions, in the sense of mental habits or attitudes that contribute causally to doing a good job of critical thinking once one starts the process. But there are many other internal critical thinking dispositions. Some of them are parasitic on one’s conception of good thinking. For example, it is constitutive of good thinking about an issue to formulate the issue clearly and to maintain focus on it. For this purpose, one needs not only the corresponding ability but also the corresponding disposition. Ennis (1991: 8) describes it as the disposition “to determine and maintain focus on the conclusion or question”, Facione (1990a: 25) as “clarity in stating the question or concern”. Other internal dispositions are motivators to continue or adjust the critical thinking process, such as willingness to persist in a complex task and willingness to abandon nonproductive strategies in an attempt to self-correct (Halpern 1998: 452). For a list of identified internal critical thinking dispositions, see the Supplement on Internal Critical Thinking Dispositions .

Some theorists postulate skills, i.e., acquired abilities, as operative in critical thinking. It is not obvious, however, that a good mental act is the exercise of a generic acquired skill. Inferring an expected time of arrival, as in Transit , has some generic components but also uses non-generic subject-matter knowledge. Bailin et al. (1999a) argue against viewing critical thinking skills as generic and discrete, on the ground that skilled performance at a critical thinking task cannot be separated from knowledge of concepts and from domain-specific principles of good thinking. Talk of skills, they concede, is unproblematic if it means merely that a person with critical thinking skills is capable of intelligent performance.

Despite such scepticism, theorists of critical thinking have listed as general contributors to critical thinking what they variously call abilities (Glaser 1941; Ennis 1962, 1991), skills (Facione 1990a; Halpern 1998) or competencies (Fisher & Scriven 1997). Amalgamating these lists would produce a confusing and chaotic cornucopia of more than 50 possible educational objectives, with only partial overlap among them. It makes sense instead to try to understand the reasons for the multiplicity and diversity, and to make a selection according to one’s own reasons for singling out abilities to be developed in a critical thinking curriculum. Two reasons for diversity among lists of critical thinking abilities are the underlying conception of critical thinking and the envisaged educational level. Appraisal-only conceptions, for example, involve a different suite of abilities than constructive-only conceptions. Some lists, such as those in (Glaser 1941), are put forward as educational objectives for secondary school students, whereas others are proposed as objectives for college students (e.g., Facione 1990a).

The abilities described in the remaining paragraphs of this section emerge from reflection on the general abilities needed to do well the thinking activities identified in section 6 as components of the critical thinking process described in section 5 . The derivation of each collection of abilities is accompanied by citation of sources that list such abilities and of standardized tests that claim to test them.

Observational abilities : Careful and accurate observation sometimes requires specialist expertise and practice, as in the case of observing birds and observing accident scenes. However, there are general abilities of noticing what one’s senses are picking up from one’s environment and of being able to articulate clearly and accurately to oneself and others what one has observed. It helps in exercising them to be able to recognize and take into account factors that make one’s observation less trustworthy, such as prior framing of the situation, inadequate time, deficient senses, poor observation conditions, and the like. It helps as well to be skilled at taking steps to make one’s observation more trustworthy, such as moving closer to get a better look, measuring something three times and taking the average, and checking what one thinks one is observing with someone else who is in a good position to observe it. It also helps to be skilled at recognizing respects in which one’s report of one’s observation involves inference rather than direct observation, so that one can then consider whether the inference is justified. These abilities come into play as well when one thinks about whether and with what degree of confidence to accept an observation report, for example in the study of history or in a criminal investigation or in assessing news reports. Observational abilities show up in some lists of critical thinking abilities (Ennis 1962: 90; Facione 1990a: 16; Ennis 1991: 9). There are items testing a person’s ability to judge the credibility of observation reports in the Cornell Critical Thinking Tests, Levels X and Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). Norris and King (1983, 1985, 1990a, 1990b) is a test of ability to appraise observation reports.

Emotional abilities : The emotions that drive a critical thinking process are perplexity or puzzlement, a wish to resolve it, and satisfaction at achieving the desired resolution. Children experience these emotions at an early age, without being trained to do so. Education that takes critical thinking as a goal needs only to channel these emotions and to make sure not to stifle them. Collaborative critical thinking benefits from ability to recognize one’s own and others’ emotional commitments and reactions.

Questioning abilities : A critical thinking process needs transformation of an inchoate sense of perplexity into a clear question. Formulating a question well requires not building in questionable assumptions, not prejudging the issue, and using language that in context is unambiguous and precise enough (Ennis 1962: 97; 1991: 9).

Imaginative abilities : Thinking directed at finding the correct causal explanation of a general phenomenon or particular event requires an ability to imagine possible explanations. Thinking about what policy or plan of action to adopt requires generation of options and consideration of possible consequences of each option. Domain knowledge is required for such creative activity, but a general ability to imagine alternatives is helpful and can be nurtured so as to become easier, quicker, more extensive, and deeper (Dewey 1910: 34–39; 1933: 40–47). Facione (1990a) and Halpern (1998) include the ability to imagine alternatives as a critical thinking ability.

Inferential abilities : The ability to draw conclusions from given information, and to recognize with what degree of certainty one’s own or others’ conclusions follow, is universally recognized as a general critical thinking ability. All 11 examples in section 2 of this article include inferences, some from hypotheses or options (as in Transit , Ferryboat and Disorder ), others from something observed (as in Weather and Rash ). None of these inferences is formally valid. Rather, they are licensed by general, sometimes qualified substantive rules of inference (Toulmin 1958) that rest on domain knowledge—that a bus trip takes about the same time in each direction, that the terminal of a wireless telegraph would be located on the highest possible place, that sudden cooling is often followed by rain, that an allergic reaction to a sulfa drug generally shows up soon after one starts taking it. It is a matter of controversy to what extent the specialized ability to deduce conclusions from premisses using formal rules of inference is needed for critical thinking. Dewey (1933) locates logical forms in setting out the products of reflection rather than in the process of reflection. Ennis (1981a), on the other hand, maintains that a liberally-educated person should have the following abilities: to translate natural-language statements into statements using the standard logical operators, to use appropriately the language of necessary and sufficient conditions, to deal with argument forms and arguments containing symbols, to determine whether in virtue of an argument’s form its conclusion follows necessarily from its premisses, to reason with logically complex propositions, and to apply the rules and procedures of deductive logic. Inferential abilities are recognized as critical thinking abilities by Glaser (1941: 6), Facione (1990a: 9), Ennis (1991: 9), Fisher & Scriven (1997: 99, 111), and Halpern (1998: 452). Items testing inferential abilities constitute two of the five subtests of the Watson Glaser Critical Thinking Appraisal (Watson & Glaser 1980a, 1980b, 1994), two of the four sections in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), three of the seven sections in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005), 11 of the 34 items on Forms A and B of the California Critical Thinking Skills Test (Facione 1990b, 1992), and a high but variable proportion of the 25 selected-response questions in the Collegiate Learning Assessment (Council for Aid to Education 2017).

Experimenting abilities : Knowing how to design and execute an experiment is important not just in scientific research but also in everyday life, as in Rash . Dewey devoted a whole chapter of his How We Think (1910: 145–156; 1933: 190–202) to the superiority of experimentation over observation in advancing knowledge. Experimenting abilities come into play at one remove in appraising reports of scientific studies. Skill in designing and executing experiments includes the acknowledged abilities to appraise evidence (Glaser 1941: 6), to carry out experiments and to apply appropriate statistical inference techniques (Facione 1990a: 9), to judge inductions to an explanatory hypothesis (Ennis 1991: 9), and to recognize the need for an adequately large sample size (Halpern 1998). The Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) includes four items (out of 52) on experimental design. The Collegiate Learning Assessment (Council for Aid to Education 2017) makes room for appraisal of study design in both its performance task and its selected-response questions.

Consulting abilities : Skill at consulting sources of information comes into play when one seeks information to help resolve a problem, as in Candidate . Ability to find and appraise information includes ability to gather and marshal pertinent information (Glaser 1941: 6), to judge whether a statement made by an alleged authority is acceptable (Ennis 1962: 84), to plan a search for desired information (Facione 1990a: 9), and to judge the credibility of a source (Ennis 1991: 9). Ability to judge the credibility of statements is tested by 24 items (out of 76) in the Cornell Critical Thinking Test Level X (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005) and by four items (out of 52) in the Cornell Critical Thinking Test Level Z (Ennis & Millman 1971; Ennis, Millman, & Tomko 1985, 2005). The College Learning Assessment’s performance task requires evaluation of whether information in documents is credible or unreliable (Council for Aid to Education 2017).

Argument analysis abilities : The ability to identify and analyze arguments contributes to the process of surveying arguments on an issue in order to form one’s own reasoned judgment, as in Candidate . The ability to detect and analyze arguments is recognized as a critical thinking skill by Facione (1990a: 7–8), Ennis (1991: 9) and Halpern (1998). Five items (out of 34) on the California Critical Thinking Skills Test (Facione 1990b, 1992) test skill at argument analysis. The College Learning Assessment (Council for Aid to Education 2017) incorporates argument analysis in its selected-response tests of critical reading and evaluation and of critiquing an argument.

Judging skills and deciding skills : Skill at judging and deciding is skill at recognizing what judgment or decision the available evidence and argument supports, and with what degree of confidence. It is thus a component of the inferential skills already discussed.

Lists and tests of critical thinking abilities often include two more abilities: identifying assumptions and constructing and evaluating definitions.

In addition to dispositions and abilities, critical thinking needs knowledge: of critical thinking concepts, of critical thinking principles, and of the subject-matter of the thinking.

We can derive a short list of concepts whose understanding contributes to critical thinking from the critical thinking abilities described in the preceding section. Observational abilities require an understanding of the difference between observation and inference. Questioning abilities require an understanding of the concepts of ambiguity and vagueness. Inferential abilities require an understanding of the difference between conclusive and defeasible inference (traditionally, between deduction and induction), as well as of the difference between necessary and sufficient conditions. Experimenting abilities require an understanding of the concepts of hypothesis, null hypothesis, assumption and prediction, as well as of the concept of statistical significance and of its difference from importance. They also require an understanding of the difference between an experiment and an observational study, and in particular of the difference between a randomized controlled trial, a prospective correlational study and a retrospective (case-control) study. Argument analysis abilities require an understanding of the concepts of argument, premiss, assumption, conclusion and counter-consideration. Additional critical thinking concepts are proposed by Bailin et al. (1999b: 293), Fisher & Scriven (1997: 105–106), Black (2012), and Blair (2021).

According to Glaser (1941: 25), ability to think critically requires knowledge of the methods of logical inquiry and reasoning. If we review the list of abilities in the preceding section, however, we can see that some of them can be acquired and exercised merely through practice, possibly guided in an educational setting, followed by feedback. Searching intelligently for a causal explanation of some phenomenon or event requires that one consider a full range of possible causal contributors, but it seems more important that one implements this principle in one’s practice than that one is able to articulate it. What is important is “operational knowledge” of the standards and principles of good thinking (Bailin et al. 1999b: 291–293). But the development of such critical thinking abilities as designing an experiment or constructing an operational definition can benefit from learning their underlying theory. Further, explicit knowledge of quirks of human thinking seems useful as a cautionary guide. Human memory is not just fallible about details, as people learn from their own experiences of misremembering, but is so malleable that a detailed, clear and vivid recollection of an event can be a total fabrication (Loftus 2017). People seek or interpret evidence in ways that are partial to their existing beliefs and expectations, often unconscious of their “confirmation bias” (Nickerson 1998). Not only are people subject to this and other cognitive biases (Kahneman 2011), of which they are typically unaware, but it may be counter-productive for one to make oneself aware of them and try consciously to counteract them or to counteract social biases such as racial or sexual stereotypes (Kenyon & Beaulac 2014). It is helpful to be aware of these facts and of the superior effectiveness of blocking the operation of biases—for example, by making an immediate record of one’s observations, refraining from forming a preliminary explanatory hypothesis, blind refereeing, double-blind randomized trials, and blind grading of students’ work. It is also helpful to be aware of the prevalence of “noise” (unwanted unsystematic variability of judgments), of how to detect noise (through a noise audit), and of how to reduce noise: make accuracy the goal, think statistically, break a process of arriving at a judgment into independent tasks, resist premature intuitions, in a group get independent judgments first, favour comparative judgments and scales (Kahneman, Sibony, & Sunstein 2021). It is helpful as well to be aware of the concept of “bounded rationality” in decision-making and of the related distinction between “satisficing” and optimizing (Simon 1956; Gigerenzer 2001).

Critical thinking about an issue requires substantive knowledge of the domain to which the issue belongs. Critical thinking abilities are not a magic elixir that can be applied to any issue whatever by somebody who has no knowledge of the facts relevant to exploring that issue. For example, the student in Bubbles needed to know that gases do not penetrate solid objects like a glass, that air expands when heated, that the volume of an enclosed gas varies directly with its temperature and inversely with its pressure, and that hot objects will spontaneously cool down to the ambient temperature of their surroundings unless kept hot by insulation or a source of heat. Critical thinkers thus need a rich fund of subject-matter knowledge relevant to the variety of situations they encounter. This fact is recognized in the inclusion among critical thinking dispositions of a concern to become and remain generally well informed.

Experimental educational interventions, with control groups, have shown that education can improve critical thinking skills and dispositions, as measured by standardized tests. For information about these tests, see the Supplement on Assessment .

What educational methods are most effective at developing the dispositions, abilities and knowledge of a critical thinker? In a comprehensive meta-analysis of experimental and quasi-experimental studies of strategies for teaching students to think critically, Abrami et al. (2015) found that dialogue, anchored instruction, and mentoring each increased the effectiveness of the educational intervention, and that they were most effective when combined. They also found that in these studies a combination of separate instruction in critical thinking with subject-matter instruction in which students are encouraged to think critically was more effective than either by itself. However, the difference was not statistically significant; that is, it might have arisen by chance.

Most of these studies lack the longitudinal follow-up required to determine whether the observed differential improvements in critical thinking abilities or dispositions continue over time, for example until high school or college graduation. For details on studies of methods of developing critical thinking skills and dispositions, see the Supplement on Educational Methods .

12. Controversies

Scholars have denied the generalizability of critical thinking abilities across subject domains, have alleged bias in critical thinking theory and pedagogy, and have investigated the relationship of critical thinking to other kinds of thinking.

McPeck (1981) attacked the thinking skills movement of the 1970s, including the critical thinking movement. He argued that there are no general thinking skills, since thinking is always thinking about some subject-matter. It is futile, he claimed, for schools and colleges to teach thinking as if it were a separate subject. Rather, teachers should lead their pupils to become autonomous thinkers by teaching school subjects in a way that brings out their cognitive structure and that encourages and rewards discussion and argument. As some of his critics (e.g., Paul 1985; Siegel 1985) pointed out, McPeck’s central argument needs elaboration, since it has obvious counter-examples in writing and speaking, for which (up to a certain level of complexity) there are teachable general abilities even though they are always about some subject-matter. To make his argument convincing, McPeck needs to explain how thinking differs from writing and speaking in a way that does not permit useful abstraction of its components from the subject-matters with which it deals. He has not done so. Nevertheless, his position that the dispositions and abilities of a critical thinker are best developed in the context of subject-matter instruction is shared by many theorists of critical thinking, including Dewey (1910, 1933), Glaser (1941), Passmore (1980), Weinstein (1990), Bailin et al. (1999b), and Willingham (2019).

McPeck’s challenge prompted reflection on the extent to which critical thinking is subject-specific. McPeck argued for a strong subject-specificity thesis, according to which it is a conceptual truth that all critical thinking abilities are specific to a subject. (He did not however extend his subject-specificity thesis to critical thinking dispositions. In particular, he took the disposition to suspend judgment in situations of cognitive dissonance to be a general disposition.) Conceptual subject-specificity is subject to obvious counter-examples, such as the general ability to recognize confusion of necessary and sufficient conditions. A more modest thesis, also endorsed by McPeck, is epistemological subject-specificity, according to which the norms of good thinking vary from one field to another. Epistemological subject-specificity clearly holds to a certain extent; for example, the principles in accordance with which one solves a differential equation are quite different from the principles in accordance with which one determines whether a painting is a genuine Picasso. But the thesis suffers, as Ennis (1989) points out, from vagueness of the concept of a field or subject and from the obvious existence of inter-field principles, however broadly the concept of a field is construed. For example, the principles of hypothetico-deductive reasoning hold for all the varied fields in which such reasoning occurs. A third kind of subject-specificity is empirical subject-specificity, according to which as a matter of empirically observable fact a person with the abilities and dispositions of a critical thinker in one area of investigation will not necessarily have them in another area of investigation.

The thesis of empirical subject-specificity raises the general problem of transfer. If critical thinking abilities and dispositions have to be developed independently in each school subject, how are they of any use in dealing with the problems of everyday life and the political and social issues of contemporary society, most of which do not fit into the framework of a traditional school subject? Proponents of empirical subject-specificity tend to argue that transfer is more likely to occur if there is critical thinking instruction in a variety of domains, with explicit attention to dispositions and abilities that cut across domains. But evidence for this claim is scanty. There is a need for well-designed empirical studies that investigate the conditions that make transfer more likely.

It is common ground in debates about the generality or subject-specificity of critical thinking dispositions and abilities that critical thinking about any topic requires background knowledge about the topic. For example, the most sophisticated understanding of the principles of hypothetico-deductive reasoning is of no help unless accompanied by some knowledge of what might be plausible explanations of some phenomenon under investigation.

Critics have objected to bias in the theory, pedagogy and practice of critical thinking. Commentators (e.g., Alston 1995; Ennis 1998) have noted that anyone who takes a position has a bias in the neutral sense of being inclined in one direction rather than others. The critics, however, are objecting to bias in the pejorative sense of an unjustified favoring of certain ways of knowing over others, frequently alleging that the unjustly favoured ways are those of a dominant sex or culture (Bailin 1995). These ways favour:

• reinforcement of egocentric and sociocentric biases over dialectical engagement with opposing world-views (Paul 1981, 1984; Warren 1998)
• distancing from the object of inquiry over closeness to it (Martin 1992; Thayer-Bacon 1992)
• indifference to the situation of others over care for them (Martin 1992)
• orientation to thought over orientation to action (Martin 1992)
• being reasonable over caring to understand people’s ideas (Thayer-Bacon 1993)
• being neutral and objective over being embodied and situated (Thayer-Bacon 1995a)
• doubting over believing (Thayer-Bacon 1995b)
• reason over emotion, imagination and intuition (Thayer-Bacon 2000)
• solitary thinking over collaborative thinking (Thayer-Bacon 2000)
• written and spoken assignments over other forms of expression (Alston 2001)
• attention to written and spoken communications over attention to human problems (Alston 2001)
• winning debates in the public sphere over making and understanding meaning (Alston 2001)

A common thread in this smorgasbord of accusations is dissatisfaction with focusing on the logical analysis and evaluation of reasoning and arguments. While these authors acknowledge that such analysis and evaluation is part of critical thinking and should be part of its conceptualization and pedagogy, they insist that it is only a part. Paul (1981), for example, bemoans the tendency of atomistic teaching of methods of analyzing and evaluating arguments to turn students into more able sophists, adept at finding fault with positions and arguments with which they disagree but even more entrenched in the egocentric and sociocentric biases with which they began. Martin (1992) and Thayer-Bacon (1992) cite with approval the self-reported intimacy with their subject-matter of leading researchers in biology and medicine, an intimacy that conflicts with the distancing allegedly recommended in standard conceptions and pedagogy of critical thinking. Thayer-Bacon (2000) contrasts the embodied and socially embedded learning of her elementary school students in a Montessori school, who used their imagination, intuition and emotions as well as their reason, with conceptions of critical thinking as

thinking that is used to critique arguments, offer justifications, and make judgments about what are the good reasons, or the right answers. (Thayer-Bacon 2000: 127–128)

Alston (2001) reports that her students in a women’s studies class were able to see the flaws in the Cinderella myth that pervades much romantic fiction but in their own romantic relationships still acted as if all failures were the woman’s fault and still accepted the notions of love at first sight and living happily ever after. Students, she writes, should

be able to connect their intellectual critique to a more affective, somatic, and ethical account of making risky choices that have sexist, racist, classist, familial, sexual, or other consequences for themselves and those both near and far… critical thinking that reads arguments, texts, or practices merely on the surface without connections to feeling/desiring/doing or action lacks an ethical depth that should infuse the difference between mere cognitive activity and something we want to call critical thinking. (Alston 2001: 34)

Some critics portray such biases as unfair to women. Thayer-Bacon (1992), for example, has charged modern critical thinking theory with being sexist, on the ground that it separates the self from the object and causes one to lose touch with one’s inner voice, and thus stigmatizes women, who (she asserts) link self to object and listen to their inner voice. Her charge does not imply that women as a group are on average less able than men to analyze and evaluate arguments. Facione (1990c) found no difference by sex in performance on his California Critical Thinking Skills Test. Kuhn (1991: 280–281) found no difference by sex in either the disposition or the competence to engage in argumentative thinking.

The critics propose a variety of remedies for the biases that they allege. In general, they do not propose to eliminate or downplay critical thinking as an educational goal. Rather, they propose to conceptualize critical thinking differently and to change its pedagogy accordingly. Their pedagogical proposals arise logically from their objections. They can be summarized as follows:

• Focus on argument networks with dialectical exchanges reflecting contesting points of view rather than on atomic arguments, so as to develop “strong sense” critical thinking that transcends egocentric and sociocentric biases (Paul 1981, 1984).
• Foster closeness to the subject-matter and feeling connected to others in order to inform a humane democracy (Martin 1992).
• Develop “constructive thinking” as a social activity in a community of physically embodied and socially embedded inquirers with personal voices who value not only reason but also imagination, intuition and emotion (Thayer-Bacon 2000).
• In developing critical thinking in school subjects, treat as important neither skills nor dispositions but opening worlds of meaning (Alston 2001).
• Attend to the development of critical thinking dispositions as well as skills, and adopt the “critical pedagogy” practised and advocated by Freire (1968 [1970]) and hooks (1994) (Dalgleish, Girard, & Davies 2017).

A common thread in these proposals is treatment of critical thinking as a social, interactive, personally engaged activity like that of a quilting bee or a barn-raising (Thayer-Bacon 2000) rather than as an individual, solitary, distanced activity symbolized by Rodin’s The Thinker . One can get a vivid description of education with the former type of goal from the writings of bell hooks (1994, 2010). Critical thinking for her is open-minded dialectical exchange across opposing standpoints and from multiple perspectives, a conception similar to Paul’s “strong sense” critical thinking (Paul 1981). She abandons the structure of domination in the traditional classroom. In an introductory course on black women writers, for example, she assigns students to write an autobiographical paragraph about an early racial memory, then to read it aloud as the others listen, thus affirming the uniqueness and value of each voice and creating a communal awareness of the diversity of the group’s experiences (hooks 1994: 84). Her “engaged pedagogy” is thus similar to the “freedom under guidance” implemented in John Dewey’s Laboratory School of Chicago in the late 1890s and early 1900s. It incorporates the dialogue, anchored instruction, and mentoring that Abrami (2015) found to be most effective in improving critical thinking skills and dispositions.

What is the relationship of critical thinking to problem solving, decision-making, higher-order thinking, creative thinking, and other recognized types of thinking? One’s answer to this question obviously depends on how one defines the terms used in the question. If critical thinking is conceived broadly to cover any careful thinking about any topic for any purpose, then problem solving and decision making will be kinds of critical thinking, if they are done carefully. Historically, ‘critical thinking’ and ‘problem solving’ were two names for the same thing. If critical thinking is conceived more narrowly as consisting solely of appraisal of intellectual products, then it will be disjoint with problem solving and decision making, which are constructive.

Bloom’s taxonomy of educational objectives used the phrase “intellectual abilities and skills” for what had been labeled “critical thinking” by some, “reflective thinking” by Dewey and others, and “problem solving” by still others (Bloom et al. 1956: 38). Thus, the so-called “higher-order thinking skills” at the taxonomy’s top levels of analysis, synthesis and evaluation are just critical thinking skills, although they do not come with general criteria for their assessment (Ennis 1981b). The revised version of Bloom’s taxonomy (Anderson et al. 2001) likewise treats critical thinking as cutting across those types of cognitive process that involve more than remembering (Anderson et al. 2001: 269–270). For details, see the Supplement on History .

As to creative thinking, it overlaps with critical thinking (Bailin 1987, 1988). Thinking about the explanation of some phenomenon or event, as in Ferryboat , requires creative imagination in constructing plausible explanatory hypotheses. Likewise, thinking about a policy question, as in Candidate , requires creativity in coming up with options. Conversely, creativity in any field needs to be balanced by critical appraisal of the draft painting or novel or mathematical theory.

• Abrami, Philip C., Robert M. Bernard, Eugene Borokhovski, David I. Waddington, C. Anne Wade, and Tonje Person, 2015, “Strategies for Teaching Students to Think Critically: A Meta-analysis”, Review of Educational Research , 85(2): 275–314. doi:10.3102/0034654314551063
• Aikin, Wilford M., 1942, The Story of the Eight-year Study, with Conclusions and Recommendations , Volume I of Adventure in American Education , New York and London: Harper & Brothers. [ Aikin 1942 available online ]
• Alston, Kal, 1995, “Begging the Question: Is Critical Thinking Biased?”, Educational Theory , 45(2): 225–233. doi:10.1111/j.1741-5446.1995.00225.x
• –––, 2001, “Re/Thinking Critical Thinking: The Seductions of Everyday Life”, Studies in Philosophy and Education , 20(1): 27–40. doi:10.1023/A:1005247128053
• American Educational Research Association, 2014, Standards for Educational and Psychological Testing / American Educational Research Association, American Psychological Association, National Council on Measurement in Education , Washington, DC: American Educational Research Association.
• Anderson, Lorin W., David R. Krathwohl, Peter W. Airiasian, Kathleen A. Cruikshank, Richard E. Mayer, Paul R. Pintrich, James Raths, and Merlin C. Wittrock, 2001, A Taxonomy for Learning, Teaching and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives , New York: Longman, complete edition.
• Bailin, Sharon, 1987, “Critical and Creative Thinking”, Informal Logic , 9(1): 23–30. [ Bailin 1987 available online ]
• –––, 1988, Achieving Extraordinary Ends: An Essay on Creativity , Dordrecht: Kluwer. doi:10.1007/978-94-009-2780-3
• –––, 1995, “Is Critical Thinking Biased? Clarifications and Implications”, Educational Theory , 45(2): 191–197. doi:10.1111/j.1741-5446.1995.00191.x
• Bailin, Sharon and Mark Battersby, 2009, “Inquiry: A Dialectical Approach to Teaching Critical Thinking”, in Juho Ritola (ed.), Argument Cultures: Proceedings of OSSA 09 , CD-ROM (pp. 1–10), Windsor, ON: OSSA. [ Bailin & Battersby 2009 available online ]
• –––, 2016a, “Fostering the Virtues of Inquiry”, Topoi , 35(2): 367–374. doi:10.1007/s11245-015-9307-6
• –––, 2016b, Reason in the Balance: An Inquiry Approach to Critical Thinking , Indianapolis: Hackett, 2nd edition.
• –––, 2021, “Inquiry: Teaching for Reasoned Judgment”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 31–46. doi: 10.1163/9789004444591_003
• Bailin, Sharon, Roland Case, Jerrold R. Coombs, and Leroi B. Daniels, 1999a, “Common Misconceptions of Critical Thinking”, Journal of Curriculum Studies , 31(3): 269–283. doi:10.1080/002202799183124
• –––, 1999b, “Conceptualizing Critical Thinking”, Journal of Curriculum Studies , 31(3): 285–302. doi:10.1080/002202799183133
• Blair, J. Anthony, 2021, Studies in Critical Thinking , Windsor, ON: Windsor Studies in Argumentation, 2nd edition. [Available online at https://windsor.scholarsportal.info/omp/index.php/wsia/catalog/book/106]
• Berman, Alan M., Seth J. Schwartz, William M. Kurtines, and Steven L. Berman, 2001, “The Process of Exploration in Identity Formation: The Role of Style and Competence”, Journal of Adolescence , 24(4): 513–528. doi:10.1006/jado.2001.0386
• Black, Beth (ed.), 2012, An A to Z of Critical Thinking , London: Continuum International Publishing Group.
• Bloom, Benjamin Samuel, Max D. Engelhart, Edward J. Furst, Walter H. Hill, and David R. Krathwohl, 1956, Taxonomy of Educational Objectives. Handbook I: Cognitive Domain , New York: David McKay.
• Boardman, Frank, Nancy M. Cavender, and Howard Kahane, 2018, Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life , Boston: Cengage, 13th edition.
• Browne, M. Neil and Stuart M. Keeley, 2018, Asking the Right Questions: A Guide to Critical Thinking , Hoboken, NJ: Pearson, 12th edition.
• Center for Assessment & Improvement of Learning, 2017, Critical Thinking Assessment Test , Cookeville, TN: Tennessee Technological University.
• Cleghorn, Paul. 2021. “Critical Thinking in the Elementary School: Practical Guidance for Building a Culture of Thinking”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessmen t, Leiden: Brill, pp. 150–167. doi: 10.1163/9789004444591_010
• Cohen, Jacob, 1988, Statistical Power Analysis for the Behavioral Sciences , Hillsdale, NJ: Lawrence Erlbaum Associates, 2nd edition.
• College Board, 1983, Academic Preparation for College. What Students Need to Know and Be Able to Do , New York: College Entrance Examination Board, ERIC document ED232517.
• Commission on the Relation of School and College of the Progressive Education Association, 1943, Thirty Schools Tell Their Story , Volume V of Adventure in American Education , New York and London: Harper & Brothers.
• Council for Aid to Education, 2017, CLA+ Student Guide . Available at http://cae.org/images/uploads/pdf/CLA_Student_Guide_Institution.pdf ; last accessed 2022 07 16.
• Dalgleish, Adam, Patrick Girard, and Maree Davies, 2017, “Critical Thinking, Bias and Feminist Philosophy: Building a Better Framework through Collaboration”, Informal Logic , 37(4): 351–369. [ Dalgleish et al. available online ]
• Dewey, John, 1910, How We Think , Boston: D.C. Heath. [ Dewey 1910 available online ]
• –––, 1916, Democracy and Education: An Introduction to the Philosophy of Education , New York: Macmillan.
• –––, 1933, How We Think: A Restatement of the Relation of Reflective Thinking to the Educative Process , Lexington, MA: D.C. Heath.
• –––, 1936, “The Theory of the Chicago Experiment”, Appendix II of Mayhew & Edwards 1936: 463–477.
• –––, 1938, Logic: The Theory of Inquiry , New York: Henry Holt and Company.
• Dominguez, Caroline (coord.), 2018a, A European Collection of the Critical Thinking Skills and Dispositions Needed in Different Professional Fields for the 21st Century , Vila Real, Portugal: UTAD. Available at http://bit.ly/CRITHINKEDUO1 ; last accessed 2022 07 16.
• ––– (coord.), 2018b, A European Review on Critical Thinking Educational Practices in Higher Education Institutions , Vila Real: UTAD. Available at http://bit.ly/CRITHINKEDUO2 ; last accessed 2022 07 16.
• ––– (coord.), 2018c, The CRITHINKEDU European Course on Critical Thinking Education for University Teachers: From Conception to Delivery , Vila Real: UTAD. Available at http:/bit.ly/CRITHINKEDU03; last accessed 2022 07 16.
• Dominguez Caroline and Rita Payan-Carreira (eds.), 2019, Promoting Critical Thinking in European Higher Education Institutions: Towards an Educational Protocol , Vila Real: UTAD. Available at http:/bit.ly/CRITHINKEDU04; last accessed 2022 07 16.
• Ennis, Robert H., 1958, “An Appraisal of the Watson-Glaser Critical Thinking Appraisal”, The Journal of Educational Research , 52(4): 155–158. doi:10.1080/00220671.1958.10882558
• –––, 1962, “A Concept of Critical Thinking: A Proposed Basis for Research on the Teaching and Evaluation of Critical Thinking Ability”, Harvard Educational Review , 32(1): 81–111.
• –––, 1981a, “A Conception of Deductive Logical Competence”, Teaching Philosophy , 4(3/4): 337–385. doi:10.5840/teachphil198143/429
• –––, 1981b, “Eight Fallacies in Bloom’s Taxonomy”, in C. J. B. Macmillan (ed.), Philosophy of Education 1980: Proceedings of the Thirty-seventh Annual Meeting of the Philosophy of Education Society , Bloomington, IL: Philosophy of Education Society, pp. 269–273.
• –––, 1984, “Problems in Testing Informal Logic, Critical Thinking, Reasoning Ability”, Informal Logic , 6(1): 3–9. [ Ennis 1984 available online ]
• –––, 1987, “A Taxonomy of Critical Thinking Dispositions and Abilities”, in Joan Boykoff Baron and Robert J. Sternberg (eds.), Teaching Thinking Skills: Theory and Practice , New York: W. H. Freeman, pp. 9–26.
• –––, 1989, “Critical Thinking and Subject Specificity: Clarification and Needed Research”, Educational Researcher , 18(3): 4–10. doi:10.3102/0013189X018003004
• –––, 1991, “Critical Thinking: A Streamlined Conception”, Teaching Philosophy , 14(1): 5–24. doi:10.5840/teachphil19911412
• –––, 1996, “Critical Thinking Dispositions: Their Nature and Assessability”, Informal Logic , 18(2–3): 165–182. [ Ennis 1996 available online ]
• –––, 1998, “Is Critical Thinking Culturally Biased?”, Teaching Philosophy , 21(1): 15–33. doi:10.5840/teachphil19982113
• –––, 2011, “Critical Thinking: Reflection and Perspective Part I”, Inquiry: Critical Thinking across the Disciplines , 26(1): 4–18. doi:10.5840/inquiryctnews20112613
• –––, 2013, “Critical Thinking across the Curriculum: The Wisdom CTAC Program”, Inquiry: Critical Thinking across the Disciplines , 28(2): 25–45. doi:10.5840/inquiryct20132828
• –––, 2016, “Definition: A Three-Dimensional Analysis with Bearing on Key Concepts”, in Patrick Bondy and Laura Benacquista (eds.), Argumentation, Objectivity, and Bias: Proceedings of the 11th International Conference of the Ontario Society for the Study of Argumentation (OSSA), 18–21 May 2016 , Windsor, ON: OSSA, pp. 1–19. Available at http://scholar.uwindsor.ca/ossaarchive/OSSA11/papersandcommentaries/105 ; last accessed 2022 07 16.
• –––, 2018, “Critical Thinking Across the Curriculum: A Vision”, Topoi , 37(1): 165–184. doi:10.1007/s11245-016-9401-4
• Ennis, Robert H., and Jason Millman, 1971, Manual for Cornell Critical Thinking Test, Level X, and Cornell Critical Thinking Test, Level Z , Urbana, IL: Critical Thinking Project, University of Illinois.
• Ennis, Robert H., Jason Millman, and Thomas Norbert Tomko, 1985, Cornell Critical Thinking Tests Level X & Level Z: Manual , Pacific Grove, CA: Midwest Publication, 3rd edition.
• –––, 2005, Cornell Critical Thinking Tests Level X & Level Z: Manual , Seaside, CA: Critical Thinking Company, 5th edition.
• Ennis, Robert H. and Eric Weir, 1985, The Ennis-Weir Critical Thinking Essay Test: Test, Manual, Criteria, Scoring Sheet: An Instrument for Teaching and Testing , Pacific Grove, CA: Midwest Publications.
• Facione, Peter A., 1990a, Critical Thinking: A Statement of Expert Consensus for Purposes of Educational Assessment and Instruction , Research Findings and Recommendations Prepared for the Committee on Pre-College Philosophy of the American Philosophical Association, ERIC Document ED315423.
• –––, 1990b, California Critical Thinking Skills Test, CCTST – Form A , Millbrae, CA: The California Academic Press.
• –––, 1990c, The California Critical Thinking Skills Test--College Level. Technical Report #3. Gender, Ethnicity, Major, CT Self-Esteem, and the CCTST , ERIC Document ED326584.
• –––, 1992, California Critical Thinking Skills Test: CCTST – Form B, Millbrae, CA: The California Academic Press.
• –––, 2000, “The Disposition Toward Critical Thinking: Its Character, Measurement, and Relationship to Critical Thinking Skill”, Informal Logic , 20(1): 61–84. [ Facione 2000 available online ]
• Facione, Peter A. and Noreen C. Facione, 1992, CCTDI: A Disposition Inventory , Millbrae, CA: The California Academic Press.
• Facione, Peter A., Noreen C. Facione, and Carol Ann F. Giancarlo, 2001, California Critical Thinking Disposition Inventory: CCTDI: Inventory Manual , Millbrae, CA: The California Academic Press.
• Facione, Peter A., Carol A. Sánchez, and Noreen C. Facione, 1994, Are College Students Disposed to Think? , Millbrae, CA: The California Academic Press. ERIC Document ED368311.
• Fisher, Alec, and Michael Scriven, 1997, Critical Thinking: Its Definition and Assessment , Norwich: Centre for Research in Critical Thinking, University of East Anglia.
• Freire, Paulo, 1968 [1970], Pedagogia do Oprimido . Translated as Pedagogy of the Oppressed , Myra Bergman Ramos (trans.), New York: Continuum, 1970.
• Gigerenzer, Gerd, 2001, “The Adaptive Toolbox”, in Gerd Gigerenzer and Reinhard Selten (eds.), Bounded Rationality: The Adaptive Toolbox , Cambridge, MA: MIT Press, pp. 37–50.
• Glaser, Edward Maynard, 1941, An Experiment in the Development of Critical Thinking , New York: Bureau of Publications, Teachers College, Columbia University.
• Groarke, Leo A. and Christopher W. Tindale, 2012, Good Reasoning Matters! A Constructive Approach to Critical Thinking , Don Mills, ON: Oxford University Press, 5th edition.
• Halpern, Diane F., 1998, “Teaching Critical Thinking for Transfer Across Domains: Disposition, Skills, Structure Training, and Metacognitive Monitoring”, American Psychologist , 53(4): 449–455. doi:10.1037/0003-066X.53.4.449
• –––, 2016, Manual: Halpern Critical Thinking Assessment , Mödling, Austria: Schuhfried. Available at https://pdfcoffee.com/hcta-test-manual-pdf-free.html; last accessed 2022 07 16.
• Hamby, Benjamin, 2014, The Virtues of Critical Thinkers , Doctoral dissertation, Philosophy, McMaster University. [ Hamby 2014 available online ]
• –––, 2015, “Willingness to Inquire: The Cardinal Critical Thinking Virtue”, in Martin Davies and Ronald Barnett (eds.), The Palgrave Handbook of Critical Thinking in Higher Education , New York: Palgrave Macmillan, pp. 77–87.
• Haran, Uriel, Ilana Ritov, and Barbara A. Mellers, 2013, “The Role of Actively Open-minded Thinking in Information Acquisition, Accuracy, and Calibration”, Judgment and Decision Making , 8(3): 188–201.
• Hatcher, Donald and Kevin Possin, 2021, “Commentary: Thinking Critically about Critical Thinking Assessment”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 298–322. doi: 10.1163/9789004444591_017
• Haynes, Ada, Elizabeth Lisic, Kevin Harris, Katie Leming, Kyle Shanks, and Barry Stein, 2015, “Using the Critical Thinking Assessment Test (CAT) as a Model for Designing Within-Course Assessments: Changing How Faculty Assess Student Learning”, Inquiry: Critical Thinking Across the Disciplines , 30(3): 38–48. doi:10.5840/inquiryct201530316
• Haynes, Ada and Barry Stein, 2021, “Observations from a Long-Term Effort to Assess and Improve Critical Thinking”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 231–254. doi: 10.1163/9789004444591_014
• Hiner, Amanda L. 2021. “Equipping Students for Success in College and Beyond: Placing Critical Thinking Instruction at the Heart of a General Education Program”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 188–208. doi: 10.1163/9789004444591_012
• Hitchcock, David, 2017, “Critical Thinking as an Educational Ideal”, in his On Reasoning and Argument: Essays in Informal Logic and on Critical Thinking , Dordrecht: Springer, pp. 477–497. doi:10.1007/978-3-319-53562-3_30
• –––, 2021, “Seven Philosophical Implications of Critical Thinking: Themes, Variations, Implications”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 9–30. doi: 10.1163/9789004444591_002
• hooks, bell, 1994, Teaching to Transgress: Education as the Practice of Freedom , New York and London: Routledge.
• –––, 2010, Teaching Critical Thinking: Practical Wisdom , New York and London: Routledge.
• Johnson, Ralph H., 1992, “The Problem of Defining Critical Thinking”, in Stephen P, Norris (ed.), The Generalizability of Critical Thinking , New York: Teachers College Press, pp. 38–53.
• Kahane, Howard, 1971, Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life , Belmont, CA: Wadsworth.
• Kahneman, Daniel, 2011, Thinking, Fast and Slow , New York: Farrar, Straus and Giroux.
• Kahneman, Daniel, Olivier Sibony, & Cass R. Sunstein, 2021, Noise: A Flaw in Human Judgment , New York: Little, Brown Spark.
• Kenyon, Tim, and Guillaume Beaulac, 2014, “Critical Thinking Education and Debasing”, Informal Logic , 34(4): 341–363. [ Kenyon & Beaulac 2014 available online ]
• Krathwohl, David R., Benjamin S. Bloom, and Bertram B. Masia, 1964, Taxonomy of Educational Objectives, Handbook II: Affective Domain , New York: David McKay.
• Kuhn, Deanna, 1991, The Skills of Argument , New York: Cambridge University Press. doi:10.1017/CBO9780511571350
• –––, 2019, “Critical Thinking as Discourse”, Human Development, 62 (3): 146–164. doi:10.1159/000500171
• Lipman, Matthew, 1987, “Critical Thinking–What Can It Be?”, Analytic Teaching , 8(1): 5–12. [ Lipman 1987 available online ]
• –––, 2003, Thinking in Education , Cambridge: Cambridge University Press, 2nd edition.
• Loftus, Elizabeth F., 2017, “Eavesdropping on Memory”, Annual Review of Psychology , 68: 1–18. doi:10.1146/annurev-psych-010416-044138
• Makaiau, Amber Strong, 2021, “The Good Thinker’s Tool Kit: How to Engage Critical Thinking and Reasoning in Secondary Education”, in Daniel Fasko, Jr. and Frank Fair (eds.), Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment , Leiden: Brill, pp. 168–187. doi: 10.1163/9789004444591_011
• Martin, Jane Roland, 1992, “Critical Thinking for a Humane World”, in Stephen P. Norris (ed.), The Generalizability of Critical Thinking , New York: Teachers College Press, pp. 163–180.
• Mayhew, Katherine Camp, and Anna Camp Edwards, 1936, The Dewey School: The Laboratory School of the University of Chicago, 1896–1903 , New York: Appleton-Century. [ Mayhew & Edwards 1936 available online ]
• McPeck, John E., 1981, Critical Thinking and Education , New York: St. Martin’s Press.
• Moore, Brooke Noel and Richard Parker, 2020, Critical Thinking , New York: McGraw-Hill, 13th edition.
• Nickerson, Raymond S., 1998, “Confirmation Bias: A Ubiquitous Phenomenon in Many Guises”, Review of General Psychology , 2(2): 175–220. doi:10.1037/1089-2680.2.2.175
• Nieto, Ana Maria, and Jorge Valenzuela, 2012, “A Study of the Internal Structure of Critical Thinking Dispositions”, Inquiry: Critical Thinking across the Disciplines , 27(1): 31–38. doi:10.5840/inquiryct20122713
• Norris, Stephen P., 1985, “Controlling for Background Beliefs When Developing Multiple-choice Critical Thinking Tests”, Educational Measurement: Issues and Practice , 7(3): 5–11. doi:10.1111/j.1745-3992.1988.tb00437.x
• Norris, Stephen P. and Robert H. Ennis, 1989, Evaluating Critical Thinking (The Practitioners’ Guide to Teaching Thinking Series), Pacific Grove, CA: Midwest Publications.
• Norris, Stephen P. and Ruth Elizabeth King, 1983, Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland.
• –––, 1984, The Design of a Critical Thinking Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland. ERIC Document ED260083.
• –––, 1985, Test on Appraising Observations: Manual , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland.
• –––, 1990a, Test on Appraising Observations , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland, 2nd edition.
• –––, 1990b, Test on Appraising Observations: Manual , St. John’s, NL: Institute for Educational Research and Development, Memorial University of Newfoundland, 2nd edition.
• OCR [Oxford, Cambridge and RSA Examinations], 2011, AS/A Level GCE: Critical Thinking – H052, H452 , Cambridge: OCR. Past papers available at https://pastpapers.co/ocr/?dir=A-Level/Critical-Thinking-H052-H452; last accessed 2022 07 16.
• Ontario Ministry of Education, 2013, The Ontario Curriculum Grades 9 to 12: Social Sciences and Humanities . Available at http://www.edu.gov.on.ca/eng/curriculum/secondary/ssciences9to122013.pdf ; last accessed 2022 07 16.
• Passmore, John Arthur, 1980, The Philosophy of Teaching , London: Duckworth.
• Paul, Richard W., 1981, “Teaching Critical Thinking in the ‘Strong’ Sense: A Focus on Self-Deception, World Views, and a Dialectical Mode of Analysis”, Informal Logic , 4(2): 2–7. [ Paul 1981 available online ]
• –––, 1984, “Critical Thinking: Fundamental to Education for a Free Society”, Educational Leadership , 42(1): 4–14.
• –––, 1985, “McPeck’s Mistakes”, Informal Logic , 7(1): 35–43. [ Paul 1985 available online ]
• Paul, Richard W. and Linda Elder, 2006, The Miniature Guide to Critical Thinking: Concepts and Tools , Dillon Beach, CA: Foundation for Critical Thinking, 4th edition.
• Payette, Patricia, and Edna Ross, 2016, “Making a Campus-Wide Commitment to Critical Thinking: Insights and Promising Practices Utilizing the Paul-Elder Approach at the University of Louisville”, Inquiry: Critical Thinking Across the Disciplines , 31(1): 98–110. doi:10.5840/inquiryct20163118
• Possin, Kevin, 2008, “A Field Guide to Critical-Thinking Assessment”, Teaching Philosophy , 31(3): 201–228. doi:10.5840/teachphil200831324
• –––, 2013a, “Some Problems with the Halpern Critical Thinking Assessment (HCTA) Test”, Inquiry: Critical Thinking across the Disciplines , 28(3): 4–12. doi:10.5840/inquiryct201328313
• –––, 2013b, “A Serious Flaw in the Collegiate Learning Assessment (CLA) Test”, Informal Logic , 33(3): 390–405. [ Possin 2013b available online ]
• –––, 2013c, “A Fatal Flaw in the Collegiate Learning Assessment Test”, Assessment Update , 25 (1): 8–12.
• –––, 2014, “Critique of the Watson-Glaser Critical Thinking Appraisal Test: The More You Know, the Lower Your Score”, Informal Logic , 34(4): 393–416. [ Possin 2014 available online ]
• –––, 2020, “CAT Scan: A Critical Review of the Critical-Thinking Assessment Test”, Informal Logic , 40 (3): 489–508. [Available online at https://informallogic.ca/index.php/informal_logic/article/view/6243]
• Rawls, John, 1971, A Theory of Justice , Cambridge, MA: Harvard University Press.
• Rear, David, 2019, “One Size Fits All? The Limitations of Standardised Assessment in Critical Thinking”, Assessment & Evaluation in Higher Education , 44(5): 664–675. doi: 10.1080/02602938.2018.1526255
• Rousseau, Jean-Jacques, 1762, Émile , Amsterdam: Jean Néaulme.
• Scheffler, Israel, 1960, The Language of Education , Springfield, IL: Charles C. Thomas.
• Scriven, Michael, and Richard W. Paul, 1987, Defining Critical Thinking , Draft statement written for the National Council for Excellence in Critical Thinking Instruction. Available at http://www.criticalthinking.org/pages/defining-critical-thinking/766 ; last accessed 2022 07 16.
• Sheffield, Clarence Burton Jr., 2018, “Promoting Critical Thinking in Higher Education: My Experiences as the Inaugural Eugene H. Fram Chair in Applied Critical Thinking at Rochester Institute of Technology”, Topoi , 37(1): 155–163. doi:10.1007/s11245-016-9392-1
• Siegel, Harvey, 1985, “McPeck, Informal Logic and the Nature of Critical Thinking”, in David Nyberg (ed.), Philosophy of Education 1985: Proceedings of the Forty-First Annual Meeting of the Philosophy of Education Society , Normal, IL: Philosophy of Education Society, pp. 61–72.
• –––, 1988, Educating Reason: Rationality, Critical Thinking, and Education , New York: Routledge.
• –––, 1999, “What (Good) Are Thinking Dispositions?”, Educational Theory , 49(2): 207–221. doi:10.1111/j.1741-5446.1999.00207.x
• Simon, Herbert A., 1956, “Rational Choice and the Structure of the Environment”, Psychological Review , 63(2): 129–138. doi: 10.1037/h0042769
• Simpson, Elizabeth, 1966–67, “The Classification of Educational Objectives: Psychomotor Domain”, Illinois Teacher of Home Economics , 10(4): 110–144, ERIC document ED0103613. [ Simpson 1966–67 available online ]
• Skolverket, 2018, Curriculum for the Compulsory School, Preschool Class and School-age Educare , Stockholm: Skolverket, revised 2018. Available at https://www.skolverket.se/download/18.31c292d516e7445866a218f/1576654682907/pdf3984.pdf; last accessed 2022 07 15.
• Smith, B. Othanel, 1953, “The Improvement of Critical Thinking”, Progressive Education , 30(5): 129–134.
• Smith, Eugene Randolph, Ralph Winfred Tyler, and the Evaluation Staff, 1942, Appraising and Recording Student Progress , Volume III of Adventure in American Education , New York and London: Harper & Brothers.
• Splitter, Laurance J., 1987, “Educational Reform through Philosophy for Children”, Thinking: The Journal of Philosophy for Children , 7(2): 32–39. doi:10.5840/thinking1987729
• Stanovich Keith E., and Paula J. Stanovich, 2010, “A Framework for Critical Thinking, Rational Thinking, and Intelligence”, in David D. Preiss and Robert J. Sternberg (eds), Innovations in Educational Psychology: Perspectives on Learning, Teaching and Human Development , New York: Springer Publishing, pp 195–237.
• Stanovich Keith E., Richard F. West, and Maggie E. Toplak, 2011, “Intelligence and Rationality”, in Robert J. Sternberg and Scott Barry Kaufman (eds.), Cambridge Handbook of Intelligence , Cambridge: Cambridge University Press, 3rd edition, pp. 784–826. doi:10.1017/CBO9780511977244.040
• Tankersley, Karen, 2005, Literacy Strategies for Grades 4–12: Reinforcing the Threads of Reading , Alexandria, VA: Association for Supervision and Curriculum Development.
• Thayer-Bacon, Barbara J., 1992, “Is Modern Critical Thinking Theory Sexist?”, Inquiry: Critical Thinking Across the Disciplines , 10(1): 3–7. doi:10.5840/inquiryctnews199210123
• –––, 1993, “Caring and Its Relationship to Critical Thinking”, Educational Theory , 43(3): 323–340. doi:10.1111/j.1741-5446.1993.00323.x
• –––, 1995a, “Constructive Thinking: Personal Voice”, Journal of Thought , 30(1): 55–70.
• –––, 1995b, “Doubting and Believing: Both are Important for Critical Thinking”, Inquiry: Critical Thinking across the Disciplines , 15(2): 59–66. doi:10.5840/inquiryctnews199515226
• –––, 2000, Transforming Critical Thinking: Thinking Constructively , New York: Teachers College Press.
• Toulmin, Stephen Edelston, 1958, The Uses of Argument , Cambridge: Cambridge University Press.
• Turri, John, Mark Alfano, and John Greco, 2017, “Virtue Epistemology”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Winter 2017 Edition). URL = < https://plato.stanford.edu/archives/win2017/entries/epistemology-virtue/ >
• Vincent-Lancrin, Stéphan, Carlos González-Sancho, Mathias Bouckaert, Federico de Luca, Meritxell Fernández-Barrerra, Gwénaël Jacotin, Joaquin Urgel, and Quentin Vidal, 2019, Fostering Students’ Creativity and Critical Thinking: What It Means in School. Educational Research and Innovation , Paris: OECD Publishing.
• Warren, Karen J. 1988. “Critical Thinking and Feminism”, Informal Logic , 10(1): 31–44. [ Warren 1988 available online ]
• Watson, Goodwin, and Edward M. Glaser, 1980a, Watson-Glaser Critical Thinking Appraisal, Form A , San Antonio, TX: Psychological Corporation.
• –––, 1980b, Watson-Glaser Critical Thinking Appraisal: Forms A and B; Manual , San Antonio, TX: Psychological Corporation,
• –––, 1994, Watson-Glaser Critical Thinking Appraisal, Form B , San Antonio, TX: Psychological Corporation.
• Weinstein, Mark, 1990, “Towards a Research Agenda for Informal Logic and Critical Thinking”, Informal Logic , 12(3): 121–143. [ Weinstein 1990 available online ]
• –––, 2013, Logic, Truth and Inquiry , London: College Publications.
• Willingham, Daniel T., 2019, “How to Teach Critical Thinking”, Education: Future Frontiers , 1: 1–17. [Available online at https://prod65.education.nsw.gov.au/content/dam/main-education/teaching-and-learning/education-for-a-changing-world/media/documents/How-to-teach-critical-thinking-Willingham.pdf.]
• Zagzebski, Linda Trinkaus, 1996, Virtues of the Mind: An Inquiry into the Nature of Virtue and the Ethical Foundations of Knowledge , Cambridge: Cambridge University Press. doi:10.1017/CBO9781139174763

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• The Nature of Critical Thinking: An Outline of Critical Thinking Dispositions and Abilities , by Robert H. Ennis

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Critical Thinking: A Model of Intelligence for Solving Real-World Problems

Diane f. halpern.

1 Department of Psychology, Claremont McKenna College, Emerita, Altadena, CA 91001, USA

Dana S. Dunn

2 Department of Psychology, Moravian College, Bethlehem, PA 18018, USA; ude.naivarom@nnud

Most theories of intelligence do not directly address the question of whether people with high intelligence can successfully solve real world problems. A high IQ is correlated with many important outcomes (e.g., academic prominence, reduced crime), but it does not protect against cognitive biases, partisan thinking, reactance, or confirmation bias, among others. There are several newer theories that directly address the question about solving real-world problems. Prominent among them is Sternberg’s adaptive intelligence with “adaptation to the environment” as the central premise, a construct that does not exist on standardized IQ tests. Similarly, some scholars argue that standardized tests of intelligence are not measures of rational thought—the sort of skill/ability that would be needed to address complex real-world problems. Other investigators advocate for critical thinking as a model of intelligence specifically designed for addressing real-world problems. Yes, intelligence (i.e., critical thinking) can be enhanced and used for solving a real-world problem such as COVID-19, which we use as an example of contemporary problems that need a new approach.

1. Introduction

The editors of this Special Issue asked authors to respond to a deceptively simple statement: “How Intelligence Can Be a Solution to Consequential World Problems.” This statement holds many complexities, including how intelligence is defined and which theories are designed to address real-world problems.

2. The Problem with Using Standardized IQ Measures for Real-World Problems

For the most part, we identify high intelligence as having a high score on a standardized test of intelligence. Like any test score, IQ can only reflect what is on the given test. Most contemporary standardized measures of intelligence include vocabulary, working memory, spatial skills, analogies, processing speed, and puzzle-like elements (e.g., Wechsler Adult Intelligence Scale Fourth Edition; see ( Drozdick et al. 2012 )). Measures of IQ correlate with many important outcomes, including academic performance ( Kretzschmar et al. 2016 ), job-related skills ( Hunter and Schmidt 1996 ), reduced likelihood of criminal behavior ( Burhan et al. 2014 ), and for those with exceptionally high IQs, obtaining a doctorate and publishing scholarly articles ( McCabe et al. 2020 ). Gottfredson ( 1997, p. 81 ) summarized these effects when she said the “predictive validity of g is ubiquitous.” More recent research using longitudinal data, found that general mental abilities and specific abilities are good predictors of several work variables including job prestige, and income ( Lang and Kell 2020 ). Although assessments of IQ are useful in many contexts, having a high IQ does not protect against falling for common cognitive fallacies (e.g., blind spot bias, reactance, anecdotal reasoning), relying on biased and blatantly one-sided information sources, failing to consider information that does not conform to one’s preferred view of reality (confirmation bias), resisting pressure to think and act in a certain way, among others. This point was clearly articulated by Stanovich ( 2009, p. 3 ) when he stated that,” IQ tests measure only a small set of the thinking abilities that people need.”

3. Which Theories of Intelligence Are Relevant to the Question?

Most theories of intelligence do not directly address the question of whether people with high intelligence can successfully solve real world problems. For example, Grossmann et al. ( 2013 ) cite many studies in which IQ scores have not predicted well-being, including life satisfaction and longevity. Using a stratified random sample of Americans, these investigators found that wise reasoning is associated with life satisfaction, and that “there was no association between intelligence and well-being” (p. 944). (critical thinking [CT] is often referred to as “wise reasoning” or “rational thinking,”). Similar results were reported by Wirthwein and Rost ( 2011 ) who compared life satisfaction in several domains for gifted adults and adults of average intelligence. There were no differences in any of the measures of subjective well-being, except for leisure, which was significantly lower for the gifted adults. Additional research in a series of experiments by Stanovich and West ( 2008 ) found that participants with high cognitive ability were as likely as others to endorse positions that are consistent with their biases, and they were equally likely to prefer one-sided arguments over those that provided a balanced argument. There are several newer theories that directly address the question about solving real-world problems. Prominent among them is Sternberg’s adaptive intelligence with “adaptation to the environment” as the central premise, a construct that does not exist on standardized IQ tests (e.g., Sternberg 2019 ). Similarly, Stanovich and West ( 2014 ) argue that standardized tests of intelligence are not measures of rational thought—the sort of skill/ability that would be needed to address complex real-world problems. Halpern and Butler ( 2020 ) advocate for CT as a useful model of intelligence for addressing real-world problems because it was designed for this purpose. Although there is much overlap among these more recent theories, often using different terms for similar concepts, we use Halpern and Butler’s conceptualization to make our point: Yes, intelligence (i.e., CT) can be enhanced and used for solving a real-world problem like COVID-19.

4. Critical Thinking as an Applied Model for Intelligence

One definition of intelligence that directly addresses the question about intelligence and real-world problem solving comes from Nickerson ( 2020, p. 205 ): “the ability to learn, to reason well, to solve novel problems, and to deal effectively with novel problems—often unpredictable—that confront one in daily life.” Using this definition, the question of whether intelligent thinking can solve a world problem like the novel coronavirus is a resounding “yes” because solutions to real-world novel problems are part of his definition. This is a popular idea in the general public. For example, over 1000 business managers and hiring executives said that they want employees who can think critically based on the belief that CT skills will help them solve work-related problems ( Hart Research Associates 2018 ).

We define CT as the use of those cognitive skills or strategies that increase the probability of a desirable outcome. It is used to describe thinking that is purposeful, reasoned, and goal directed--the kind of thinking involved in solving problems, formulating inferences, calculating likelihoods, and making decisions, when the thinker is using skills that are thoughtful and effective for the particular context and type of thinking task. International surveys conducted by the OECD ( 2019, p. 16 ) established “key information-processing competencies” that are “highly transferable, in that they are relevant to many social contexts and work situations; and ‘learnable’ and therefore subject to the influence of policy.” One of these skills is problem solving, which is one subset of CT skills.

The CT model of intelligence is comprised of two components: (1) understanding information at a deep, meaningful level and (2) appropriate use of CT skills. The underlying idea is that CT skills can be identified, taught, and learned, and when they are recognized and applied in novel settings, the individual is demonstrating intelligent thought. CT skills include judging the credibility of an information source, making cost–benefit calculations, recognizing regression to the mean, understanding the limits of extrapolation, muting reactance responses, using analogical reasoning, rating the strength of reasons that support and fail to support a conclusion, and recognizing hindsight bias or confirmation bias, among others. Critical thinkers use these skills appropriately, without prompting, and usually with conscious intent in a variety of settings.

One of the key concepts in this model is that CT skills transfer in appropriate situations. Thus, assessments using situational judgments are needed to assess whether particular skills have transferred to a novel situation where it is appropriate. In an assessment created by the first author ( Halpern 2018 ), short paragraphs provide information about 20 different everyday scenarios (e.g., A speaker at the meeting of your local school board reported that when drug use rises, grades decline; so schools need to enforce a “war on drugs” to improve student grades); participants provide two response formats for every scenario: (a) constructed responses where they respond with short written responses, followed by (b) forced choice responses (e.g., multiple choice, rating or ranking of alternatives) for the same situations.

There is a large and growing empirical literature to support the assertion that CT skills can be learned and will transfer (when taught for transfer). See for example, Holmes et al. ( 2015 ), who wrote in the prestigious Proceedings of the National Academy of Sciences , that there was “significant and sustained improvement in students’ critical thinking behavior” (p. 11,199) for students who received CT instruction. Abrami et al. ( 2015, para. 1 ) concluded from a meta-analysis that “there are effective strategies for teaching CT skills, both generic and content specific, and CT dispositions, at all educational levels and across all disciplinary areas.” Abrami et al. ( 2008, para. 1 ), included 341 effect sizes in a meta-analysis. They wrote: “findings make it clear that improvement in students’ CT skills and dispositions cannot be a matter of implicit expectation.” A strong test of whether CT skills can be used for real-word problems comes from research by Butler et al. ( 2017 ). Community adults and college students (N = 244) completed several scales including an assessment of CT, an intelligence test, and an inventory of real-life events. Both CT scores and intelligence scores predicted individual outcomes on the inventory of real-life events, but CT was a stronger predictor.

Heijltjes et al. ( 2015, p. 487 ) randomly assigned participants to either a CT instruction group or one of six other control conditions. They found that “only participants assigned to CT instruction improved their reasoning skills.” Similarly, when Halpern et al. ( 2012 ) used random assignment of participants to either a learning group where they were taught scientific reasoning skills using a game format or a control condition (which also used computerized learning and was similar in length), participants in the scientific skills learning group showed higher proportional learning gains than students who did not play the game. As the body of additional supportive research is too large to report here, interested readers can find additional lists of CT skills and support for the assertion that these skills can be learned and will transfer in Halpern and Dunn ( Forthcoming ). There is a clear need for more high-quality research on the application and transfer of CT and its relationship to IQ.

5. Pandemics: COVID-19 as a Consequential Real-World Problem

A pandemic occurs when a disease runs rampant over an entire country or even the world. Pandemics have occurred throughout history: At the time of writing this article, COVID-19 is a world-wide pandemic whose actual death rate is unknown but estimated with projections of several million over the course of 2021 and beyond ( Mega 2020 ). Although vaccines are available, it will take some time to inoculate most or much of the world’s population. Since March 2020, national and international health agencies have created a list of actions that can slow and hopefully stop the spread of COVID (e.g., wearing face masks, practicing social distancing, avoiding group gatherings), yet many people in the United States and other countries have resisted their advice.

Could instruction in CT encourage more people to accept and comply with simple life-saving measures? There are many possible reasons to believe that by increasing citizens’ CT abilities, this problematic trend can be reversed for, at least, some unknown percentage of the population. We recognize the long history of social and cognitive research showing that changing attitudes and behaviors is difficult, and it would be unrealistic to expect that individuals with extreme beliefs supported by their social group and consistent with their political ideologies are likely to change. For example, an Iranian cleric and an orthodox rabbi both claimed (separately) that the COVID-19 vaccine can make people gay ( Marr 2021 ). These unfounded opinions are based on deeply held prejudicial beliefs that we expect to be resistant to CT. We are targeting those individuals who beliefs are less extreme and may be based on reasonable reservations, such as concern about the hasty development of the vaccine and the lack of long-term data on its effects. There should be some unknown proportion of individuals who can change their COVID-19-related beliefs and actions with appropriate instruction in CT. CT can be a (partial) antidote for the chaos of the modern world with armies of bots creating content on social media, political and other forces deliberately attempting to confuse issues, and almost all media labeled “fake news” by social influencers (i.e., people with followers that sometimes run to millions on various social media). Here, are some CT skills that could be helpful in getting more people to think more critically about pandemic-related issues.

Reasoning by Analogy and Judging the Credibility of the Source of Information

Early communications about the ability of masks to prevent the spread of COVID from national health agencies were not consistent. In many regions of the world, the benefits of wearing masks incited prolonged and acrimonious debates ( Tang 2020 ). However, after the initial confusion, virtually all of the global and national health organizations (e.g., WHO, National Health Service in the U. K., U. S. Centers for Disease Control and Prevention) endorse masks as a way to slow the spread of COVID ( Cheng et al. 2020 ; Chu et al. 2020 ). However, as we know, some people do not trust governmental agencies and often cite the conflicting information that was originally given as a reason for not wearing a mask. There are varied reasons for refusing to wear a mask, but the one most often cited is that it is against civil liberties ( Smith 2020 ). Reasoning by analogy is an appropriate CT skill for evaluating this belief (and a key skill in legal thinking). It might be useful to cite some of the many laws that already regulate our behavior such as, requiring health inspections for restaurants, setting speed limits, mandating seat belts when riding in a car, and establishing the age at which someone can consume alcohol. Individuals would be asked to consider how the mandate to wear a mask compares to these and other regulatory laws.

Another reason why some people resist the measures suggested by virtually every health agency concerns questions about whom to believe. Could training in CT change the beliefs and actions of even a small percentage of those opposed to wearing masks? Such training would include considering the following questions with practice across a wide domain of knowledge: (a) Does the source have sufficient expertise? (b) Is the expertise recent and relevant? (c) Is there a potential for gain by the information source, such as financial gain? (d) What would the ideal information source be and how close is the current source to the ideal? (e) Does the information source offer evidence that what they are recommending is likely to be correct? (f) Have you traced URLs to determine if the information in front of you really came from the alleged source?, etc. Of course, not everyone will respond in the same way to each question, so there is little likelihood that we would all think alike, but these questions provide a framework for evaluating credibility. Donovan et al. ( 2015 ) were successful using a similar approach to improve dynamic decision-making by asking participants to reflect on questions that relate to the decision. Imagine the effect of rigorous large-scale education in CT from elementary through secondary schools, as well as at the university-level. As stated above, empirical evidence has shown that people can become better thinkers with appropriate instruction in CT. With training, could we encourage some portion of the population to become more astute at judging the credibility of a source of information? It is an experiment worth trying.

6. Making Cost—Benefit Assessments for Actions That Would Slow the Spread of COVID-19

Historical records show that refusal to wear a mask during a pandemic is not a new reaction. The epidemic of 1918 also included mandates to wear masks, which drew public backlash. Then, as now, many people refused, even when they were told that it was a symbol of “wartime patriotism” because the 1918 pandemic occurred during World War I ( Lovelace 2020 ). CT instruction would include instruction in why and how to compute cost–benefit analyses. Estimates of “lives saved” by wearing a mask can be made meaningful with graphical displays that allow more people to understand large numbers. Gigerenzer ( 2020 ) found that people can understand risk ratios in medicine when the numbers are presented as frequencies instead of probabilities. If this information were used when presenting the likelihood of illness and death from COVID-19, could we increase the numbers of people who understand the severity of this disease? Small scale studies by Gigerenzer have shown that it is possible.

Analyzing Arguments to Determine Degree of Support for a Conclusion

The process of analyzing arguments requires that individuals rate the strength of support for and against a conclusion. By engaging in this practice, they must consider evidence and reasoning that may run counter to a preferred outcome. Kozyreva et al. ( 2020 ) call the deliberate failure to consider both supporting and conflicting data “deliberate ignorance”—avoiding or failing to consider information that could be useful in decision-making because it may collide with an existing belief. When applied to COVID-19, people would have to decide if the evidence for and against wearing a face mask is a reasonable way to stop the spread of this disease, and if they conclude that it is not, what are the costs and benefits of not wearing masks at a time when governmental health organizations are making them mandatory in public spaces? Again, we wonder if rigorous and systematic instruction in argument analysis would result in more positive attitudes and behaviors that relate to wearing a mask or other real-world problems. We believe that it is an experiment worth doing.

7. Conclusions

We believe that teaching CT is a worthwhile approach for educating the general public in order to improve reasoning and motivate actions to address, avert, or ameliorate real-world problems like the COVID-19 pandemic. Evidence suggests that CT can guide intelligent responses to societal and global problems. We are NOT claiming that CT skills will be a universal solution for the many real-world problems that we confront in contemporary society, or that everyone will substitute CT for other decision-making practices, but we do believe that systematic education in CT can help many people become better thinkers, and we believe that this is an important step toward creating a society that values and practices routine CT. The challenges are great, but the tools to tackle them are available, if we are willing to use them.

Author Contributions

Conceptualization, D.F.H. and D.S.D.; resources, D.F.H.; data curation, writing—original draft preparation, D.F.H.; writing—review and editing, D.F.H. and D.S.D. All authors have read and agreed to the published version of the manuscript.

This research received no external funding.

Institutional Review Board Statement

No IRB Review.

Informed Consent Statement

No Informed Consent.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

• Abrami Philip C., Bernard Robert M., Borokhovski Evgueni, Wade C. Anne, Surkes Michael A., Tamim Rana, Zhang Dai. Instructional interventions affecting critical thinking skills and dispositions: A Stage 1 meta-analysis. Review of Educational Research. 2008; 78 :1102–34. doi: 10.3102/0034654308326084. [ CrossRef ] [ Google Scholar ]
• Abrami Philip C., Bernard Robert M., Borokhovski Evgueni, Waddington David I., Wade C. Anne. Strategies for teaching students to think critically: A meta-analysis. Review of Educational Research. 2015; 85 :275–341. doi: 10.3102/0034654314551063. [ CrossRef ] [ Google Scholar ]
• Burhan Nik Ahmad Sufian, Kurniawan Yohan, Sidek Abdul Halim, Mohamad Mohd Rosli. Crimes and the Bell curve: Th e role of people with high, average, and low intelligence. Intelligence. 2014; 47 :12–22. doi: 10.1016/j.intell.2014.08.005. [ CrossRef ] [ Google Scholar ]
• Butler Heather A., Pentoney Christopher, Bong Maebelle P. Predicting real-world outcomes: Critical thinking ability is a better predictor of life decisions than intelligence. Thinking Skills and Creativity. 2017; 25 :38–46. doi: 10.1016/j.tsc.2017.06.005. [ CrossRef ] [ Google Scholar ]
• Cheng Vincent Chi-Chung, Wong Shuk-Ching, Chuang Vivien Wai-Man, So Simon Yung-Chun, Chen Jonathan Hon-Kwan, Sridhar Sidharth, To Kelvin Kai-Wwang, Chan Jasper Fuk-Wu, Hung Ivan Fan-Ngai, Ho Pak-Leung, et al. The role of community-wide wearing of face mask for control of coronavirus disease 2019 (COVID-19) epidemic due to SARS-CoV-2. Journal of Infectious Disease. 2020; 81 :107–14. doi: 10.1016/j.jinf.2020.04.024. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Chu Derek K., Aki Elie A., Duda Stephanie, Solo Karla, Yaacoub Sally, Schunemann Holger J. Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: A system atic review and meta-analysis. Lancet. 2020; 395 :1973–87. doi: 10.1016/S0140-6736(20)31142-9. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Donovan Sarah J., Guss C. Dominick, Naslund Dag. Improving dynamic decision-making through training and self-re flection. Judgment and Decision Making. 2015; 10 :284–95. [ Google Scholar ]
• Drozdick Lisa Whipple, Wahlstrom Dustin, Zhu Jianjun, Weiss Lawrence G. The Wechsler Adult Intelligence Scale—Fourth Edition and the Wechsler Memory Scale—Fourth Edition. In: Flanagan Dawn P., Harrison Patti L., editors. Contemporary Intellectual as Sessment: Theories, Tests, and Issues. The Guilford Press; New York: 2012. pp. 197–223. [ Google Scholar ]
• Gigerenzer Gerd. When all is just a click away: Is critical thinking obsolete in the digital age? In: Sternberg Robert J., Halpern Diane F., editors. Critical Thinking IN Psychology. 2nd ed. Cambridge University Press; Cambridge: 2020. pp. 197–223. [ Google Scholar ]
• Gottfredson Linda S. Why g matters: The complexity of everyday life. Intelligence. 1997; 24 :79–132. doi: 10.1016/S0160-2896(97)90014-3. [ CrossRef ] [ Google Scholar ]
• Grossmann Igor, Varnum Michael E. W., Na Jinkyung, Kitayama Shinobu, Nisbett Richard E. A route to well-being: Intelligence ver sus wise reasoning. Journal of Experimental Psychology: General. 2013; 142 :944–53. doi: 10.1037/a0029560. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Halpern Diane F. Halpern Critical Thinking Assessment. Schuhfried Test Publishers; Modling: 2018. [(accessed on 30 March 2021)]. Available online: www.schuhfried.com [ Google Scholar ]
• Halpern Diane F., Butler Heather A. Is critical thinking a better model of intelligence? In: Sternberg Robert J., editor. The nature of Intelligence. 2nd ed. Cambridge University Press; Cambridge: 2020. pp. 183–96. [ Google Scholar ]
• Halpern Diane F., Dunn Dana S. Thought and Knowledge: An Introduction to Critical Thinking. 6th ed. Taylor & Francis; New York: Forthcoming. in press. [ Google Scholar ]
• Halpern Diane F., Millis Keith, Graesser Arthur, Butler Heather, Forsyth Carol, Cai Zhiqiang. Operation ARA: A computerized learn ing game that teaches critical thinking and scientific reasoning. Thinking Skills and Creativity. 2012; 7 :93–100. doi: 10.1016/j.tsc.2012.03.006. [ CrossRef ] [ Google Scholar ]
• Hart Research Associates [(accessed on 30 March 2021)]; Employers Express Confidence in Colleges and Universities: See College as Worth the Investment, New Research Finds. 2018 Aug 29; Available online: https://hartresearch.com/employers-express-confidence-in-colleges-and-universities-see-college-as-worth-the-investment-new-research-finds/
• Heijltjes Anita, Gog Tamara van, Lippink Jimmie, Paas Fred. Unraveling the effects of critical thinking instructions, practice, and self-explanation on students’ reasoning performance. Instructional Science. 2015; 43 :487–506. doi: 10.1007/s11251-015-9347-8. [ CrossRef ] [ Google Scholar ]
• Holmes Natasha G., Wieman Carl E., Bonn DougA. Teaching critical thinking. Proceedings of the National Academy of Sciences. 2015; 112 :11199–204. doi: 10.1073/pnas.1505329112. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Hunter John E., Schmidt Frank L. Intelligence and job performance: Economic and social implications. Psychology, Public Policy, and Law. 1996; 2 :447–72. doi: 10.1037/1076-8971.2.3-4.447. [ CrossRef ] [ Google Scholar ]
• Kozyreva Anastasia, Lewandowsky Stephan, Hertwig Ralph. Citizens versus the internet: Confronting digital challenges with cognitive tools. [(accessed on 30 March 2021)]; Psychological Science in the Public Interest. 2020 21 doi: 10.1177/1529100620946707. Available online: https://www.psychologi calscience.org/publications/confronting-digital-challenges-with-cognitive-tools.html [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Kretzschmar Andre, Neubert Jonas C., Wusternberg Sascha, Greiff Samuel. Construct validity of complex problem- solv ing: A comprehensive view on different facts of intelligence and school grades. Intelligence. 2016; 54 :55–69. doi: 10.1016/j.intell.2015.11.004. [ CrossRef ] [ Google Scholar ]
• Lang Jonas W.B., Kell Harrison J. General mental ability and specific abilities: Their relative importance for extrinsic career success. Journal of Applied Psychology. 2020; 105 :1047–61. doi: 10.1037/apl0000472. [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Lovelace Berkeley., Jr. Medical Historians Compare the Coronavirus to the 1918 Flu Pandemic: Both Were Highly Political. [(accessed on 30 March 2021)]; CNBC. 2020 Available online: https://www.cnbc.com/2020/09/28/comparing-1918-flu-vs-corona virus.html?fbclid=IwAR1RAVRUOIdN9qqvNnMPimf5Q4XfV-pn_qdC3DwcfnPu9kavwumDI2zq9Xs
• Marr Rhuaridh. Iranian Cleric Claims COVID-19 Vaccine Can Make People Gay. [(accessed on 30 March 2021)]; Metro Weekly. 2021 Available online: https://www.metroweekly.com/2021/02/iranian-cleric-claims-covid-19-vaccine-can-make-people-gay/
• McCabe Kira O., Lubinski David, Benbow Camilla P. Who shines most among the brightest?: A 25-year longitudinal study of elite STEM graduate students. Journal of Personality and Social Psychology. 2020; 119 :390–416. doi: 10.1037/pspp0000239. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Mega Emiliano R. COVID Has Killed more than One Million People. How Many more will Die? [(accessed on 30 March 2021)]; Nature. 2020 Available online: https://www.nature.com/articles/d41586-020-02762-y [ PubMed ]
• Nickerson Raymond S. Developing intelligence through instruction. In: Sternberg Robert J., editor. The Cambridge Handbook of Intelligence. 2nd ed. Cambridge University Press; Cambridge: 2020. pp. 205–37. [ Google Scholar ]
• OECD . The Survey of Adult Skills: Reader’s Companion. 3rd ed. OECD Publishing; Paris: 2019. OECD Skills Studies. [ CrossRef ] [ Google Scholar ]
• Smith Matthew. Why won’t Britons Wear Face Masks? [(accessed on 30 March 2021)]; YouGov. 2020 Available online: https://yougov.co.uk/topics/health/articles-reports/2020/07/15/why-wont-britons-wear-face-masks
• Stanovich Keith E. What Intelligence Tests Miss: The Psychology of Rational Thought. Yale University Press; New Haven: 2009. [ Google Scholar ]
• Stanovich Keith E., West Richard F. On the failure of cognitive ability to predict my-side bias and one-sided thinking biases. Thinking & Reasoning. 2008; 14 :129–67. doi: 10.1080/13546780701679764. [ CrossRef ] [ Google Scholar ]
• Stanovich Keith E., West Richard F. What intelligence tests miss. The Psychologist. 2014; 27 :80–83. doi: 10.5840/inquiryctnews201126216. [ CrossRef ] [ Google Scholar ]
• Sternberg Robert J. A theory of adaptive intelligence and its relation to general intelligence. Journal of Intelligence. 2019; 7 :23. doi: 10.3390/jintelligence7040023. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Tang Julian W. COVID-19: Interpreting scientific evidence—Uncertainty, confusion, and delays. BMC Infectious Diseases. 2020; 20 :653. doi: 10.1186/s12879-020-05387-8. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Wirthwein Linda, Rost Detlef H. Giftedness and subjective well-being: A study with adults. Learning and Individuals Differences. 2011; 21 :182–86. doi: 10.1016/j.lindif.2011.01.001. [ CrossRef ] [ Google Scholar ]

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6.3 Probability sampling

Learning objectives.

• Describe how probability sampling differs from nonprobability sampling
• Define generalizability, and describe how it is achieved in probability samples
• Identify the various types of probability samples, and describe why a researcher may use one type over another

Quantitative researchers are often interested in making generalizations about groups larger than their study samples — that is, they are seeking nomothetic causal explanations. While there are certainly instances when quantitative researchers rely on nonprobability samples (e.g., when doing exploratory research), quantitative researchers tend to rely on probability sampling techniques. The goals and techniques associated with probability samples differ from those of nonprobability samples. We’ll explore those unique goals and techniques in this section.

Probability sampling

Unlike nonprobability sampling, probability sampling refers to sampling techniques for which a person’s likelihood of being selected from the sampling frame is known. You might ask yourself why we should care about a potential participant’s likelihood of being selected for the researcher’s sample. The reason is that, in most cases, researchers who use probability sampling techniques are aiming to identify a representative sample from which to collect data. A representative sample is one that resembles the population from which it was drawn in all the ways that are important for the research being conducted. If, for example, you wish to be able to say something about differences between men and women at the end of your study, you better make sure that your sample doesn’t contain only women. That’s a bit of an oversimplification, but the point with representativeness is that if your population contains variations that are important to your study, your sample should contain the same sorts of variation.

Obtaining a representative sample is important in probability sampling because of generalizability. In fact, generalizability is perhaps the key feature that distinguishes probability samples from nonprobability samples. Generalizability refers to the idea that a study’s results will tell us something about a group larger than the sample from which the findings were generated. In order to achieve generalizability, a core principle of probability sampling is that all elements in the researcher’s sampling frame have an equal chance of being selected for inclusion in the study. In research, this is the principle of random selection . Researchers often use a computer’s random number generator to determine which elements from the sampling frame get recruited into the sample.

Using random selection does not mean that the sample will be perfect. No sample is perfect. The only way to come with a sample that perfectly reflects the population would be to include everyone in the population in your sample, which defeats the whole point of sampling! Generalizing from a sample to a population always contains some degree of error. This is referred to as sampling error, the difference between results from a sample and the actual values in the population.

Generalizability is a pretty easy concept to grasp. Imagine a professor who takes a sample of individuals in your class to see if the material is too hard or too easy. The professor, however, only sampled individuals whose grades were over 90% in the class. Would that be a representative sample of all students in the class? That would be a case of sampling error—a mismatch between the results of the sample and the true feelings of the overall class. In other words, the results of the professor’s study don’t generalize to the overall population of the class.

Taking this one step further, imagine your professor is conducting a study on binge drinking among college students. The professor uses undergraduates at your school as her sampling frame. Even if that professor were to use probability sampling, perhaps your school differs from other schools in important ways. There are schools that are “party schools” where binge drinking may be more socially accepted, “commuter schools” at which there is little nightlife, and so on. If your professor plans to generalize her results to all college students, she will have to make an argument that her sampling frame (undergraduates at your school) is representative of the population (all undergraduate college students).

Types of probability samples

There are a variety of types of probability samples that researchers may use. These include simple random samples , systematic random samples , stratified random samples , and cluster samples . Let’s build on the previous example. Imagine we were concerned with binge drinking and chose the target population of fraternity members. How might you go about getting a probability sample of fraternity members that is representative of the overall population?

Simple random sampling

Simple random samples are the most basic type of probability sample. A simple random sample requires a sampling frame than contains a list of each person in the sampling frame. Your school likely has a list of all of the fraternity members on campus, as Greek life is subject to university oversight. You could use this as your sampling frame. Using the university’s list, you would number each fraternity member, or element , sequentially and then randomly select the elements from which you will collect data.

True randomness is difficult to achieve, and it takes complex computational calculations to do so. Although you think you can select things at random, human-generated randomness is actually quite predictable. To truly randomly select elements, researchers must rely on computer-generated help. Many free websites have good pseudo-random number generators. A good example is the website Random.org , which contains a random number generator that can also randomize lists of participants. Sometimes, researchers use a table of numbers that have been generated randomly. There are several possible sources for obtaining a random number table. Some statistics and research methods textbooks offer such tables as appendices to the text.

Systematic random sampling

As you might have guessed, drawing a simple random sample can be quite tedious. Systematic random sampling techniques are somewhat less tedious but offer the benefits of a random sample. As with simple random samples, you must possess a list of everyone in your sampling frame. Once you’ve done that, to draw a systematic sample you’d simply select every k th element on your list. But what is k , and where on the list of population elements does one begin the selection process? k is your selection interval or the distance between the elements you select for inclusion in your study. To begin the selection process, you’ll need to figure out how many elements you wish to include in your sample. Let’s say you want to interview 25 fraternity members on your campus, and there are 100 men on campus who are members of fraternities. In this case, your selection interval, or k , is 4. To arrive at 4, simply divide the total number of population elements by your desired sample size. This process is represented in Figure 6.2.

To determine where on your list of population elements to begin selecting the names of the 25 men you will interview, randomly select a number between 1 and k, and begin there. If we randomly select 3 as our starting point, we’d begin by selecting the third fraternity member on the list and then select every fourth member from there. This might be easier to understand if you can see it visually. Table 6.2 lists the names of our hypothetical 100 fraternity members on campus. You’ll see that the third name on the list has been selected for inclusion in our hypothetical study, as has every fourth name after that. A total of 25 names have been selected.

There is one clear instance in which systematic sampling should not be employed. If your sampling frame has any pattern to it, you could inadvertently introduce bias into your sample by using a systemic sampling strategy. (Bias will be discussed in more depth in the next section.) This is sometimes referred to as the problem of periodicity. Periodicity refers to the tendency for a pattern to occur at regular intervals. Let’s say, for example, that you wanted to observe binge drinking on campus each day of the week. Perhaps you need to have your observations completed within 28 days and you wish to conduct four observations on randomly chosen days. Table 6.3 shows a list of the population elements for this example. To determine which days we’ll conduct our observations, we’ll need to determine our selection interval. As you’ll recall from the preceding paragraphs, to do so we must divide our population size, in this case 28 days, by our desired sample size, in this case 4 days. This formula leads us to a selection interval of 7. If we randomly select 2 as our starting point and select every seventh day after that, we’ll wind up with a total of 4 days on which to conduct our observations. You’ll see how that works out in the following table.

Do you notice any problems with our selection of observation days in Table 6.3? Apparently, we’ll only be observing on Tuesdays. Moreover, Tuesdays may not be an ideal day to observe binge drinking behavior because binge drinking may be more likely to happen over the weekend.

Stratified random sampling

Another type of random sampling that could be helpful in cases such as this is stratified random sampling. In stratified random sampling , a researcher divides the sampling frame into relevant subgroups and then draw a sample from each subgroup. In this example, we might wish to first divide our sampling frame into two lists: weekend and weekdays. Once we have our two lists, we can then apply either simple random or systematic sampling techniques to each subgroup.

Stratified sampling is a good technique to use when, as in our example, a subgroup of interest makes up a relatively small proportion of the overall sample. In our example of a study of binge drinking, we want to include weekdays and weekends in our sample, but because weekends make up less than a third of an entire week, there’s a chance that a simple random or systematic strategy would not yield sufficient weekend observation days. As you might imagine, stratified sampling is even more useful in cases where a subgroup makes up an even smaller proportion of the sampling frame—for example, if we want to be sure to include in our study students who are in year five of their undergraduate program but this subgroup makes up only a small percentage of the population of undergraduates. There’s a chance simple random or systematic sampling strategy might not yield any fifth-year students, but by using stratified sampling, we could ensure that our sample contained the proportion of fifth-year students that is reflective of the larger population.

In this case, class year (e.g., freshman, sophomore, junior, senior, and fifth-year and higher) is our strata , or the characteristic by which the sample is divided. In using stratified sampling, we are often concerned with how well our sample reflects the population. A sample with too many freshmen may skew our results in one direction because perhaps they binge drink more (or less) than students in other class years. Proportionate stratified random sampling allows us to make sure our sample has the same proportion of people from each class year as the overall population of the school. Disproportionate stratified random samplin g allows us to over-sample smaller groups to ensure we have enough elements from the smaller group(s) for statistical analyses.

Cluster sampling

Up to this point in our discussion of probability samples, we’ve assumed that researchers will be able to access a list of population elements in order to create a sampling frame. This, as you might imagine, is not always the case. Let’s say, for example, that you wish to conduct a study of binge drinking across fraternity members at each undergraduate program in your state. Just imagine trying to create a list of every single fraternity member in the state. Even if you could find a way to generate such a list, attempting to do so might not be the most practical use of your time or resources. When this is the case, researchers turn to cluster sampling. Cluster sampling occurs when a researcher begins by randomly sampling groups (or clusters) of population elements and then selects elements from within those groups.

Let’s work through how we might use cluster sampling in our study of binge drinking. While creating a list of all fraternity members in your state would be next to impossible, you could easily create a list of all undergraduate colleges in your state. Thus, you could draw a random sample of undergraduate colleges (your cluster) and then draw another random sample of elements (in this case, fraternity members) from within the undergraduate college you initially selected. Cluster sampling works in stages. In this example, we sampled in two stages— (1) undergraduate colleges and (2) fraternity members at the undergraduate colleges we selected. However, we could add another stage if it made sense to do so. We could randomly select (1) undergraduate colleges (2) specific fraternities at each school and (3) individual fraternity members. As you might have guessed, sampling in multiple stages does introduce the possibility of greater error (each stage is subject to its own sampling error), but it is nevertheless highly efficien.

Jessica Holt and Wayne Gillespie (2008) used cluster sampling in their study of students’ experiences with violence in intimate relationships. Specifically, the researchers randomly selected 14 classes on their campus and then drew a random subsample of students from those classes. But you probably know from your experience with college classes that not all classes are the same size. So, if Holt and Gillespie had simply randomly selected 14 classes and then selected the same number of students from each class to complete their survey, then students in the smaller of those classes would have had a greater chance of being selected for the study than students in the larger classes. Keep in mind, with random sampling the goal is to make sure that each element has the same chance of being selected. When clusters are of different sizes, as in the example of sampling college classes, researchers often use a method called probability proportionate to size (PPS). This means that they take into account that their clusters are of different sizes. They do this by giving clusters different chances of being selected based on their size so that each element within those clusters winds up having an equal chance of being selected.

Comparing random sampling techniques

To summarize, probability samples are used to help a researcher make conclusions about larger groups. Probability samples require a sampling frame from which elements, usually human beings, can be selected at random from a list. The use of random selection reduces the error and bias present in the nonprobability sample types reviewed in the previous section, though some error will always remain. This strength is common to all probability sampling approaches summarized in Table 6.4.

In determining which probability sampling approach makes the most sense for your project, it helps to know more about your population. A simple random sample and systematic random  sample are relatively similar to carry out. They both require a list of all elements in your sampling frame. Systematic random sampling is slightly easier in that it does not require you to use a random number generator for each element; instead it uses a sampling interval that is easy to calculate by hand.

The relative simplicity of both approaches is counter-weighted by their lack of sensitivity to characteristics in of your population. Stratified random samples help ensure that smaller subgroups are included in your sample, thus making the sample more representative of the overall population or allowing statistical analyses on subgroup differences possible. While these benefits are important, creating strata for this purpose requires knowing information about your population before beginning the sampling process. In our binge drinking example, we would need to know how many students are in each class year to make sure our sample contained the same proportions. We would need to know that, for example, fifth-year students make up 5% of the student population to make sure 5% of our sample is comprised of fifth-year students. If the true population parameters are unknown, stratified sampling becomes significantly more challenging.

Common to each of the previous probability sampling approaches is the necessity of using a real list of all elements in your sampling frame. Cluster sampling is different. It allows a researcher to perform probability sampling in cases for which a list of elements is not available or pragmatic to create. Cluster sampling is also useful for making claims about a larger population, in our example, all fraternity members within a state. However, because sampling occurs at multiple stages in the process, in our example at the university and student level, sampling error increases. For many researchers, this weakness is outweighed by the benefits of cluster sampling.

Key Takeaways

• In probability sampling, the aim is to identify a sample that resembles the population from which it was drawn.
• There are several types of probability samples including simple random samples, systematic samples, stratified samples, and cluster samples.
• Probability samples usually require a real list of elements in your sampling frame, though cluster sampling can be conducted without one.
• Cluster sampling- a sampling approach that begins by sampling groups (or clusters) of population elements and then selects elements from within those groups
• Disproportionate stratified random sampling-stratified random sampling where the proportion of elements from each group is not proportionate to that in the population (usually used to oversample small groups).
• Generalizability – the idea that a study’s results will tell us something about a group larger than the sample from which the findings were generated
• Periodicity- the tendency for a pattern to occur at regular intervals
• Probability proportionate to size- in cluster sampling, giving clusters different chances of being selected based on their size so that each element within those clusters has an equal chance of being selected
• Probability sampling- sampling approaches for which a person’s (or element’s) likelihood of being selected from the sampling frame is known
• Proportionate stratified random sampling-stratified random sampling where the proportion of elements from each group is proportionate to that in the population
• Random selection- using a randomly generated numbers to determine who from the sampling frame gets recruited into the sample
• Representative sample- a sample that resembles the population from which it was drawn in all the ways that are important for the research being conducted
• Sampling error- a statistical calculation of the difference between results from a sample and the actual parameters of a population
• Simple random sampling- selecting elements from a list using randomly generated numbers
• Strata- the characteristic by which the sample is divided
• Stratified random sampling- dividing the study population into relevant subgroups and then draw a sample from each subgroup
• Systematic random sampling- selecting every k th element from a list

Image attributions

crowd men women by DasWortgewand CC-0

roll the dice by 955169 CC-0

Figure 10.2 copied from Blackstone, A. (2012) Principles of sociological inquiry: Qualitative and quantitative methods. Saylor Foundation. Retrieved from: https://saylordotorg.github.io/text_principles-of-sociological-inquiry-qualitative-and-quantitative-methods/ Shared under CC-BY-NC-SA 3.0 License

Foundations of Social Work Research Copyright © 2020 by Rebecca L. Mauldin is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Science and the Spectrum of Critical Thinking

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Since the nineteenth century, the scientific method has crystallized as the embodiment of scientific inquiry. But this paradigm of rigor is not confined to the natural sciences, and it has contributed to a sense of scientific “exceptionalism,” which obscures the deep connections between scientific and other kinds of thought. The scientific method has also indirectly given rise to the complex and contested idea of “critical thinking.” Both the scientific method and critical thinking are applications of logic and related forms of rationality that date to the Ancient Greeks. The full spectrum of critical/rational thinking includes logic, informal logic, and systemic or analytic thinking. This common core is shared by the natural sciences and other domains of inquiry share, and it is based on following rules, reasons, and intellectual best practices.

Graphical Abstract/Art Performance

The spectrum of critical thinking.

• Critical thinking
• Informal logic
• Rationality
• Scientific method

The term ‘critical thinking ’ is a bit like the Euro: a form of currency that not long ago many were eager to adopt but that has proven troublesome to maintain. And in both cases, the Greeks bear an outsized portion of the blame. Peter Wood [ 1 ]

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Wood P (2012) Some critical thoughts. Chronicle of higher education. chronicle.com/blogs/innovations/some-critical-thoughts/31252/ .

Lepore J (2016) After the fact: in the history of truth, a new chapter begins. The New Yorker, 21 Mar 21, pp 91–94

Google Scholar  

Wrightstone JW (1938) Test of critical thinking in the social studies. Bureau of Publications, Teachers College, Columbia University

Novaes CD (2017) What is logic? https://aeon.co/essays/the-rise-and-fall-and-rise-of-logic . Accessed Jan 12, 2017

Williams B (2006) Philosophy as a humanistic discipline

Ferry L (2011) A brief history of thought

Ennis RH (1964) A definition of critical thinking. Read Teach 17(8):599–612

Dobelli R (2013) The art of thinking clearly: better thinking, better decisions. Hachette UK

Phillips DZ (1979) Is moral education really necessary? Br J Educ Stud 27(1):42–56

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Kuprenas J, Frederick M (2013) 101 things I learned in engineering school

Grudin R (1997) Time and the art of living. Houghton Mifflin Harcourt

Bambrough JR (1965) Aristotle on justice: a paradigm of philosophy. In: Bambrough JR (ed) New essays on plato and Aristotle, pp 162–165

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Scheuer, J. (2023). Science and the Spectrum of Critical Thinking. In: Rezaei, N. (eds) Brain, Decision Making and Mental Health. Integrated Science, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-031-15959-6_3

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13 Types of Common Cognitive Biases That Might Be Impairing Your Judgment

Which of these sway your thinking the most?

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

The Confirmation Bias

The hindsight bias, the anchoring bias, the misinformation effect, the actor-observer bias, the false consensus effect, the halo effect, the self-serving bias, the availability heuristic, the optimism bias.

• Other Kinds

Although we like to believe that we're rational and logical, the fact is that we are continually under the influence of cognitive biases . These biases distort thinking , influence beliefs, and sway the decisions and judgments that people make each and every day.

Sometimes, cognitive biases are fairly obvious. You might even find that you recognize these tendencies in yourself or others. In other cases, these biases are so subtle that they are almost impossible to notice.

At a Glance

Attention is a limited resource. This means we can't possibly evaluate every possible detail and event ​when forming thoughts and opinions. Because of this, we often rely on mental shortcuts that speed up our ability to make judgments, but this can sometimes lead to bias. There are many types of biases—including the confirmation bias, the hindsight bias, and the anchoring bias, just to name a few—that can influence our beliefs and actions daily.

The following are just a few types of cognitive biases that have a powerful influence on how you think, how you feel, and how you behave.

Tara Moore / Getty Images

The confirmation bias is the tendency to listen more often to information that confirms our existing beliefs. Through this bias, people tend to favor information that reinforces the things they already think or believe.

Examples include:

• Only paying attention to information that confirms your beliefs about issues such as gun control and global warming
• Only following people on social media who share your viewpoints
• Choosing news sources that present stories that support your views
• Refusing to listen to the opposing side
• Not considering all of the facts in a logical and rational manner

There are a few reasons why this happens. One is that only seeking to confirm existing opinions helps limit mental resources we need to use to make decisions. It also helps protect self-esteem by making people feel that their beliefs are accurate.

People on two sides of an issue can listen to the same story and walk away with different interpretations that they feel validates their existing point of view. This is often indicative that the confirmation bias is working to "bias" their opinions.

The problem with this is that it can lead to poor choices, an inability to listen to opposing views, or even contribute to othering people who hold different opinions.

Things that we can do to help reduce the impact of confirmation bias include being open to hearing others' opinions and specifically looking for/researching opposing views, reading full articles (and not just headlines), questioning the source, and [doing] the research yourself to see if it is a reliable source.

The hindsight bias is a common cognitive bias that involves the tendency to see events, even random ones, as more predictable than they are. It's also commonly referred to as the "I knew it all along" phenomenon.

Some examples of the hindsight bias include:

• Insisting that you knew who was going to win a football game once the event is over
• Believing that you knew all along that one political candidate was going to win an election
• Saying that you knew you weren't going to win after losing a coin flip with a friend
• Looking back on an exam and thinking that you knew the answers to the questions you missed
• Believing you could have predicted which stocks would become profitable

Classic Research

In one classic psychology experiment, college students were asked to predict whether they thought then-nominee Clarence Thomas would be confirmed to the U.S. Supreme Court.

Prior to the Senate vote, 58% of the students thought Thomas would be confirmed. The students were polled again following Thomas's confirmation, and a whopping 78% of students said they had believed Thomas would be confirmed.  

The hindsight bias occurs for a combination of reasons, including our ability to "misremember" previous predictions, our tendency to view events as inevitable, and our tendency to believe we could have foreseen certain events.

The effect of this bias is that it causes us to overestimate our ability to predict events. This can sometimes lead people to take unwise risks.

The anchoring bias is the tendency to be overly influenced by the first piece of information that we hear. Some examples of how this works:

• The first number voiced during a price negotiation typically becomes the anchoring point from which all further negotiations are based.
• Hearing a random number can influence estimates on completely unrelated topics.
• Doctors can become susceptible to the anchoring bias when diagnosing patients. The physician’s first impressions of the patient often create an anchoring point that can sometimes incorrectly influence all subsequent diagnostic assessments.

While the existence of the anchoring bias is well documented, its causes are still not fully understood. Some research suggests that the source of the anchor information may play a role. Other factors such as priming and mood also appear to have an influence.

Like other cognitive biases, anchoring can have an effect on the decisions you make each day. For instance, it can influence how much you are willing to pay for your home. However, it can sometimes lead to poor choices and make it more difficult for people to consider other factors that might also be important.

The misinformation effect is the tendency for memories to be heavily influenced by things that happened after the actual event itself. A person who witnesses a car accident or crime might believe that their recollection is crystal clear, but researchers have found that memory is surprisingly susceptible to even very subtle influences.

For example:

• Research has shown that simply asking questions about an event can change someone's memories of what happened.
• Watching television coverage may change how people remember the event.
• Hearing other people talk about a memory from their perspective may change your memory of what transpired.

Classic Memory Research

In one classic experiment by memory expert Elizabeth Loftus , people who watched a video of a car crash were then asked one of two slightly different questions: “How fast were the cars going when they hit each other?” or “How fast were the cars going when they smashed into each other?”  

When the witnesses were then questioned a week later whether they had seen any broken glass, those who had been asked the “smashed into” version of the question were more likely to report incorrectly that they had seen broken glass.

There are a few factors that may play a role in this phenomenon. New information may get blended with older memories.   In other cases, new information may be used to fill in "gaps" in memory.

The effects of misinformation can range from the trivial to much more serious. It might cause you to misremember something you thought happened at work, or it might lead to someone incorrectly identifying the wrong suspect in a criminal case.

The actor-observer bias is the tendency to attribute our actions to external influences and other people's actions to internal ones. The way we perceive others and how we attribute their actions hinges on a variety of variables, but it can be heavily influenced by whether we are the actor or the observer in a situation.

When it comes to our own actions, we are often far too likely to attribute things to external influences. For example:

• You might complain that you botched an important meeting because you had jet lag.
• You might say you failed an exam because the teacher posed too many trick questions.

When it comes to explaining other people’s actions, however, we are far more likely to attribute their behaviors to internal causes. For example:

• A colleague screwed up an important presentation because he’s lazy and incompetent (not because he also had jet lag).
• A fellow student bombed a test because they lack diligence and intelligence (and not because they took the same test as you with all those trick questions).

While there are many factors that may play a role, perspective plays a key role. When we are the actors in a situation, we are able to observe our own thoughts and behaviors. When it comes to other people, however, we cannot see what they are thinking. This means we focus on situational forces for ourselves, but guess at the internal characteristics that cause other people's actions.

The problem with this is that it often leads to misunderstandings. Each side of a situation is essentially blaming the other side rather than thinking about all of the variables that might be playing a role.

The false consensus effect is the tendency people have to overestimate how much other people agree with their own beliefs, behaviors, attitudes, and values. For example:

• Thinking that other people share your opinion on controversial topics
• Overestimating the number of people who are similar to you
• Believing that the majority of people share your preferences

Researchers believe that the false consensus effect happens for a variety of reasons. First, the people we spend the most time with, our family and friends, do often tend to share very similar opinions and beliefs. Because of this, we start to think that this way of thinking is the majority opinion even when we are with people who are not among our group of family and friends.

Another key reason this cognitive bias trips us up so easily is that believing that other people are just like us is good for our self-esteem . It allows us to feel "normal" and maintain a positive view of ourselves in relation to other people.

This can lead people not only to incorrectly think that everyone else agrees with them—it can sometimes lead them to overvalue their own opinions. It also means that we sometimes don't consider how other people might feel when making choices.

The halo effect is the tendency for an initial impression of a person to influence what we think of them overall. Also known as the "physical attractiveness stereotype" or the "what is beautiful is 'good' principle" we are either influenced by or use the halo to influence others almost every day. For example:

• Thinking people who are good-looking are also smarter, kinder, and funnier than less attractive people
• Believing that products marketed by attractive people are also more valuable
• Thinking that a political candidate who is confident must also be intelligent and competent

One factor that may influence the halo effect is our tendency to want to be correct. If our initial impression of someone was positive, we want to look for proof that our assessment was accurate. It also helps people avoid experiencing cognitive dissonance , which involves holding contradictory beliefs.

This cognitive bias can have a powerful impact in the real world. For example, job applicants perceived as attractive and likable are also more likely to be viewed as competent, smart, and qualified for the job.

The self-serving bias is a tendency for people tend to give themselves credit for successes but lay the blame for failures on outside causes. When you do well on a project, you probably assume that it’s because you worked hard. But when things turn out badly, you are more likely to blame it on circumstances or bad luck.

Some examples of this:

• Attributing good grades to being smart or studying hard
• Believing your athletic performance is due to practice and hard work
• Thinking you got the job because of your merits

The self-serving bias can be influenced by a variety of factors. Age and sex have been shown to play a part. Older people are more likely to take credit for their successes, while men are more likely to pin their failures on outside forces.  

This bias does serve an important role in protecting self-esteem. However, it can often also lead to faulty attributions such as blaming others for our own shortcomings.

The availability heuristic is the tendency to estimate the probability of something happening based on how many examples readily come to mind. Some examples of this:

• After seeing several news reports of car thefts in your neighborhood, you might start to believe that such crimes are more common than they are.
• You might believe that plane crashes are more common than they really are because you can easily think of several examples.

It is essentially a mental shortcut designed to save us time when we are trying to determine risk. The problem with relying on this way of thinking is that it often leads to poor estimates and bad decisions.

Smokers who have never known someone to die of a smoking-related illness, for example, might underestimate the health risks of smoking. In contrast, if you have two sisters and five neighbors who have had breast cancer, you might believe it is even more common than statistics suggest.

The optimism bias is a tendency to overestimate the likelihood that good things will happen to us while underestimating the probability that negative events will impact our lives. Essentially, we tend to be too optimistic for our own good.

For example, we may assume that negative events won't affect us such as:

The optimism bias has roots in the availability heuristic. Because you can probably think of examples of bad things happening to other people it seems more likely that others will be affected by negative events.

This bias can lead people to take health risks like smoking, eating poorly, or not wearing a seat belt. The bad news is that research has found that this optimism bias is incredibly difficult to reduce.

There is good news, however. This tendency toward optimism helps create a sense of anticipation for the future, giving people the hope and motivation they need to pursue their goals.

Other Kinds of Cognitive Bias

Many other cognitive biases can distort how we perceive the world. Just a partial list:

• Status quo bias reflects a desire to keep things as they are.
• Apophenia is the tendency to perceive patterns in random occurrences.
• Framing is presenting a situation in a way that gives a certain impression.

Keep in Mind

The cognitive biases above are common, but this is only a sampling of the many biases that can affect your thinking. These biases collectively influence much of our thoughts and ultimately, decision making.

Many of these biases are inevitable. We simply don't have the time to evaluate every thought in every decision for the presence of any bias. Understanding these biases is very helpful in learning how they can lead us to poor decisions in life.

Dietrich D, Olson M. A demonstration of hindsight bias using the Thomas confirmation vote . Psychol Rep . 1993;72(2):377-378. doi:/10.2466/pr0.1993.72.2.377

Lee KK.  An indirect debiasing method: Priming a target attribute reduces judgmental biases in likelihood estimations .  PLoS ONE . 2019;14(3):e0212609. doi:10.1371/journal.pone.0212609

Saposnik G, Redelmeier D, Ruff CC, Tobler PN. Cognitive biases associated with medical decisions: A systematic review .  BMC Med Inform Decis Mak . 2016;16(1):138. doi:10.1186/s12911-016-0377-1

Furnham A., Boo HC. A literature review of anchoring bias .  The Journal of Socio-Economics.  2011;40(1):35-42. doi:10.1016/j.socec.2010.10.008

Loftus EF.  Leading questions and the eyewitness report .  Cognitive Psychology . 1975;7(4):560-572. doi:10.1016/0010-0285(75)90023-7

Challies DM, Hunt M, Garry M, Harper DN. Whatever gave you that idea? False memories following equivalence training: a behavioral account of the misinformation effect .  J Exp Anal Behav . 2011;96(3):343-362. doi:10.1901/jeab.2011.96-343

Miyamoto R, Kikuchi Y.  Gender differences of brain activity in the conflicts based on implicit self-esteem .  PLoS ONE . 2012;7(5):e37901. doi:10.1371/journal.pone.0037901

Weinstein ND, Klein WM.  Resistance of personal risk perceptions to debiasing interventions .  Health Psychol . 1995;14(2):132–140. doi:10.1037//0278-6133.14.2.132

Gratton G, Cooper P, Fabiani M, Carter CS, Karayanidis F. Dynamics of cognitive control: theoretical bases, paradigms, and a view for the future . Psychophysiology . 2018;55(3). doi:10.1111/psyp.13016

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."