The Wason Selection Test Explained
(Maybe, Sort of, Perhaps)

(In Defense of the Kids)

There is a famous psychology experiment that was first run in the 1960's called the Wason Selection Test. Yes, that's WASON (no "t" before the "s"). What makes the test so odd is there's only one question and it involves simple reasoning. And yet almost everyone gets the answer wrong.

The most discourteous say the test shows us that your typical university student just doesn't know diddly how to think (most of the test subjects are college kids). Critics of a more charitable mind have suggested the strange results are because of the way our brains are hardwired. Or perhaps its the way our reasoning is shaped by our society.

Well, before we go further, perhaps we should show what the Wason Selection Test is.

Not Quite That Elementary

All right. Take four cards with different colors on one side and numbers on the other. Place the card up with the numbers and color sides alternating like this:

7

4

Then we make this statement:

If the color on one side is red, the number of the other side is odd.

And we ask the following question:

Which cards must be turned over to see if the statement is TRUE?

We mean, of course, only the cards that are necessary to see if the statement is TRUE. You may not need to turn over all the cards. Just the minimum that are necessary.

This test is an example of what psychologists call a test for "abstract" reasoning. That is, there is no real-life application here. It's just a test on how well you think.

And yet 80% of college kids - quote - "get the answer wrong" - unquote. Hence the conclusion that college kids can't think.

But before we show you the - quote - "correct answer" - unquote - we'll look at the test again.

Interesting, Though Elementary

But not as an abstract problem. We pose it in a more practical - even lowbrow - manner.

So now look at these cards:

25

Pepsi

14

Schlitz

And this statement:

If you have a beer, then you must be at least 18.

Again we ask:

Which cards must be turned over to see if the statement is TRUE?

This problem, the professors tell us, is exactly the same as the first one.

But in this case almost everyone gets the answer right!

The reasoning goes like this:

You don't need to turn the first card over. If you're an adult it doesn't matter what you drink.

You don't need the next card either. If you drink a soda, you can be a kid or an adult.

But you do need to turn over the third card. After all, if someone is fourteen, you have to make sure they're drinking a soda.

You also need to turn over the last card. That is, if someone's drinking a beer, you must make sure they're an adult.

So you only have to turn over the last two cards.

It Is Not Logical, Captain.

So why is the first problem - the "abstract" version - so hard to figure out and the second is so easy?

Well, one popular explanation is that the human mind is fashioned to detect cheating. And as the second problem has a possibility of cheating - an underage customer trying to sneak a swig - it's easy to figure out. But the abstract version has no possibility of someone cheating. Ergo, the mind doesn't figure the problem out as well.

Now one author said if you read articles about the Wason Test, you might think the "it-might-be-cheating" answer has been universally accepted. That, though, is not really true. There is no real consensus as to what's going on.

But we've left out one other question.

Just what the heck are we testing?

It's How You Tell It

Note the way we phrase our statements.

IF the back of the card is red, THEN the number on the front is odd.

IF you have a beer, THEN you must be at least 18.

The Wason Selection Test, then, is testing if the subjects can correctly reason using a logical IF-THEN statement. In formal logic, an IF-THEN is called MATERIAL IMPLICATION.

Material implication is a statement with the form:

IF [Statement A], THEN [Statement B].

... which is usually represented by:

A → B

... and is sometimes also read as "A implies B".

Now according to logic professors, an IF-THEN statement is only FALSE when the IF part is TRUE and the THEN part is FALSE. Otherwise, the statement is TRUE.

A nice way to summarize logical statements is to put them in a Truth Table. For the IF-THEN statement the Truth Table is:

Truth Table: If-Then Statements
A	B	A → B
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

So when analyzing IF-THEN statements, you only have to identify the one FALSE statement. The other three are TRUE by default.

And returning to the "abstract" Wason Test, we can write down the Truth Table as:

Truth Table: "Abstract" Wason Selection Test
The back of the card is red.	The number is odd.	If the back of the card is red, then the number is odd.
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	TRUE
FALSE	FALSE	TRUE

... and use this in our reasoning.

So let's look at the problem again:

7

4

If the back of the card is red, then the number on the front is odd.

So guided by the Truth Table, we can reason like this:

The first card has a 7. Since 7 is odd, the THEN part is TRUE. Therefore the overall IF-THEN statement is always TRUE. So you don't need to check the other side of this card.

The second card has a blue side. Therefore the IF part of the statement is FALSE. So the overall IF-THEN statement is always TRUE and you don't need to check the other side of this card, either.

The third card has an even number. So the THEN part of the statement is FALSE. So to determine if the IF-THEN statement is TRUE we must check the color on the other side. We have to turn over this card.

The fourth card has a red side. So the IF part of the statement is TRUE. So to determine if the IF-THEN statement is TRUE we must check the color the other side is. We have to turn over this card.

So we only have to check Cards 3 and 4, just as in the practical test.

We see then that once the IF-THEN statements are explained as Material Implication, the problem is simple. We just skip any cards with an IF part that is FALSE and also skip all the cards where the THEN part is TRUE. All these IF-THEN statements will be TRUE.

Instead, the only cards we need to check are where it's possible the IF-Part is TRUE and the THEN part is FALSE. These statements can be false and we have to check.

Seems easy, doesn't it?

Give Me That Old Time Philosophy

So does this mean 80 % of the college kids can't reason? Well, to paraphrase Sportin' Life said, this ain't necessarily so.

It's a sad truth that the IF-THEN Truth Table has caused considerable consternation for - to misquote Carl Sagan - thousands and thousands of years. Even some professional philosophers don't like it and have tried to get rid of it.

So what, we ask, is the beef?

The beef is that with this with the IF-THEN Truth Table you can come up with weird statements. Consider these sentences, all of which the Truth Table tell us are TRUE.

Truth Table: Weird IF-THEN Statements
A → B	Truth Values	Overall Truth Value
If George Washington was the first King of France, then Napoleon would have been the first US President.	FALSE → FALSE	TRUE
If I break my leg today, then I will climb Mount Everest tomorrow.	FALSE → FALSE	TRUE
If I break my leg today, then I will NOT climb Mount Everest tomorrow.	FALSE → TRUE	TRUE
If 1 + 1 = 3, then C. S. Lewis wrote The Lion, the Witch, and the Wardrobe.	FALSE → TRUE	TRUE

So if we don't like it, how do we get rid of it? Well, one possibility is to allow a third TRUTH value like "Unknown". You can also try to mandate that the IF and THEN parts have to be "relevant" - that is, they have to have some real connection.

But so far none of the methods have worked out that well. You end up with bigger and more complex Truth Tables, and you still end up with oddball sentences.

So like it or not, the dang IF-THEN Truth Table here to stay. That's because it really, really works (to see why it works, just click here.)

But what does any of this brouhaha have to do with the Wason Selection Test?

Changing the Rules

We mentioned the Wason Selection Test is usually administered to college kids by professors. So the professors naturally use the professorial IF-THEN Truth Table we gave above. So to get the "correct" answer, the students have to use Material Implication.

There's just a few wee-little problems when the professors give the test.

They don't tell the kids they are defining an IF-THEN statement as formal Material Implication.

And then there's the matter that:

They don't teach the kids the Material Implication Truth Table.

And finally:

They don't mention that IF-THEN statements in everyday conversation are not necessarily the IF-THEN statements of logical Material Implication.

And it's this last point that really goober things up

(Bi)Conditionals

If you've taken math courses, you see theorems that say such-and-such is TRUE IF AND ONLY IF this-and-that is TRUE. .

But have you ever heard anyone say IF AND ONLY IF in ordinary conversation?

Of course not. They make the sentence an IF-THEN statement.

Look at it in this way. Say you don't want to go to the movies, but your friend does. After a while you say, "OK. If the movie is The Night of the Living Logicians, then we'll go to the movies.

What you mean, of course, is that you will only go to the movies if it's The Night of the Living Logicians. Otherwise you'll do something else. This is clear from the context of the conversation.

So let's set up the Truth Table for what we are calling our Conversational IF-THEN Statement:

Truth Table: "Conversation IF" Statements
The Movie	What You Do	Conversational A → B	Overall Truth Value
Night of the Living Logicians	Go to the Movies.	TRUE → TRUE	?
Night of the Living Logicians	Don't Go to the Movies.	TRUE → FALSE	?
Ernest Goes to Cookietown, Oklahoma	Go to the Movies.	FALSE → TRUE	?
Ernest Goes to Cookietown, Oklahoma	Don't Go to the Movie.	FALSE → FALSE	?

Now we'll start reasoning, starting from Line #1 and going down.

The movie was the Night of the Living Logicians. And we also went to the movie. So the overall statement is TRUE.

The movie was Night of the Living Logicians. But we didn't go to the movies. So the overall statement is FALSE.

The movie was NOT the Night of the Living Logicians. But we went to the movies anyway. Although this could be a wise decision, this isn't what we meant. So in the context of the conversation, the overall statement is FALSE.

The movie was NOT the Night of the Living Logicians and we didn't go to the movies anyway. That's was part of the agreement so the overall statement is TRUE.

So our final Truth Table is:

Truth Table: "Conversational IF" Statements
The Movie	What You Do	Conversational A → B	Overall Truth Value
Night of the Living Logicians	Go to the Movies.	TRUE → TRUE	TRUE
Night of the Living Logicians	Don't Go to the Movies.	TRUE → FALSE	FALSE
Ernest Goes to Cookietown, Oklahoma	Go to the Movies.	FALSE → TRUE	FALSE
Ernest Goes to Cookietown, Oklahoma	Don't Go to the Movie.	FALSE → TRUE	TRUE

Now turn to a logic textbook (if we can find one we can afford) and look up the Truth Table for what the author calls a Biconditional. And sure enough, you'll find a biconditional is the same as what we called the "Conversationa IF-THEN statement which as we saw is really the IF AND ONLY IF statement.

Biconditionals are often abbreviated IFF and is written as a double arrow.

A IFF B

... or:

A ↔ B

And the Truth Table is:

Truth Table: If-Then Statements
A	B	A ↔ B
TRUE	TRUE	TRUE
TRUE	FALSE	FALSE
FALSE	TRUE	FALSE
FALSE	FALSE	TRUE

Yep, exactly what we were calling the "Conversational IF-THEN Statements".

The point, then, is that in ordinary conversation, when we say "if", we can can also mean mean "if-and-only-if". True, "if" can also mean the same as Material Implication as we saw is the second Wason Test. In conversation we rely on context and custom to determine if we mean the Material Implication or the Biconditional.

But if you reason using the Biconditional Truth Table, and your professor considers Material Implication in the right answer, he'll say you're wrong.

But remember the first problem? The Abstract Wason Selection Test?

There was, in fact, no context. So it's not clear to the kids what IF to use. Probably they'll use the Biconditional because that's what they use in their everyday conversation.

OK, let's summarize what goes on in the Wason Selection Test:

The professor gives the kids a test asking to determine if an "IF-THEN" statement is TRUE or FALSE.

He doesn't explain to them that the IF-THEN in the test is not the way they normally use IF-THEN.

The kids get the wrong answer.

Dr. Wason, What Does It All Mean?

Now lest we draw the ire of college professors everywhere, we should point out that the Wason Selection Test certainly shows us that people reason better when confronted with a problem in a familiar context. And sometimes "if" of ordinary speech does mean the IF-THEN as in the logic textbook.

And perhaps we are indeed tuned to better recognize the possibility of deception. The various explanations of the Wason Selection are by no means mutually exclusive.

One thing the Wason Test does tells us is about education. You can't simply toss a problem at people who have not been trained in something and expect them to get the right answer. Particularly when the training requires distinction between formal logic and natural language - which is an advanced topic of philosophy and linguistics.

So a Humble CooperToons Suggestion is that a New and Improved Wason Test should be given as follows:

Give the test to the kids as usual, both the "abstract" and practical versions.

Give them a lecture on formal Material Implication pointing out it is only false when the IF part is TRUE and the THEN part is FALSE.

Give them the abstract Wason Test again and see if more of them get it right.

That might make the coming to conclusions a bit more elementary.

References

"Conditional Reasoning and the Wason Selection Task: Biconditional interpretation Instead of Reasoning Bias", Pascal Wagner-Egger Thinking and Reasoning, Volume 13, Issue 4, pp. 484 - 505, 2007.

"Elementary, My Dear Wason: The Role of Problem Representation in the THOG Task", Cynthia S. Koenig and Richard A. Griggs, Psychological Research, Volume 65, Issue 4, pp 289 - 293, 2001. This seems to be the first documented of the horrible pun but it seems to ahve occurred to others independently.