The Wason card problem

The Wason card problem is a well-known psychological test that probes how people think about hypothesis testing. The version I use in one of my first-year lectures is shown below. I think the original version used letters and numbers, but I’m a biologist, so obviously I use pictures of dead pets instead of numbers.

  • We know that each of the four cards shown below has a letter on one side and an animal on the other.
  • We suspect that if there is a vowel on one side of a card, then there is a mammal on the other. Which card(s) do we need to turn over to determine whether this hypothesis is false?

It’s well worth doing this for real yourself before reading any further:

Wason cards [CC-BY-SA-3.0 Steve Cook]

Wason cards: an ‘A’, a snake, a cat, and a ‘Q’

Pretty much everyone thinks we should turn ‘A’, and they’re right. If there’s a lizard on the other side, it contradicts the hypothesis “if vowel, then mammal” immediately.

Pretty much everyone thinks we need not turn ‘Q’, and they’re right. Our hypothesis is “if vowel, then mammal”; it says nothing about what a consonant implies, so turning this card is irrelevant.

The sticky bit is that pretty much everyone wants to turn over the cat, but not the snake. In this they are quite wrong.

Having done this test with my fresh-faced biology undergraduates for the past two years, I can confirm that they perform very similarly to the population at large, or at least to the self-selecting and weird subset of the adult population that finds itself being asked deliberately tricky questions by smart-arses. 10-20% want to turn over the snake, but 80%-90% want to turn over the cat.

It’s important to note that the hypothesis is “if vowel, then mammal”, not “if mammal, then vowel”. It doesn’t actually matter one jot what is on the other side of the cat:

  • If it’s the letter ‘Z’, then we have evidence for “if consonant, then sometimes mammal”. This says nothing about the truth of “if vowel, then mammal”.
  • If it’s the letter ‘U’, then we’ve found a card that is consistent with “if vowel, then mammal”, but we already suspected that.

In either case, the thing on the other side of the cat is guaranteed to be either consistent with the hypothesis, or irrelevant to the hypothesis, so there is no point in turning it. The result could never contradict the hypothesis “if vowel, then mammal”.

The snake, on the other hand, must be turned over.

  • If it’s the letter ‘Z’, then we have evidence for “if consonant, then sometimes reptile”. Again, this says nothing about the truth of “if vowel, then mammal”.
  • However, if it’s the letter ‘U’, then we’ve found a card that is inconsistent with “if vowel, then mammal”, and which immediately contradicts the hypothesis.

The reason so many choose the wrong cards can be partly put down to the rather tricksy use of ‘if’: unfortunately, English doesn’t really distinguish between mathematics’ ‘if’ and mathematics’ ‘iff‘ (if-and-only-if).

However, the main reason so many choose the wrong cards is (probably) down to the human inclination to look for data that confirm our hypotheses, rather than actively searching for data that might contradict them. Unless we’re very careful, we humans tend to turn cards, perform experiments, and follow Twitterfolk that stand little or no chance of ever contradicting our beliefs.

We flip the cat, even though what is on the other side cannot change our mind. We read the newspaper, even though what is inside is unlikely to challenge our prejudices. And – shame of shames – we inflict logic puzzles on our students, even though we know the result will almost certainly be consistent with our unworthy suspicions about their deductive abilities. Hypocrisy, thy name is Cook.

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