Thinking and Deciding

LOGICAL ERRORS IN HYPOTHESIS TESTING 89
be true if the number on the other side were even? If it were odd?” For the last two
cards you would ask, “Could the rule be true if the letter on the other side were a
vowel? What if it were a consonant?” If the rule could be true no matter what is on
the other side, you do not need to turn over the card.
If you try this approach, you will find that you do need to turn over the A card,
because if there is an odd number on the other side, the rule is false. You do not
need to turn over the K. One surprise (for some) is that you do not need to turn over
the 4. Whether the letter on the other side is a vowel or a consonant, the rule could
still be true. (The rule does not say anything about what should happen when there
is a consonant.) A second surprise (for some) is that you do need to turn over the 7.
There could be a vowel on the other side, and then the rule would be false.
What has interested psychologists about this problem is that it seems easy, but it
is actually hard. Subjects frequently give the wrong answer, while stating (if asked)
that they are sure they are correct. Why is this problem so hard? What causes the
errors? A large literature has grown up around this problem, and the results seem to
illustrate some interesting facts about human thinking.
The error as poor thinking
First, some evidence suggests that the error here is in part a failure to search for
evidence and subgoals — in particular (1) the subgoal of determining the relevance
of each card; (2) the possibility of determining the relevance of each possible result
of turning over each card; and (3) the evidence from whether these results could
affect the truth of the rule. In sum, the error results from insufficient search. This
hypothesis is supported by the finding that performance improves if subjects are
asked to consider only the last two cards, the 4 and the 7. They are more likely to
choose the 7 and less likely to choose the 4. When the task is made more manageable
by cutting it down, the subjects are perhaps inclined to think more thoroughly about
the two remaining cards (Johnson-Laird and Wason, 1970).
In an extension of this experiment, the same researchers gave subjects the task of
testing the rule, “All triangles are black.” Each subject was assigned a stack of fifteen
black shapes and fifteen white shapes. The subject could ask to inspect a black shape
or a white shape on each trial, for up to thirty trials. After the subject selected a color,
the experimenter told the subject whether or not it was a triangle. It is apparent here
that the black shapes are not relevant, just as the 4 is not relevant in the card problem.
If a black shape is selected, the rule (“All triangles are black”) could be true, whether
the shape is a triangle or not.
All subjects selected all of the white shapes eventually: They realized that these
shapes were indeed relevant. Also, most of the subjects stopped selecting black
shapes (which were irrelevant) even before they found a black shape that was not a
triangle. (A black shape that was not a triangle would make them realize that black
shapes were irrelevant.) Very likely, the repeated trials gave the subjects a chance to
think about their strategy, and they realized that black shapes were irrelevant even