The 2-4-6 Task

What it is

Wason published the study as On the failure to eliminate hypotheses in a conceptual task, in the Quarterly Journal of Experimental Psychology, volume 12, issue 3. The task takes its name from the numbers participants started from, and the aim was to discover the rule behind them.

Wason's question was about method. He wanted to know whether intelligent young adults test a hypothesis only by collecting instances that agree with it, a route he called enumerative, or whether they also look for instances that would rule it out, a route he called eliminative. He designed the task so that the two routes would part company. The correct rule was implied by many more obvious rules, and the number of possible instances was infinite, so a person who only ever tried sets that fitted a favourite guess could go on hearing yes without getting nearer the truth.

Twenty-nine people took part. Six reached the correct conclusion without first reaching an incorrect one. Thirteen reached one incorrect conclusion, nine reached two or more, and one reached no conclusion. Wason treated the participants with two or more incorrect conclusions as unable or unwilling to test their hypotheses, and he discussed the result in relation to scientific thinking.

In effect

The task gives the clearest small-scale picture of how a test can be uninformative. A yes from a test that would also have said yes under many other rules cannot separate those rules. The participant feels progress, because each answer agrees with the guess, but the answers were never capable of disagreeing.

This is the sense in which the task is used in the article What is confirmatory hypothesis testing. The procedure is described separately from belief. Nobody in the task is asked what they want to be true. The difficulty arises from which questions are put, and from what the answers can and cannot show.

Later work refined how the result should be read. Klayman and Ha argued in 1987 that examining cases one expects to have the property in question is often a good way to learn whether a hypothesis is true, and that the question is how the strategy fits the task. The 2-4-6 task is a case in which the fit is poor by design, which is why it works as a demonstration and why it should not be taken as a portrait of everyday reasoning.

What it does not say

The study does not show that people cannot test ideas well, and it does not show that looking for confirming cases is always an error. It reports how a group of 29 young adults behaved on one task that was designed to mislead a confirming-only approach. The count of participants is small, and the abstract-level record available here does not give further detail of the procedure, so the figures above are the ones that can be stated with confidence.

It also does not describe the motives of the participants. What it records is behaviour on the task, not character.

---