Could an enormous part of the experimental psychology literature on cognitive dissonance be wrong? Keith Chen thinks so. (Link to his working paper, PDF).

The problem is this: a large class of studies compare how subjects' choices influence each other: suppose A, B and C are comparable, and the subject prefers A to B, they find that more often than not the subject also prefers C to B. The researchers can't understand why that would happen when B and C are comparable, and conclude that when the subject compares A to B and prefers A, the subject also decides that B is bad. (Monkeys do that too, so the researchers conclude that monkeys suffer cognitive dissonance.)

Chen points out that, if you do have an internal ranking of A, B, C -- not visible on the point scale the researchers give you (say, you give them all 3 points out of 5, but you have finer preferences among them) -- then if you prefer A to B, the probability of your preferring C to B is well over 1/2. To be precise, it is 2/3. This is because there are only three ranking scenarios where A is preferred to B: ABC, ACB, CAB; and in two of these three, C is preferred to B. (2/3 corresponds quite well to what was seen in the experiments on monkeys.)

Can this trivial detail really have escaped the psychology community for half a century?

A large number of cognitive-dissonance experiments fall in another category, which is a bit trickier to analyse, but Chen does that in his working paper above and comes to a similar conclusion.

A final thought: if an otherwise rational psychologist does not admit the error, can we take that as evidence of cognitive dissonance?

## 5 comments:

I am not sure whether it is a trivial detail. I never studied 'Probability and Statistics' and recently started reading a text book. One of the first exercises was Monty Hall problem and it took a day to covince myself that one should switch doors. The discussion at

http://tierneylab.blogs.nytimes.com/2008/04/07/monty-hall-meets-cognitive-dissonance/

shows that I am not the only one who has difficulties. May be it depends on how early one gets in to these things.

gs - yes, it's not trivial, and even experts sometimes struggle with probability theory. (According to Martin Gardner, d'Alembert couldn't see that flipping a coin twice is the same as flipping two coins once, and he believed that a run of heads makes tails more likely -- the popular bogus "law of averages"). But if an experimental psychologist has not studied probability and statistics, his paper should be vetted by someone else who has. (That goes for most other experimentalists.)

For many, it may not be trivial that all numbers aren't equally likely when rolling a pair of dice (7 is the most likely, 2 and 12 the least). But you can't write a paper on dice-rolling without knowing that.

(I have seen some responses online that only a few papers on cognitive dissonance are flawed in this way, the majority of the literature is OK, and Chen has an axe to grind. I don't know about that.)

May be you can suggest some good boks. I started with "Weighng the odds" by David Williams and find it challenging. Now I am in the hat problem and the miraculous appearence of 1/e as the limit of a probability as n tends to infinity.

As I remember, you're a trained mathematician so should not be new to a lot of it.

I learned much of my basic probability theory as a kid from Martin Gardner (collections of his Scientific American columns), in general they are fun books to read. I never did any really good courses and don't know any very good standard books. Recently I've been looking at E T Jaynes's book (much of it available online here). Jaynes was a physicist who can take much of the credit for the Bayesian revolution in statistics, and he more or less invented the maximum entropy technique (though he says it was all known already to Gibbs in the 19th century). He fought with "traditional" statisticians for much of his career and a lot of his writing is therefore rather polemical, but fun to read and insightful.

Thanks. I am not sure whether I am a trained mathematician; it was passion. It is more or less extinct now and I feel that I need to learn some probability and statistics to 'understand' the world.

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