Statistics: Reasoning under uncertainty

From MathWiki


CBC As I Happens Duration: 00:07:43 (

...And, the next contestant on "Let's Make a Deal" is...YOU. Behind me in the studio are three doors. Behind each of two is a goat. Behind the third is a brand new car! Now go ahead and select a door. OK? Alright, now I'll show you what's behind one of the two remaining doors...
Aha! It's a goat. Alright then. Would like to stay with your first choice, or switch to the other closed door?
If you think it doesn't really matter -- that you've now got a fifty-fifty chance of winning the car whether you switch or not -- you're wrong.
To tell us how to increase your chances of winning, and why this is so important to psychological research, we reached Dr. Keith Chen. He's an economics professor at Yale University.

But the best part, not mentioned here, is Dr. Chen's description of a experiment on cognitive dissonance conducted by colleagues in Psychology. They wanted to test chimpanzees for evidence of cognitive dissonance so they trained them to choose their favourite colour M&M. The psychologist used 3 colours, say Red, Green and Blue, and offered a pair at random to a chimpanzee. The chimpanzee choose his/her favourite colour. Then the colour rejected at stage one was presented with the remaining colour. The researchers found that the chimpanzees would choose the new colour about 2/3 of the time which was taken as evidence for cognitive dissonance!

Abstract of his unpublished paper:
Cognitive dissonance is one of the most influential theories in social psychology, and its oldest experiential realization is choice-induced dissonance. Since 1956, dissonance theorists have claimed that people rationalize past choices by devaluing rejected alternatives and upgrading chosen ones, an effect known as the spreading of preferences. Here, I show that every study which has tested this suffers from a fundamental methodological flaw. Specifically, these studies (and the free-choice methodology they employ) implicitly assume that before choices are made, a subject's preferences can be measured perfectly, i.e. with infinite precision, and under-appreciate that a subject's choices reflect their preferences. Because of this, existing methods will mistakenly identify cognitive dissonance when there is none. This problem survives all controls present in the literature, including control groups, high and low dissonance conditions, and comparisons of dissonance across cultures or affirmation levels. The bias this problem produces can be fixed, and correctly interpreted several prominent studies actually reject the presence of choice-induced dissonance in their subjects. This suggests that mere choice may not be enough to induce rationalization, a reversal that may significantly change the way we think about cognitive dissonance as a whole.