You have probably heard about the science that shows how incompetent people are overconfident.  Here is a nice article which cuts through some of the hype and then presents a variety of ways to debunk the finding as a statistical illusion.  (Which comes as a relief to me, but perhaps a little late.) Let me give you an even easier way, one that is related to the “regression toward the mean” idea given in the article. First, here is the finding summarized in a graph.

Suppose you have competent and incompetent people in equal proportions.  They will take a test which will give them a score ranging from 0 to 4.  The competent people score a 3 on average and they know this.  The incompetent people score 1 on average and they know this.  Due to idiosyncratic features of the test, the weather, etc. each subject’s actual score is random and it will range from one less to one more than their average.

You ask everyone to predict their outcome.  The incompetent people predict a score of 1 and the competent people predict a score of 3.  These are the best predictions.  Then they take the test.  The actual scores range from 0 to 4.  Everyone who scored 0 predicted a score of 1, everyone who scored 4 predicted a score of 3, and the average prediction of those who scored 2 is about 2.

Trilby tribute:  Marginal Revolution.