Statistical Regression

What Is Statistical Regression?

Statistical regression (also called regression to the mean) is the statistical tendency for extreme scores or extreme behavior to be followed by others that are less extreme and closer to average.

In principle, statistical regression is a tendency for persons who initially obtain extreme scores on a test to converge (at the second occasion) toward the mean when given the same test gain. The tendency results from error of measurement assumed to be uncorrelated across occasions. The effect is especially pronounced when the test is low in reliability.

In the 19th century, Sir Francis Galton (1822-1911) introduced the concept of statistical regression (also called regression to the mean), which refers to the statistical tendency for extreme scores or extreme behavior to return toward the average. In his study of men’s heights, Galton found that the tallest men usually had sons shorter than themselves, whereas the shortest men usually had sons taller than themselves. In both cases, the height of the children was less extreme than the height of the fathers.

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To make it onto the cover of a major sports magazine, such as Sports Illustrated, an athlete or team must perform exceptionally well in addition to being lucky. However, appearing on the cover of Sports Illustrated got the reputation of being a jinx because athletes consistently performed worse afterward. For example, the Kansas City Chiefs football team lost to the Cincinnati Bengals on November 17, 2003, right after the team’s previously undefeated season had been celebrated on the cover of that magazine. This loss has been blamed on the “Sports Illustrated jinx.”

The belief in the Sports Illustrated jinx is so strong that some athletes have even refused to appear on the cover (Ruscio, 2002). Many people attribute the subsequent poor performance to internal factors rather than to chance (e.g., after appearing on the cover of Sports Illustrated, athletes feel so much pressure that they choke). But the “Sports Illustrated jinx” can also be explained by the concept of regression to the mean (Gilovich, 1991).

The magazine puts a team or athlete on the cover after an exceptionally good performance, and regression to the mean dictates that in most cases the next performance won’t be as great, just as really short men don’t usually have sons who are even shorter. If the magazine instead used cover photos featuring teams that had performed unbelievably badly that week, the magazine would get a reputation as a miracle worker for improving a team’s luck and performance! But that too would be just a misunderstanding of regression to the mean.

In summary, the key to regression to the mean is that when one selects an instance (or a group) for extreme performance, it is almost always true that one will have selected a more extreme instance than is warranted. When events deviate from the average, people are more likely to think about the bad exceptions than about the good exceptions.