A person who scored 750 out of a possible 800 on the quantitative portion of the SAT takes the SAT again (a different form of the test is used). Assuming the second test is the same difficulty as the first and that there was no learning or practice effect, what score would you expect the person to get on the second test? The surprising answer is that the person is more likely to score below 750 than above 750; the best guess is that the person would score about 725. If this surprises you, you are not alone. This phenomenon, called regression to the mean, is counter intuitive and confusing to many professionals as well as students.

The conclusion that the expected score on the second test is below 750 depends on the assumption that scores on the test are, at least in some small part, due to chance or luck. Assume that there is a large number, say 1,000 parallel forms of a test and that (a) someone takes all 1,000 tests and (b) there are no learning, practice, or fatigue effects. Differences in the scores on these tests are therefore due to luck. This luck may be a function of simple guessing or may be a function of knowing more of the answers on some tests than on others.