REGRESSION TOWARD THE MEAN AND THE PAIRED SAMPLE T-TEST

This article shows how one should properly conduct a paired-sample comparison of means in a test-retest situation where only a subset of the population retakes the exam. For example, suppose all who fail an exam are given the opportunity to retake a similar exam. If the usual paired-sample t test is conducted from data in this setting, the "regression effect" may lead to the incorrect conclusion that some intervention (such as remedial tutoring) has been effective in raising the scores when this is not necessarily true. A correct test when the mean score for the first exam is known is a test involving the intercept for a simple regression model.