Therefore a student who was lucky on the first test is more likely to have a worse score on the second test than a better score. Some of the lucky students on the first test will be lucky again on the second test, but more of them will have average or below average luck. The lucky ones are more likely to score above the mean than below it, because their good luck improves their score. On the first test, some will be lucky, and score higher than their ability, and some will be unlucky and score lower than their ability. Student scores are determined in part by underlying ability and in part by purely stochastic, unpredictable chance. ![]() The phenomenon occurs because each sample is affected by random variance. Thus, regression to the mean is a mathematical inevitability: any measurement of any variable that is affected by random variance must show regression to the mean.įor example, if you give a class of students a test on two successive days, the worst performers on the first day will tend to improve their scores on the second day, and the best performers on the first day will tend to do worse on the second day. On the second measurement, these samples will appear to regress because the random variance affecting the samples in the second measurement is independent of the random variance affecting the first. Regression to the mean relies on random variance affecting the measurement of any variable this random variance will cause some samples to be extreme. Regression toward the mean is a principle in statistics that states that if you take a pair of independent measurements from the same distribution, samples far from the mean on the first set will tend to be closer to the mean on the second set, and the farther from the mean on the first measurement, the stronger the effect. ![]() ![]() A scatterplot demonstrating regression toward the mean, distinguished by a football-shaped cloud of points
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