3.B Regression Toward the Mean

Any score on a test with some randomness in it is a mix of true ability and chance. When someone scores extremely high, it's likely that both their real skill and a bit of good luck pushed that score up. Luck doesn't carry over to the next attempt, so their second score tends to fall back closer to the average, not because they got worse, but because the lucky part wasn't there to repeat. The same logic works in reverse for extremely low scores: they tend to rise back toward the mean. This drift happens even if nothing about the person changed at all.

You can estimate the size of this drift using the test-retest correlation, a number between -1 and 1 that measures how consistent scores are across two attempts. If a group scores z1 standard deviations above the mean on round one, the predicted z-score on round two is z1 times r, where r is that correlation. The weaker the correlation, the more the score regresses toward zero, which represents the mean. The amount of regression itself is just z1 minus that prediction, which works out to z1 times (1 minus r).

This idea matters across the research methods unit because it's a classic alternative explanation for why something seems to 'work.' A coach yells at an athlete after a terrible game, the athlete plays better next time, and it looks like yelling helped, but regression toward the mean predicts that bounce-back anyway. Any study comparing extreme scorers before and after some treatment has to rule this out before claiming a real effect.