Regression effectSome historySlide 3Quiz and re-quiz scoresRegression effect … or regression to the meanSp 03 midterm exam scoresSpring 04 midterm exam scoresWhy does it happen?Slide 9Regression fallacySlide 11Slide 12Regression effect… or regression to the mean … and how it leads to regression fallacySome history•Sir Francis Galton (1822-1911) found …–sons of tall fathers tended to be tall, but on average not as tall as their fathers–sons of short fathers tended to be short, but on average not as short as their fathers•He called it “regression to mediocrity.”•Hence the term “regression analysis.”xy"69y"68x"7.2ys"7.2xs1xy355.0ˆ xyThe 1,078 pairs of fathers and sons …5.0r5 6 7 8 9 10 11 12 13 1456789101112131415quiz1quiz2q2 = q1 + 0.83q2 = 4.6 + 0.577 q1Quiz and re-quiz scores70.0r92.8x75.9y55.2xs11.2ysRegression effect …or regression to the mean•In virtually all test-retest situations …–the group scoring low on the first test will on average show improvement on the second test–the group scoring high on the first test will on average fall back on the second test•We say the scores “regress to the mean.” The phenomenon is called the “regression effect.”10090801009080exam1exam2y = xy = 62.2 + 0.30 xSp 03 midterm exam scores4.88x5.88y37.0r6.5xs4.4ysSpring 04 midterm exam scores100908070601009080706050Exam 1Exam 2y = x + 2.6y = 34.75 + 0.61 x60.0r8.82x4.85y1.11xs3.11ysWhy does it happen?xyssrbSuch patterns occur in any pair of variables with similar standard deviations and whose correlation less than 1.People with the highest scores on the first test will decline (relative to the population) and those with the lowest scores will improve, on average.Why does it happen?Regression fallacy•The regression fallacy occurs when one attributes changes from pre-measurement to post-measurement necessarily to some kind of intervention.Regression fallacyRegression fallacy•A flight instructor in the Israeli air force claimed that…–when pilots are praised for well-executed maneuvers, they do worse on next maneuver–when pilots are criticized for poorly-executed maneuvers, they improve on next maneuver•The conclusion that “praise spoils, criticism improves” is
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