Regression effect

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Regression effect

• or regression to the mean and how it leads to
  regression fallacy

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Some 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.

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The 1,078 pairs of fathers and sons
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Quiz and re-quiz scores
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Regression 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.

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Sp 03 midterm exam scores
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Spring 04 midterm exam scores
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Why does it happen?
Such 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.
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Why does it happen?
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Regression fallacy

• The regression fallacy occurs when one attributes
  changes from pre-measurement to post-measurement
  necessarily to some kind of intervention.

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Regression fallacy
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Regression 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 unwarranted.