Regression Towards the Mean
David A. Kenny
University of Connecticut
http://davidakenny.net/old/series/primer.htm
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An Opening Quote
“The list of studies in which the
regression factor has been
neglected grows monotonous as
well as distressing” (Rulon,
1941).
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Galton Squeeze Diagram
• Two vertical axes.
• left line the pretest
• right line the posttest
• A line from the the pretest
score to the mean on the
posttest.
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Definition
A person’s score on a variable that
is extreme (in the sense of being
far away from the mean) tends to
be less extreme in standard
deviation units when that person is
measured on another variable.
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Common Misconceptions
• RTM results in mediocrity.
• RTM is unidirectional.
• RTM is entirely due to
measurement error.
• RTM is some mysterious force.
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Illustrations
• The Sophomore Jinx
• The Gifted and Not So Gifted
• Spontaneous Remission
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Is There a Sophomore Jinx?
• 39 Hitting Winners from 1970 and
1994
• Rookie average .285
• Sophomore average .266
• 28 declined and 11 improved
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Jinx?: Scatter-plot
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The Gifted and Not So Gifted
• Extreme Score Used for Treatment
Selection
• educational programs
• medical treatments
• What is the probability that the
score will remain extreme after
re-testing?
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A Computer Simulation
• Specifications
• randomly pick a score from a normal
distribution
• consider only scores greater than two
standard deviations above the mean.
• reliability of .8
• What is the probability that the score
will remain extreme (> 2sd’s) after
re-testing?
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How Much?
• only 43%
• research
• dementia: 39%
• ADHD: 45%
• depression: 40%
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True Score Correction
• The most important but forgotten
formula in psychometrics.
• Given a score with a reliability of
r, what is the best guess of the true
score or XTʹ?
• XTʹ = r(X - MX) + MX
• Correlation of XTʹ with X is one.
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Spontaneous Remission
Change in the control group using
Cohen’s d (over-time mean
difference divided by the pretest
standard deviation).
 depression: -0.35
 pain: -0.58
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Final Points
• RTM is not so mysterious:
• change happens.
• RTM is bidirectional.
• Whether the score is above or
below the mean in applications
may not be clear.
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Concluding Quote from
Francis Galton (1889)
“Some hate the very name of statistics
but I find them full of beauty and
interest. Whenever they are not
brutalized, but handled by higher
methods, and warily interpreted, their
power of dealing with complicated
phenomena is extraordinary.”
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