Regression toward the mean

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Regression toward the mean

The tendency that a random variable will ultimately have a value closer to its mean value.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.
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TABLE 9 RESULTS OF THE VOUCHER THREAT VARIABLE ON ALL ADVANCED PROFICIENCY LEVEL ANALYSES Effect Variable Coefficient P-value Size 4th Grade Reading 2.75 0.004 0.38 4th Grade Math 4.07 0.000 0.30 6th Grade Reading 6.58 0.000 0.48 6th Grade Math -6.15 0.000 -0.43 TABLE 10 REGRESSION TO THE MEAN TESTS Variable Coefficient P-value 4th Grade Reading (P) * 0.13 0.929 4th Grade Math (P) * 2.97 0.077 6th Grade Reading (P) 2.76 0.096 6th Grade Math (P) 0.76 0.676 Performance Index Score * -3.08 0.231 4th Grade Reading (L) 4.66 0.000 4th Grade Math (L) * 0.35 0.787 6th Grade Reading (L) * 4.39 0.021 6th Grade Math (L) * 0.97 0.484 * Indicates a dependent variable where a significant effect was found from the voucher threat.
On the other hand, the student who obtains the highest score is also the person whose test score at some later date is most likely to show the greatest amount of regression to the mean. How is this possible?
The effect of regression to the mean in epidemiologic and clinical studies.
The objective of this study was to test provider response to the implementation of recent threshold-based P4P while controlling for regression to the mean. Specifically, we test whether providers farthest below the threshold are least likely to improve and whether providers close to the threshold are most likely to improve.
These two methods are likely biased toward underestimating the CMFs for lower values, and thereby exaggerating crash reductions, because regression to the mean is likely at play and is not accounted for in these methods.
As Alex Bellos explained in his book Alex's Adventures in Numberland: "regression to the mean is not a complicated idea.
The pre-test value of the dependent variable can also be included as a covariate to avoid confounding by the phenomenon of regression to the mean. Graphs of change scores plotted against the covariate show visually how the treatment effect is adjusted to the chosen value of the covariate.
This illustrates the well-known regression to the mean status phenomenon.
One group of pre-post designs, although the most prominent design used for program evaluation (Johnson 2003; Linden, Adams, and Roberts 2003), can be limited by a number of confounders, including history, maturation, and regression to the mean. History effects may call into question the results if an event occurred between the pre and post measurements that impacted the outcome but was unrelated to the intervention or not of specific interest (Cook and Campbell 1979).
The reason is something called regression to the mean. Ignorance of regression to the mean explains why clubs can fail to get value for money for a manager, or players.
Observed crash data are subject to regression to the mean, because high short-term crash frequencies are likely to decrease and low short-term crash frequencies are likely to increase as a matter of course, even if no improvements are made.
This tendency may be a genuine effect of the pre-test value, but it may also be partly or wholly an artefact of regression to the mean (Hopkins, 2003d).