The effect of a nonlinear regression function on the
accuracy of the restriction of range correction formula
was investigated using analytic methods. Expressions
were derived for the expected mean square error
(EMSE) of both the correction formula and the squared
correlation computed in the selected group, with respect
to their use as estimators of the population relationship.
The relative accuracy of these two estimators
was then studied as a function of the form of the
regression, the form of the marginal distribution of x
scores, the strength of the relationship, sample size,
and the degree of selection. Although the relative accuracy
of the correction formula was comparable for
both linear and concave regression forms, the correction
formula performed poorly when the regression
form was convex. Further, even when the regression
is linear or concave, it may not be advantageous to
employ the correction formula unless the xy relationship
is strong and sample size is large.
Gross, Alan L & Fleischman, Lynn E. (1987). The correction for restriction of range and nonlinear regressions: An analytic study. Applied Psychological Measurement, 11, 211-217. doi:10.1177/014662168701100210
Gross, Alan L.; Fleischman, Lynn E..
The correction for restriction of range and nonlinear regressions: An analytic study.
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