Accuracy of Corrections for Restriction in Range Due to Explicit Selection in Heteroscedastic and Nonlinear Distributions

Abstract

Corrections for restriction in range due to explicit selection assume linearity of regression and homoscedastic array variances. Violation of one or both of these assumptions can lead to serious errors in estimating the unrestricted population correlation. A Monte Carlo study was conducted to examine the effects of some common forms of violation of these assumptions. The results suggested that the corrected correlation provides a fairly good estimate of the population correlation for moderately restricted samples but becomes progressively less accurate with increasing degrees of restriction. In addition, corrected estimates were generally more accurate than corresponding uncorrected estimates of the population correlation.