Effect of Range Restriction on Correlation Coefficient Estimation

摘要

Suppose it is desired to estimate the correlation coefficient between randomvariables X and Y in some population P and the only data available are from some population Q where Q is a proper subset of P. X and Y are defined on P, while X and Y will denote X and Y restricted to 0. A simulation program was written to study the effect of this restricted sampling on the estimation of correlation coefficients. The Air Force is studying the implementation of new selection devices that optimize the selection and classification of individuals. Whenever a new measurement instrument is suggested, it must be evaluated by estimating its correlation with performance criteria and with tests and selection devices that are currently part of the selection process. The difficulty is that the new test can only be administered to Air Force personnel. That is, people who have already been selected. Air Force personnel constitute the population Q and the applicants constitute the population P. It is necessary to use a sample from Q to estimate correlations between tests that are to be used in P. This is called the range restriction problem. The purpose of this paper is to present the results of a study which addresses a number of issues related to the range restriction problem. The performance of the F-statistic, confidence intervals, and 'hidden variables' are considered.