Univariate selection: The effects of size of correlation,degree of skew,and degree of restriction

Pearson's formula for univariate selection was derived with the assumption of normality of variates before and after selection. This study examined the influence of skew upon estimates from Pearson's formula under certain conditions. It was found that even with essentially symmetric distributions, a large proportion of the data is necessary to obtain reasonably precise estimates of low correlations. With increasing skew, estimates become increasingly erroneous, the direction of the error depending upon which tail of the distribution is the basis of the estimates. Difficulties in applying correction for univariate selection in several studies of the predictability of college-grades for Negroes from scores on standard aptitude tests are discussed.