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

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Abstract

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.

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Authors and Affiliations

  1. Florida State University, USA

    James K. Brewer & John R. Hills

Authors
  1. James K. Brewer
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  2. John R. Hills
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Additional information

This manuscript was completed while the senior author was on an NSF Science Faculty Fellowship at Stanford University.

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Brewer, J.K., Hills, J.R. Univariate selection: The effects of size of correlation, degree of skew, and degree of restriction. Psychometrika 34, 347–361 (1969). https://doi.org/10.1007/BF02289363

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  • DOI: https://doi.org/10.1007/BF02289363

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