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Fisher Transformations for Correlations Corrected for Selection and Missing Data

Published online by Cambridge University Press:  01 January 2025

Jorge L. Mendoza
Jorge L. Mendoza*
Affiliation:
University of Oklahoma
*
Requests for reprints should be sent to Jorge L. Mendoza, Department of Psychology, Dale Hall, University of Oklahoma, Norman OK 73019.
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Abstract

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher's Z transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisher r to Z transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The two Z transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.

Keywords

selectionmissing datarestriction in in rangevalidationcorrelationZ transformation
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 4 , December 1993 , pp. 601 - 615
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

I would like to thank Alan Nicewander for his invaluable help in this project. Also, I would like to thank the referees and the editors for their thoughtful comments.

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