Averaging Correlations: Expected Values and Bias in Combined Pearson rs and Fisher's z Transformations

R. A. Fisher's z (z'; 1958) essentially normalizes the sampling distribution of Pearson r and can thus be used to obtain an average correlation that is less affected by sampling distribution skew, suggesting a less biased statistic. Analytical formulae, however, indicate less expected bias...

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Bibliographic Details
Published inThe Journal of general psychology Vol. 125; no. 3; pp. 245 - 261
Main Authors Corey, David M., Dunlap, William P., Burke, Michael J.
Format Journal Article
LanguageEnglish
Published Provincetown, Mass., etc Taylor & Francis Group 01.07.1998
Journal Press, etc
Taylor & Francis Inc
Subjects
Averaging
Bias
Estimates
Estimation bias
Expected values
Experiments
Meta-analysis
Population
Psychology
Reservoirs
Sample size
Social sciences
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Summary:R. A. Fisher's z (z'; 1958) essentially normalizes the sampling distribution of Pearson r and can thus be used to obtain an average correlation that is less affected by sampling distribution skew, suggesting a less biased statistic. Analytical formulae, however, indicate less expected bias in average r than in average z' back-converted to average r z' . In large part because of this fact, J. E. Hunter and F. L. Schmidt (1990) have argued that average r is preferable to average r z' . In the present study, bias in average r and average r z' was empirically examined. When correlations from a matrix were averaged, the use of z' decreased bias. For independent correlations, contrary to analytical expectations, average r z' was also generally the less biased statistic. It is concluded that (a) average r z' is a less biased estimate of the population correlation than average r and (b) expected values formulae do not adequately predict bias in average r z' when a small number of correlations are averaged.
ISSN:0022-1309
1940-0888
DOI:10.1080/00221309809595548