alexa Averaging correlations: expected values and bias in combined Pearson rs and Fisher’s z transformations ,Tunney RJ and Ziegler FV. Surrogate utility estimation by long-term partners and unfamiliar dyads.
Medicine

Medicine

General Medicine: Open Access

Author(s): Corey DM, Dunlap WP, Burke MJ

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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 rz' . In large part because of this fact, J. E. Hunter and F. L. Schmidt (1990) have argued that average r is preferable to average rz' . In the present study, bias in average r and average rz' was empirically examined. When correlations from a matrix were averaged, the use of z' decreased bias. For independent correlations, contrary to analytical expectations, average rz' was also generally the less biased statistic. It is concluded that (a) average rz' is a less biased estimate of the population correlation than average r and (b) expected values formulae do not adequately predict bias in average rz' when a small number of correlations are averaged.

This article was published in The Journal of General Psychology and referenced in General Medicine: Open Access

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