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

摘要: Abstract 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 skew, suggesting a biased statistic. Analytical formulae, however, indicate expected bias in than z' back-converted rz' . In large part because this fact, J. E. Hunter F. L. Schmidt (1990) have argued preferable present study, was empirically examined. When correlations from matrix were averaged, use decreased bias. For independent correlations, contrary analytical expectations, also generally It concluded (a) estimate population (b) values formulae do not adequately predict when small number are averaged.