Averaging correlation coefficients: Should Fisher's z transformation be used?

Article Abstract:

Averaging correlations leads to underestimation because the sampling distribution of the correlation coefficient is skewed. It is also known that if correlations are transformed by Fisher's z prior to averaging, the resulting average overestimates the population value of z. The behavior of these procedures for averaging correlations was investigated via Monte Carlo simulation, both in terms of bias (under- and overestimation) and precision (standard errors). It was found that average z backtransformed to r is less biased positively than average r is biased negatively. The standard error of average r was smaller than that of average z when the population correlation was small; however, the reverse was true when the population correlation exceeded .5. Regardless of sample size, backtransformed average z was always less biased; therefore, the use of the z transformation is recommended when averaging coefficients, particularly when sample size is small. (Reprinted by permission of the publisher.)

Analysis of variance, Correlation (Statistics)

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Sampling variance in the correlation coefficient under range restriction: a Monte Carlo study

Article Abstract:

Validity generalization methods require accurate estimates of the sampling variance in the correlation coefficient when the range of variation in the data is restricted. This article presents the results of computer simulations examining the accuracy of the sampling variance estimator under sample range restrictions. Range restriction is assumed to occur by direct selection on the predictor. Sample sizes of 25, 60, and 100 are used, with the selection ratio ranging from .10 to 1.0 and the population correlation ranging from .10 to .90. The estimator is found to have a slight negative bias in unrestricted data.In restricted data, the bias is substantial in sample sizes of 60 or less. In all sample sizes, the negative bias increases as the selection ratio becomes smaller. Implications of the results for studies of validity generalization are discussed. (Reprinted by permission of the publisher.)

Statistics, Statistics (Data), Statistical hypothesis testing

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