Estimation of sampling error variance in the meta-analysis of correlations: use of average correlation in the homogeneous case. - Hunter, John E.; Schmidt, Frank L. (Journal of Applied Psychology, 1994)
The estimate of the population correlation used in the formula for sampling error variance of a correlation is typically the observed correlation, but in meta-analysis the average of the observed correlations can be used. For the case in which there is no variation in the study population correlations or sample sizes and the number of studies is very large, the authors found that use of the average correlation estimator is more accurate than use of the traditional, individual correlation estimator, except in those rare cases in which the uncorrected population correlation is greater than .60. For typical sample sizes, when the uncorrected population correlation is between -.40 and .40, there is virtually no error in the meta-analysis credibility interval based on the average correlation estimator. On the other hand, the amount of the error in the individual correlation estimator is qualitatively important if the sample is 25 or less and the population correlation is less than .40. Reprinted by permission of the publisher.