A Monte Carlo Study of Using the First Eigenvalue for Averaging Intercorrelations

Abstract

A procedure proposed by Kaiser (1968) for averaging correlation coefficients using the first eigenvalue of an intercorrelation matrix was studied via Monte Carlo methods. The Kaiser average if applied to sample intercorrelations was found to be markedly biased toward overestimation of the population correlation when the population correlation was small, and to show a slight negative bias similar to average r when the population correlation was large. A modification of the Kaiser average substantially reduced the bias for correlations near zero and showed slightly smaller standard errors (greater efficiency) than the other averages for small correlations. The least biased averaging procedure still appears to be the backtransformed average Fisher's z, particularly when sample size is small.