Using Results From Replicated Studies to Estimate Linear Models

This article outlines analyses for the results of a series of studies examining intercorrelations among a set of p + 1 variables. A test of whether a common population correlation matrix underlies the set of empirical results is given. Methods are presented for estimating either a pooled or average correlation matrix, depending on whether the studies appear to arise from a single population. A random effects model provides the basis for estimation and testing when the series of correlation matrices may not share a common population matrix. Finally, I show how a pooled correlation matrix (or average matrix) can be used to estimate the standardized coefficients of a regression model for variables measured in the series of studies. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures illustrate the procedures.