Analyses for results of a series of studies examining intercorrelations among a set of as many as p+1 variables are presented. Several estimators of a pooled or average correlation vector and its variances are derived for cases in which some studies do not report complete correlation matrices. A test of the homogeneity (consistency) of the correlation matrices is also given. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures illustrate the procedures. These data are taken from 10 samples (sample sizes 74, 153, 48, 55, 51, 18, 27, 43, 35, and 34, respectively) from 4 studies exploring the relationship of spatial ability to Scholastic Aptitude Test scores for high school or junior high school students. The empirical Bayes procedure (based on the EM algorithm) involves no data loss and is recommended if it is reasonable to assume that the unobserved correlations are missing at random. Three tables present illustrative data. (Author/SLD)