Techniques have been developed that use a linear model to analysing the structure of correlation matrices. These provide for an analysis of variance in which the total variation in Fisher's z-transformation of the elements of a correlation matrix is partitioned. The correlation matrices may be the correlation between p variables or be between variables that are cross-classified by two factors, such as multitrait-multimethod matrices. As well as providing a simple tests for the equality of correlation hypotheses, the procedure indicates how familiar techniques can be used to investigate correlation matrices.
Brien, C.J. (1981). Patterns in correlation matrices arising in wine-tasting and other experiments. unpublished M. Agr. Sc. thesis (in a PDF file), Adelaide University.
Brien, C.J., Venables, W.N., James, A.T., and Mayo, O. (1984). An analysis of correlation matrices: equal correlations. Biometrika, 71, 545-553.
Brien, C.J., James, A.T., and Venables, W.N. (1988). An analysis of correlation matrices: variables cross-classified by two factors. Biometrika, 75, 469-476