The Distribution of Chance Congruence Coefficients from Simulated Data

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Abstract
All attempts to study the stability of factors depend on having some useful statistic that measures the degree of similarity between factors. This study attempts to provide some normative data about the distribution of one measure of similarity, the congruence coefficient, through a Monte Carlo technique. The matching of “chance” factor patterns was done by the method of Tucker. Statistical tests of the results, based on similarities of the method to canonical and multiple correlation, seemed satisfactory. The tabled results can be used as guides to the significance of congruence coefficients for some cases. The consistencies of the data indicate that a functional resolution may be possible, but none was found.