A Monte Carlo Study of the Sampling Distribution of the Congruence Coefficient

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Abstract
The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. The results indicated that when the population congruence coefficient is zero, the sampling distribution of the congruence coefficient is relatively stable and is similar to the sampling distribution of the correlation coefficient. The congruence coefficient was found to be positively biased for values of psi from .10 to .40 and negatively biased for the following values of psi: .50, .60, .90, and .99. The amount of bias (a) depends on the sample size and the number of variables used and (b) tends to decrease as sample size increases.