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.

The Fennema-Sherman Mathematics Attitudes Scales were administered to 1541 junior high school students. To investigate the construct validity of the scales, factor analyses were performed on the responses to the 108 items comprising the scales. Additional factor analyses of the scale scores were performed, and a comparison was made with results reported by Fennema and Sherman (1976). Analysis of the items led to the interpretation of eight factors. The results generally provided empirical evidence to support the theoretical structure of the Fennema-Sherman Mathematics Attitudes Scales.