A procedure is proposed for testing the significance of group differences in the standard error of measurement of a psychological test. Wilks' criterion is used to assure that the tests used in ascertaining reliability and hence variance of errors of measurement may be assumed parallel for each group. Votaw's criterion may be used to check whether the test scores of all the groups have the same mean, variance, and covariance. It is possible, however, for the variance and reliability of the test to differ widely from group to group, so that Votaw's criterion is not satisfied even though the variance of errors of measurement stays relatively constant. For this case a modification of Neyman and Pearson's criterion is developed to test agreement among standard errors of measurement despite group differences in mean, variance, and reliability of the test.