## ABSTRACT

I. Introduction As indicated in Chapters 2, 3, 6, 7, 8, and 9 , parallel tests are tests

that have equal means, equal variances, and equal intercorrelations . For any given set of experimental data, where the parallel forms of a test are given to a single group, there will be, even under the best condi tions, some small sampling differences. To be certain that the tests may be regarded as parallel, it is necessary to have some statistical criterion that will show whether or not the means may be regarded as samples from a population in which the means are identical, the variances may be regarded as samples from a population in which variances are identical , and the intercorrelations may be regarded as samples from a population in which the correlations are identical . Such a test has recently been provided by Dr. S. S. Wilks (Wilks, 1946) . Since two parallel forms have only one intercorrelation, it is possible in this case to check only for equality of means and of variances ; hence we must consider the case of three or more parallel tests in order to demonstrate the statistical criterion for parallel tests .