Statistical criteria for parallel tests: A comparison of accuracy and power

Parallel tests are needed so that alternate forms can be applied to different groups or on different occasions, but also in the context of split-half reliability estimation for a given test. Statistically, parallelism holds beyond reasonable doubt when the null hypotheses of equality of observed means and variances across the two forms (or halves) are not rejected. Several statistical tests have been proposed for this purpose, but their performance has never been compared. This study assessed the relative performance (type I error rate and power) of the Student–Pitman–Morgan, Bradley–Blackwood, and Wilks tests of equality of means and variances in the typical conditions surrounding studies of parallelism—namely, integer-valued and bounded test scores with distributions that may not be bivariate normal. The results advise against the use of the Wilks test and support the use of the Bradley–Blackwood test because of its simplicity and its minimally better performance in comparison with the more cumbersome Student–Pitman–Morgan test.