A Computer Program to Test a Repeated Measures Hypothesis Using Hotelling's One-Sample T2 Statistic

Abstract

The extent and direction of bias in an approximate test ( T_A²) of a one-way repeated measures hypothesis was studied. Monte Carlo methods were used to simulate nine multinormal parent populations. Five thousand samples were drawn from each population and an F statistic (transformed from T_A²) was calculated for each sample. Nine sampling distributions, each containing 5,000 Fs, were then observed. T_A² was shown to be very conservative—the proportions observed in the upper tails of the nine distributions were much smaller (in most cases one-half the size) than the proportions expected. The exact T² test was also presented along with the description of a program which computes this statistic. The program is recommended, over available package programs, because it requires minimum input.