ROBUSTNESS OF THE INDEPENDENT SAMPLES HOTELLING T2 TO VARIANCE COVARIANCE HETEROSCEDASTICITY WHEN SAMPLE SIZES ARE UNEQUAL AND IN SMALL RATIOS

Type I error rates for the independent samples Hotelling's T2 were estimated using simulated data for conditions in which the variance-covariance matrices were heteroscedastic and the ratios of unequal sample sizes were small (n1:n2 = 1:1.25, 1.25:1, 1:1.1, and 1.1:1). Type I error rates were estimated for various combinations of the number of variables, sample-size-to-variables ratio, and degree and type of heteroscedasticity. Even with a sample size ratio as small as 1.1:1, the T2 procedure can be seriously nonrobust. As expected, the procedure became less robust as the number of variables and degree of heteroscedasticity increased.