A Monte Carlo Investigation of the Robustness of T²

Abstract

The robustness of T² for samples of size 5, 10 and 20 from several bivariate distributions is investigated. Samples are presented from bivariate normal, uniform, exponential, gamma, lognormal and double exponential distributions. Related observations on the one sample t and paired t are also given. Highly skewed distributions resulted in too many extreme values of T² Other distributions gave conservative results. The use of the t-test and non-simultaneous techniques gave large overall levels of significance.