Abstract

Hotelling's T² is seriously nonrobust when the variance-covariance (v-c) matrices are heteroscedastic and when the sampled populations are skewed and have positive kurtosis. Based on some relevant empirical studies, four alternatives to T² — James' first order, James' second order, Yao's, and Johansen's tests —, were reviewed, Under v-c heteroscedasticity and/or nonnormality, although James' first order test performs better than T², its estimated Type I error rates are not as good as those produced by the other three tests.

摘要

在做兩組間多變項分析（multivariate analysis）時，如果兩組間的變異數與共變數矩陣（variance-covariance matrices）不相同且兩組的分析不是成對常態時，Hotelling's T²則不是一個合適的統計分析方法。因此，有很多統計學者曾試着提出能替代Hotelling's T²的一些統計分析方法。本篇文章旨在對四個能替代Hotelling's T²的一些統計分析法：James' first order test，及James' second order test，Johansen's test，及Yao's test做一介紹及文獻整理，以期能讓教育研究學者在做多變項分析欲選擇一合適的統計分析方法時，能有一個較明確的方向或原則去遵行。