Effects of the generalized Box-Cox transformation on Type Ⅰ error rate and power of Hotelling's T~2

摘要

Most multivariate statistical techniques rely on the assumption of multivariate normality. The effects of nonnormality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators usually do not attempt to assess multivariate normality. In this simulation study, the effects of skewed and leptokurtic multivariate data on the Type Ⅰ error and power of Hotelling's T~2 were examined by manipulating distribution, sample size, and variance-covariance matrix. The empirical Type I error rate and power of Hotelling's T~2 were calculated before and after the application of generalized Box-Cox transformation. The findings demonstrated that even when variance-covariance matrices and sample sizes are equal, small to moderate changes in power still can be observed.