Testing significance of a mean vector—A possible alternative to Hotelling'sT 2

Robust step-down tests for multivariate independent group designs

A composite step-down procedure, in which a set of step-down tests are summarized collectively with Fisher's combination statistic, was considered to test for multivariate mean equality in two-group designs. An approximate degrees of freedom (ADF) composite procedure based on trimmed/Winsorized estimators and a non-pooled estimate of error variance is proposed, and compared to a composite procedure based on trimmed/Winsorized estimators and a pooled estimate of error variance. The step-down procedures were also compared to Hotelling's T (2) and Johansen's ADF global procedure based on trimmed estimators in a simulation study. Type I error rates of the pooled step-down procedure were sensitive to covariance heterogeneity in unbalanced designs; error rates were similar to those of Hotelling's T (2) across all of the investigated conditions. Type I error rates of the ADF composite step-down procedure were insensitive to covariance heterogeneity and less sensitive to the number of dependent variables when sample size was small than error rates of Johansen's test. The ADF composite step-down procedure is recommended for testing hypotheses of mean equality in two-group designs except when the data are sampled from populations with different degrees of multivariate skewness.