Numerical evaluation of cytologic data. VII. Multivariate significance tests.

Multivariate analysis is commonly used to "prove" the existence of significant, if frequently small, differences between samples. Methods with numerical examples are presented for three test statistics used in multivariate analysis to assess the chance of an error of the first kind, alpha, that the differences observed are merely the result of chance. Hotelling's T2 test is a measure of the significance of the difference between groups. Wilks' lambda is used to assess the significance of the separation between groups. Box's M statistic is used to test the hypothesis that two variance-covariance matrices are the same. The question is raised of the power of test statistics: while they may possess high sensitivity in terms of assessing the significance of differences observed, alone they lack the specificity to determine absolutely the cause of the differences.