Assessing the contribution of individual variables following rejection of a multivariate hypothesis

Abstract

There are two basic approaches for examining the contribution of in-dividual variables to separation of groups after rejection of a multivariate hypothesis: (1) a multivariate approach showing the contribution of each variable in the presence of the other variables, and (2) a univariate approach showing the contribution of each variable by itself ignoring the other vari-ables. For the multivariate approach, we express the standardized (canonical) discriminant function coefficients in a form showing that the contribution of each variable is due to its multiple correlation with the other variables and how well its separation of groups can be predicted from the other variables. For the univariate approach, we present the results of a Monte Carlo study comparing four methods of testing individual variables. A “protected” pro-cedure that performs F tests only if the overall Wilks' A rejects, appears to be preferred.

Keywords:

• protected tests
• univariate tests
• simultaneous tests
• discrimi-nant functions