THE CONTRIBUTION OF INDIVIDUAL VARIABLES TO HOTELLINGS T(2), WILKS LAMBDA, AND R(2)

We examine the effect of each variable on the following statistics: the one-sample and two-sample Hotelling's T2, Wilks' LAMBDA for multivariate analysis of variance, and R2 in multiple regression. For T2, the net effect of each variable is an increase in the multivariate statistic, and the particular factors determining the amount of increase are (i) the multiple correlation of the variable with all other variables, and (ii) how well the variable's contribution to falsifying the hypothesis can be linearly predicted from the other variables. The effect of each predictor variable on R2 is similar to the effect of each variable on T2. For Wilks' LAMBDA, each variable induces a decrease, due to (i) the F for that variable alone, and (ii) the change in multiple correlation from within-sample to total-sample.