A measure of the magnitude of the effect in a one-factor multivariate analysis of variance design is considered. Cooley and Lohnes have proposed the use of the quantity (1 — |
W
|/|
T
|) as a multivariate extension of the correlation ratio, where |
W
| is the determinant of the within-groups cross-products matrix and |
T
| is the determinant of the total cross-products matrix. The measure is based on the use of |
W
| as the estimate of a generalized measure of within-groups variation and |
T
| as the estimate of a generalized measure of total variation. If a multivariate correlation ratio is defined as the proportion of variance in the multivariate domain predictable from the factor, it is argued that crM
= 1 - Tr(
WW
-1)/ Tr(
TW
-1) is a more suitable multivariate generalization of the univariate correlation ratio.
