Wilks's lambda or X

a test used in multivariate statistical procedures such as canonical correlation, discriminant function analysis and multivariate analysis of variance to determine whether the means of the groups differ on a discriminant function or characteristic root. It varies from 0 to 1. A lambda of 1 indicates that the means of all the groups have the same value and so do not differ. Lambdas close to 0 signify that the means of the groups differ. It can be transformed as a chi-square or an F ratio. It is the most widely used of several such tests which include Hotelling's trace criterion, Pillai's criterion and Roy's gcr criterion.

When there are only two groups, the F ratios for Wilks's lambda, Hotelling's trace, Pillai's criterion and Roy's gcr criterion are the same. When there are more than two groups, the F ratios for Wilks's lambda, Hotelling's trace and Pillai's criterion may differ slightly. Pillai's criterion is said to be the most robust when the assumption of the homogeneity of the variance-covariance matrix is violated.

Tabachnick and Fidell (2001)