Wilks' lambda is a statistic used in particular by Discriminant Factor Analysis as a measure of the class centers separation.
Eigen Value: An eigenvalue indicates the proportion of variance explained. (Between-groups sums of squares divided by within-groups sums of squares). A large eigenvalue is associated with a strong function. These eigenvalues are related to the canonical correlations and describe how much discriminating ability a function possesses. The magnitudes of the eigenvalues are indicative of the functions' discriminating abilities.
Wilks’ Lambda is the ratio of within-groups sums of squares to the total sums of squares. This is the proportion of the total variance in the discriminant scores not explained by differences among groups. A lambda of 1.00 occurs when observed group means are equal (all the variance is explained by factors other than difference between those means), while a small lambda occurs when within-groups variability is small compared to the total variability. A small lambda indicates that group means appear to differ. The associated significance value indicates whether the difference is significant.
If eigen value is very high in comparison to wilks lambda, it means the groups are very well formed.
Normally there is an inverse relationship between eigen value and wilks lambda
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