Bartlett's Correction to Wilk's Lambda for MANOVA

The test statistic tests for independence between a set of $k$ numeric variables and a categorical variable containing $g$ groups:

$\mathrm{\Lambda }=\frac{|\text{W}|}{|\text{T}|}$

where

$\text{W}$ is the withinsum of squares and cross-products matrix (computed using the Calibrated Weight),

$\text{T}$ is the total sum of squares and cross-products matrix (computed using the Calibrated Weight), and

$p\approx \mathrm{Pr}({\chi }_{k(g-1)}^2\ge \mathrm{\Lambda })$.

See also

Multivariate Tests