# Bartlett's Correction to Wilk's Lambda for MANOVA

The test statistic tests for independence between a set of ${\displaystyle k}$ numeric variables and a categorical variable containing ${\displaystyle g}$ groups:
${\displaystyle \Lambda ={\frac {|{\textbf {W}}|}{|{\textbf {T}}|}}}$
${\displaystyle {\textbf {W}}}$ is the withinsum of squares and cross-products matrix (computed using the Calibrated Weight),
${\displaystyle {\textbf {T}}}$ is the total sum of squares and cross-products matrix (computed using the Calibrated Weight), and
${\displaystyle p\approx \Pr(\chi _{k(g-1)}^{2}\geq \Lambda )}$.