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

\[\begin{align} \Lambda = \frac{| \textbf{W} |}{| \textbf{T} |} \end{align}\]

where:

\(W\) is the within sum of squares and cross-products matrix (computed using the Calibrated Weight),

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

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

## See Also

Multivariate Tests