Calculates Pillai's trace statistic for a given super_sample object.
This function ensures that the within-group
and total covariance matrices are computed,
then computes the sum of the eigenvalues of
the matrix (Total - Within) %*% solve(Total).
Calculates Pillai's trace statistic for a given super_sample object.
This function ensures that the within-group
and total covariance matrices are computed,
then computes the sum of the eigenvalues of
the matrix (Total - Within) %*% solve(Total).