The two-sample version of Hotelling T². The quantity D², introduced by Mahalanobis in a 1930 paper, may be considered to be a measure of the distance between two groups of p-dimensional observations. Let x̄_j be the p×1 vector of means for group j (j=1,2), with S_j the corresponding variance–covariance matrix. D² is given by where S is given by and n₁ and n₂ are the sample sizes.