On a Transvariation Based Measure of Group Separability

In this paper, the potentialities of transvariation (Gini, 1959) in measuring the separation between two groups of multivariate observations are explored. With this aim, a modified version of Gini’s notion of multidimensional transvariation is proposed. According to Gini (1959), two groups G1 and G2 are said to transvary on the k-dimensional variable X=(X1,..., Xh,..., Xk) if there exists at least one pair of units, belonging to different groups, such that for h=1, ..., k the sign of the difference between their Xh values is opposite to that of m1h −m2h, where m1h and m2h are the corresponding group mean values of Xh. We introduce a modification that allows us to derive a measure of group separation, which can be profitably used in discriminating between two groups. The performance of the measure is tested through simulation experiments. The results show that the proposed measure is not sensitive to distributional assumptions and highlight its robustness against outliers.