A More Informative Approach to Compare Scedasticity under the Assumption of Multivariate Normality

This paper extends the usual scedasticity comparison among several groups of observations, usually complying to the homoscedastic and heteroscedastic cases, in order to deal with data sets laying in an intermediate situation. As it is well known, homoscedasticity corresponds to equality in orientation, shape and size of the group scatters. Here our attention is focused on a weaker requirement: scatters with the same orientation, but with different shape and size, and scatters with the same shape and size but different orientation. Under the assumption of multivariate normality, we introduce multiple tests for the evaluation of each of the above conditions. Some well-known data sets, chosen in the multivariate literature, allow us to apply the new inferential methodology and to show how it can offer a more informative approach. Further, a wide simulation study illustrates and compares the performance of the proposed tests, applied on data sets with a gradual departure from homoscedasticity.