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With the aim to clarify some confusion apparently still present in part of the literature on testing for multivariate normality, we collect and discuss some facts on invariance and ancillarity of various variants of, so-called, configuration of a multivariate normal sample. In particular, we show how the choice of the rotation matrix, used in the definition of the configuration, influences its invariance, distribution and ancillarity.

A Comment on Affine Invariance and Ancillarity in Testing Multivariate Normality