摘要：Multinormal distributions are symmetric. The degree of deviations from axial symmetry can be assessed using the well known Bowker test. A recently proposed test (von Eye & Bogat, 2004; von Eye & Gardiner, 2004) is based on comparing the observed frequencies in sectors of the multivariate space with the corresponding expected frequencies that were estimated based on multinormality. Because this test is an omnibus test of multinormality, it should also be sensitive to deviations from axial symmetry. In this article, we describe the results of simulations that were performed on four types of bivariate distributions: normal, uniform, inverse Laplace-transformed, and cube-root transformed. As expected, the Bowker test showed that inverse Laplace-transformed distributions are likely to show deviations from axial symmetry. None of the other distributions was asymmetric. The new omnibus test of multinormality exhibited 100 % sensitivity to violations of axial symmetry, but was also sensitive to elevated skewness and kurtosis. Thus, it also flagged the uniform and the cube root-transformed distributions as deviating from multinormality. Results also show that the Bowker test is sensitive only to violations of axial symmetry.
关键词：multinormality; testing multinormality; symmetry; Monte Carlo
