A new test for shape differences when variance–covariance matrices are unequal

Abstract This paper presents a new statistical testing procedure for testing the equality of two shapes based on landmark coordinate data. Lele & Richtsmeier (1991) propose a test for shape differences based on Euclidean distance matrix analysis (EDMA). One of the assumptions needed for their test to be valid is the equality of the variance–covariance matrices in the two populations under consideration. Using recent results from Lele (1993), we propose an alternative test procedure based on EDMA. This new procedure is valid even if the variance–covariance matrices in two populations are not equal. We study the validity (i.e., the correctness of the probability of type-I error) and the power (i.e., the probability of correct rejection of the null hypothesis when it is false) of the test via simulations. We provide also a biological example, comparing the shapes of the midfacial region in Neandertals and anatomically modern humans, where the variance–covariance structures are quite different.