Statistical power comparisons among alternative morphometric methods

This paper compares the statistical power of various tests that have been p roposed to test for equality of shape in two populations. Power surfaces ar e computed with emphasis on the simplest case of three points in the plane (i.e., landmarks at the vertices of a triangle). Goodall's ([1991] J Roy St at Soc Serb 53:285-339) F-test was found to have the highest power followed by T-2-tests using Kendall tangent space coordinates. Power for T2-tests u sing Bookstein shape coordinates was good if the baseline was not the short est side of the triangle. The Rao and Suryawanshi ([1996] Proc Natl Acad Sc i 93:12132-12136 and [1998] Proc Natl Acad Sci 95:4121-4125) shape variable s had much lower power when triangles were not close to being equilateral. Power surfaces for the EDMA-I T statistic revealed very low power for many shape comparisons including those between very different shapes. Power surf ace for the EDMA-II Z statistic were also complicated and depended strongly on the choice of baseline used for size scaling. The type I error rate was also often not correct for this method. Results for more than three landma rks are also presented. The implications of the results for practical appli cations of morphometrics are discussed. (C) 2000 Wiley-Liss, Inc.