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This paper compares the statistical power of various tests that have been proposed to test for equality of shape in two populations. Power surfaces are 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 Stat 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 T(2)-tests using Bookstein shape coordinates was good if the baseline was not the shortest side of the triangle. The Rao and Suryawanshi (1996 Proc Natl Acad Sci 93:12132-12136 and Rao and Suryawanshi 1998 Proc Natl Acad Sci 95:4121-4125) shape variables 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 surface 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 landmarks are also presented. The implications of the results for practical applications of morphometrics are discussed.
F. James Rohlf (Sat,) studied this question.