Dow and Cheverud (Am. J. Phys. Anthropol. 68:367–373, 1985) have published a statistical test for comparing any three similarity matrices. Using both simulations and analytical arguments, I establish that the presence of spatial autocorrelation, a common feature of geographically based anthropological and biological data, causes this test to reject too often. Increasing the spatial autocorrelation increases the spurious rejection rate. About 20% of the papers that reference Dow and Cheverud's paper have used their test with spatially autocorrelated data. Mantel's (Cancer Res. 27:209–220, 1967) method, when used as a test of spatial autocorrelation, is unaffected by these considerations, since its null hypothesis is that the data are uncorrelated. © 1992 Wiley-Liss, Inc.