Biologists often compare average phenotypes of groups of species defined cladistically or on behavioral, ecological, or physiological criteria (e.g., carnivores vs. herbivores, social vs. nonsocial species, endotherms vs. ectotherms). Hypothesis testing typically is accomplished via analysis of variance (ANOVA) or covariance (ANCOVA; often with body size as a covariate). Because of the hierarchical nature of phylogenetic descent, however, species may not represent statistically independent data points, degrees of freedom may be inflated, and significance levels derived from conventional tests cannot be trusted. As one solution to this degrees of freedom problem, we propose using empirically scaled computer simulation models of continuous traits evolving along “known” phylogenetic trees to obtain null distributions of F statistics for ANCOVA of comparative data sets. These empirical null distributions allow one to set critical values for hypothesis testing that account for nonindependence due to specified phylogenetic topology, branch lengths, and model of character change. Computer programs that perform simulations under a variety of evolutionary models (gradual and speciational Brownian motion, Ornstein-Uhlenbeck, punctuated equilibrium; starting values, trends, and limits to phenotypic evolution can also be specified) and that will analyze simulated data by ANCOVA are available from the authors on request. We apply the proposed procedures to the analysis of differences in homerange area between two clades of mammals, Carnivora and ungulates, that differ in diet. We also apply the phylogenetic autocorrelation approach and show how phylogenetically independent contrasts can be used to test for clade differences. All three phylogenetic analyses lead to the same surprising conclusion: for our sample of 49 species, members of the Carnivora do not have significantly larger home ranges than do ungulates. The power of such tests can be increased by sampling species so as to reduce the correlation between phylogeny and the independent variable (e.g., diet), thus increasing the number of independent evolutionary transitions available for study.