Sibley and Ahlquist compared the single-copy nuclear DNA sequences of the hominoid primates using DNA-DNA hybridization. From this data set they estimated a phylogeny that clusters man and chimpanzees using a distance Wagner procedure. However, no assessment of statistical confidence in this estimated phylogeny was made, despite the fact that their data set contains internal inconsistencies concerning the correct branching order. This paper presents a modification of Pielou's Q-statistic that allows one to make nonparametric tests of phylogenetic relationship from distance data. The results of this analysis indicate that the estimated phylogeny of Sibley and Ahlquist is without statistical significance owing to the internal inconsistencies of the data set. A survey and additional analyses of other types of molecular data indicate that the phylogeny that clusters chimpanzees and gorillas and has the human lineage splitting off earlier is statistically consistent with all the molecular data (including the DNA-DNA hybridization data), whereas the phylogeny estimated by Sibley and Ahlquist can be rejected at the 5% level using the data on restriction-endonuclease sites in the mitochondrial genome.