While there is no doubt among evolutionary biologists that all living species, or merely all living species within a particular group (e.g., animals), share descent from a common ancestor, formal statistical methods for evaluating common ancestry from aligned DNA sequence data have received criticism. One primary criticism is that prior methods take sequence similarity as evidence for common ancestry while ignoring other potential biological causes of similarity, such as functional constraints. We present a new statistical framework to test separate ancestry versus common ancestry that avoids this pitfall. We illustrate the efficacy of our approach using a recently published large molecular alignment to examine common ancestry of all primates (including humans). We find overwhelming evidence against separate ancestry and in favor of common ancestry for orders and families of primates. We also find overwhelming evidence that humans share a common ancestor with other primate species. The novel statistical methods presented here provide formal means to test separate ancestry versus common ancestry from aligned DNA sequence data while accounting for functional constraints that limit nucleotide base usage on a site-by-site basis.