Evolutionary trends and processes can distort phylogenetic information in sequences such that they do not reliably reflect the evolutionary processes that generate them. This fact of molecular evolution has a ubiquitous influence on the ability of researchers to adequately reconstruct genealogical relationships and histories of the processes of molecular evolution. This feature of phylogenetic inference can limit the capacity of researchers to adequately specify a relevant null hypothesis for testing hypothesis of relationships, data informativeness, and processes of molecular evolution. We show how this feature of historical inference also influences the exactness of the relative apparent synapomorphy analysis (RASA) test for phylogenetic signal and demonstrate how a permutation modification of the null hypothesis can improve the robustness of the underlying distributional assumption of the test. The RASA test (using either null model) was found not only to appropriately reject the combinability of independent lines of evidence for the relationships among the Physalaemus pustulosusfrog species group, but also to be more appropriately sensitive to individual uninformative data sets than commonly used tree-based measures of signal, including the consistency index, the retention index, and the permutation tail probability test statistic.