Human health risk assessment consists of bringing to bear a large body of in vitro, animal, and epidemiologic studies on the question of whether environmental exposures to a substance are a potential risk to humans. The body of scientific information is typically less than definitive and often contains apparent contradictions. Often various possible conclusions about potential human risks may be drawn from the data and these may vary from very strong to tenuous. The task, therefore, is to communicate the uncertainties in the inferences from the data effectively, giving proper consideration to contrary data and alternative scientifically plausible interpretations. We propose an approach, Hypothesis-Based Weight of Evidence (HBWoE), to organize, evaluate, and communicate the large body of available relevant data on a given chemical, using naphthalene as an example. The goal for our use of the term "weight of evidence" (WoE) is broad in that we express the relative degrees of credence that should be placed in alternative possible interpretations of the naphthalene data and hypothesized carcinogenic modes of action (MoAs), expressed in a way that shows how such credence is tied to specific scientific interpretations, considering consistencies, inconsistencies, and contradictions within the data set.