Abductive reasoning assigns special status to the explanatorypower of a hypothesis. But how do people make explana-tory judgments? Our study clarifies this issue by asking: (i)How does the explanatory power of a hypothesis cohere withother cognitive factors? (ii) How does probabilistic informa-tion affect explanatory judgments? In order to answer thesequestions, we conducted an experiment with 671 participants.Their task was to make judgments about a potentially explana-tory hypothesis and its cognitive virtues. In the responses, weisolated three constructs: Explanatory Value, Rational Accept-ability, and Entailment. Explanatory judgments strongly co-hered with judgments of causal relevance and with a sense ofunderstanding. Furthermore, we found that Explanatory Valuewas sensitive to manipulations of statistical relevance relationsbetween hypothesis and evidence, but not to explicit infor-mation about the prior probability of the hypothesis. Theseresults indicate that probabilistic information about statisticalrelevance is a strong determinant of Explanatory Value. Moregenerally, our study suggests that abductive and probabilisticreasoning are two distinct modes of inference.