Bayesian confirmation measures give numerical expression to the impact of evidence E on a hypothesis H. All measures proposed to date are formal-that is, functions of the probabilities Pr[see equation in text], Pr[see equation in text], Pr[see equation in text], Pr[see equation in text], and nothing more. Experiments reported in Tentori, Crupi, and Osherson (2007) suggest that human confirmation judgment is not formal, but this earlier work leaves open the possibility that formality holds relative to a given semantic domain. The present study discredits even this weaker version of formality by demonstrating the role in confirmation judgments of a probability distribution defined over the possible values of Pr[see equation in text], Pr[see equation in text], Pr[see equation in text], and Pr[see equation in text]-that is, a second-order probability. Specifically, when for each of the latter quantities a pointwise value is fixed with a maximal second-order probability, evidence impact is rated in accordance with formal and normatively credible confirmation measures; otherwise evidence impact is systematically judged as more moderate.