Two experiments used a rich and systematic set of noncontingent problems to examine humans' ability to detect the absence of an inter-event relation. Each found that subjects who used nonnormative strategies were quite inaccurate in judging some types of noncontingent problems. Group data indicated that subjects used the 2 × 2 information in the order Cell A > Cell B > Cell C > Cell D; individual subject data indicated that subjects considered the information in Cell A to be most important, that in Cell D to be least important, and that in Cells B and C to be of intermediate importance. Trial-by-trial presentation led to less accurate contingency judgments and to more uneven use of 2 × 2 cell information than did summary-table presentation. Finally, the judgment processes of about 70% and 80%, respectively, of nonnormative strategy users under trial-by-trial and summary-table procedures could be accounted for by an averaging model.