The authors discuss a new method that combines the randomized response technique with item response theory. This method allows the researcher to obtain information at the individual person level without knowing the true responses. With this new method, it is possible to compare groups of individuals by means of analysis of variance or regression analysis. To illustrate the advantages of this new method, 349 students of a university in the Netherlands were surveyed with respect to frequency and reasons to cheat on exams, and students' attitudes toward cheating were investigated. Thirty-six items tapping different types of cheating behavior were used to measure attitude toward cheating, and responses to questions were obtained via a randomized response technique. The new method was used to explain differences among students' attitudes using different kinds of background information. (Contains 2 tables and 2 figures.)