Score differencing is one of six categories of statistical methods used to detect test fraud (Wollack & Schoenig, 2018) and involves the testing of the null hypothesis that the performance of an examinee is similar over two item sets versus the alternative hypothesis that the performance is better on one of the item sets. We suggest, to perform score differencing, the use of the posterior probability of better performance on one item set compared to another. In a simulation study, the suggested approach performs satisfactory compared to several existing approaches for score differencing. A real data example demonstrates how the suggested approach may be effective in detecting fraudulent examinees. The results in this paper call for more attention to the use of posterior probabilities, and Bayesian approaches in general, in investigations of test fraud. [This paper was published in "Journal of Educational and Behavioral Statistics" (EJ1300427).]