Many standardized tests are now administered via computer rather than paper-and-pencil format. In a computer-based testing environment, it is possible to record not only the test taker’s response to each question (item) but also the amount of time spent by the test taker in considering and answering each item. Response times (RTs) provide information not only about the test taker’s ability and response behavior but also about item and test characteristics. This study focuses on the use of RTs to detect aberrant test-taker responses. An example of such aberrance is a correct answer with a short RT on a difficult question. Such aberrance may be displayed when a test taker or test takers have preknowledge of the items. Another example is rapid guessing, wherein the test taker displays unusually short RTs for a series of items. When rapid guessing occurs at the end of a timed test, it often indicates that the test taker has run out of time before completing the test. In this study, Bayesian tests of significance for detecting various types of aberrant RT patterns are proposed and evaluated. In a simulation study, the tests were successful in identifying aberrant response patterns. A real data example is given to illustrate the use of the proposed person-fit tests for RTs.