A potential negative consequence of high-stakes testing is inappropriate test behaviour involving individuals and/or institutions. Inappropriate test behaviour and test collusion can result in aberrant response patterns and anomalous test scores and invalidate the intended interpretation and use of test results. A variety of statistical techniques have been developed to investigate anomaly in test results at individual test-taker and group levels. This article provides a brief introduction to some of the most widely studied techniques, with a particular focus on their underlying concepts and principles employed to derive indices for identifying anomalous test results. Detailed mathematical derivations of the various statistical models discussed are not given, but relevant references are provided.