Graph Theory Approach to Detect Examinees Involved in Test Collusion

Test collusion (TC) is sharing of test materials or answers to test questions before or during the test (important special case of TC is item preknowledge). Because of potentially large advantages for examinees involved, TC poses a serious threat to the validity of score interpretations. The proposed approach applies graph theory methodology to response similarity analyses for identifying groups of examinees involved in TC without using any knowledge about parts of test that were affected by TC. The approach supports different response similarity indices (specific to a particular type of TC) and different types of groups (connected components, cliques, or near-cliques). A comparison with an up-to-date method using real and simulated data is presented. Possible extensions and practical recommendations are given.