In the context of reviewing an article for this journal (van der Linden & Sotaridona, this issue, pp. 283-304) the topic of unconditional and conditional hypothesis testing came under consideration. While this is hardly a new issue (consider, for example, arguments regarding the chi square vs. Fisher exact test of independence for a 2 x 2 frequency table; see Lehmann [1986] and Cox & Hinkley [1974] for more details and more general discussion), it still has the potential to cause some confusion. For this reason, it seemed useful to compare unconditional and conditional testing, using a special case of the two hypothesis tests proposed by van der Linden and Sotaridona. This comparison has several advantages over another look at better-known alternatives. First, these tests are designed to address a serious practical problem in educational testing, namely, the copying of one student's answers by another student. Second, both tests are "exact" for small samples, so issues related to the adequacy of asymptotic sampling distributions do not arise. Third, the new tests function within the framework provided by item response theory, broadening the relevance of the discussion beyond the problem of copying. Finally, the null hypothesis under consideration (that two students were working independently in arriving at their answers) is one of the few such that can actually be taken seriously.