Evaluation of evidence that treatment efficacy varies substantially among different subsets of patients is an important feature of the analysis of large clinical trials. Qualitative or crossover interactions are said to occur when one treatment is superior for some subsets of patients and the alternative treatment is superior for other subsets. A non-crossover interaction arises when there is variation in the magnitude, but not in the direction, of treatment effects among subsets. Some authors use the term quantitative interaction to mean non-crossover interaction. Non-crossover interactions are usually of less clinical importance than qualitative interactions, which often have major therapeutic significance. A likelihood ratio test is developed to test for qualitative interactions. Exact critical values are determined and tabulated.