Increasing the students’ understanding of the methods of science is often one of the goals of an introductory course in physics for nonscientists. To supplement the examples arising directly from the usual subject matter and to stimulate clearer thought concerning the nature of scientific inquiry, discussion of some subjects which have a surface resemblance to science is proposed. The history of research into extrasensory perception appears to be ideal as such a counterexample, allowing for explicit comparisons which illuminate the subject of methodology in science while maintaining high student interest. Lecture suggestions, including demonstrations, are discussed.