An essay on inequalities and order-restricted inference

This essay was prompted by a concern on the part of many senior members of the Society for Mathematical Psychology that the training of contemporary cognitive scientists exhibits a trend away from quantitative sophistication. Such a trend, if it goes unchallenged, can only serve to further marginalize mathematical psychology. There are several ways to combat this disturbing situation. Members of the Society might involve themselves more vigorously with scientific problems that are widely viewed as substantively or methodologically important, problems that require technical skill for their resolution; one example, discussed here, concerns order-restricted inference. We can also do more to encourage graduate students to develop and explore sophisticated theoretical models by giving them the tools to do so; that last battle must take place in the classroom.