Investigations of the simplex

Abstract

I am honored to be able to speak on the 25th anniversary of the founding of the Psychometric Society. I t would be appropriate for your president on this occasion to review the 25-year history of our society and of mathematical methods in psychology. Fortunately our committee headed by Charles Wrigley has taken care of this need, and speakers better qualified than I will speak to these issues. I shall turn to a less demanding problem. In limiting my topic I was faced with certain constraints arising from my training, background, and interests. One constraint arises from a misspent youth during which too many years were spent studying disciplines other than mathematics. A second constraint, which probably stems from my training in experimental psychology, is a tendency to be more interested in data than theory. Finally, there is the Air Force personnel research experience which developed in me an abiding interest in applied prediction problems. If you consider this combination to be an odd one for the President of the Psychometric Society, don't blame me. You elected me! Although I shall introduce my topic by discussing the weather, I am not trying to avoid coming to grips with a problem. My problem does have something to do with the weather, and it also has something to do with Guttman's simplex [5]. My discussion will be a little bit mathematical and quite a bit empirical. I t also has applied implications.