THE MATHEMATICAL MODELS BEHIND PSYCHOLOGICAL TESTING

INTRODUCTION Psychological tests have become part of our life. If you decide to enlist in the Army, you will be given the Armed Services Vocational Aptitude Battery (ASVAB). This is a general measure of your cognitive skills, with some emphasis on skills that are likely to be useful to the Army. If instead you decide to go to college, you will probably have to take the Scholastic Assessment Test (SAT), which measures cognitive skills relevant to academic pursuits. Standardized interviews are part of the initial stage of employment for many jobs, ranging literally from a policeman to a computer programmer. Often these include a personality test to see if you are the right person for the job. What has mathematics got to do with the development of these tests? The answer turns out to be “quite a bit.” The reason has to do with the way that cognitive and personality traits have been defined. In an idealized scientific investigation concepts are defined first, and measures to evaluate them are defined second. For instance, we have a concept of weight, the gravitational attraction between a body's mass and the Earth. The typical bathroom scale measures weight by the distortion of a spring when someone steps on the platform. The idea of building this sort of scale came from the definition of weight. Weight itself is not defined by distortion of the spring. In many cases, theorists interested in intelligence and personality have done things in the opposite way.