An Individualistic Approach to Item Analysis

Traditionally the properties of a psychological test are defined in terms of variations within some specified population. In practice such populations may be selected in various reasonable ways, and accordingly the properties referred to—for example, the reliability coefficient —are not specific to the test itself but may vary according to how the population is defined. Similarly, the evaluation of a subject is usually linked up with a population by a staldardization of some kind and is therefore not specific to the subject per se. Our .Aim is to develop probabilistic models in the application of which the population can be ignored. It was a discovery of some mathematical significance that such models could be constructed, and it seemed remarkable that data collected in routine psychological testing could be fairly well represented by such models. in a previous study (2) an attempt was made to build up a general framework within which the models:of an ca..lier study ;3) ap ear to be special cases, and some properties of this general fr%rnework were recognized. Bat only recently it become quite clear that this model is in fact the complete answer to the requirement that stateincat.% -thout the parameters and adequacv of a discrete probabilistic model be ohjecti"e in a seise to he fully specified. At present, at least, the theory leading to this result is rather invOlved, and it is not going to be a main topic fcir this parer. However, it is intended that the following discussion on one of the models in the earlier study (3), the model for item analysis in case of only two possible answers, should demonstrate the nature of the type of objectivity we are aiming at, thus pointing to the more general problem to be treated elsewhere.