ANALYSIS OF TEST SCORES BY HAYASHI'S THIRD METHOD OF QUANTIFICATION

Abstract

It is shown in this paper that Hayashi's third method of quantification, whose algorithm is same as that of correspondence analysis, is effectively applicable to statistical analysis of test scores. The procedure is based on a scoring method; each item is characterized by two numerical values, which are called “ correct-answer weight ” and “ wrong-anaswer weight ”, and each examinee is characterized by a numerical value called “ score ”. In order to make the interpretation of the result easy some useful quantities are defined.They are “ index of incon sistency ” of examinees, “ difficulty level ” and “ index of discriminating power ” of test items. We also investigate the relationship between the scoring method proposed here and the methods based on the latent trait theory and so-called S-P curve theory.Examples are shown illustrate how to apply the method to real data.