Use of Generalized Person-Fit Indexes, Zetas for Statistical Pattern Classification

Person-fit indexes have often been used for detecting aberrant response patterns resulting from unusual behavior such as cheating. Because the focus of these indexes is on an individual's performance on a test rather than on sample statistics, they should be able to be used for cognitive diagnosis. However, cognitive theories show that a number of different sources of misconception affect test performance, and some misconceptions can be seen in many class- rooms. Therefore, application of person-fit statistics to cognitive diagnosis requires a special consideration, whereby we have to detect "normal" and "usual" response patterns resulting from several sources of misconception that are frequently observed among students. This study shows a solution for this problem by introducing an extension of Tatsuoka's (1985) ζ index-generalzed ζs-and discusses their statistical properties in the context of cognitive diagnosis.