The number of Guttman errors as a simple and powerful person-fit statistic

A number of studies have examined the power of several statistics that can be used to detect examinees with unexpected (nonfitting) item score patterns, or to determine person fit. This study compared the power of the U3 statistic with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases studied, (a weighted version of) the latter statistic performed as well as the U3 statistic. Counting the number of Guttman errors seems to be a useful and simple alternative to more complex statistics for determining person fit. Index terms: aberrance detection, appropriateness measurement, Guttman errors, nonparametric item response theory, person fit.