Indices for detecting unusual patterns: Links between two general approaches and potential applications

Abstract

Two distinct approaches, one based on item response theory and the other based on observed item responses and standard summary statistics, have been proposed to identify unusual response patterns of responses to test items. A link between these two approaches is provided by showing certain correspondences between Sato’s S-P curve theory and item response theory. This link makes possible several extensions of Sato’s caution index that take advantage of the results of item response theory. Several such indices are introduced and their use illustrated by application to a set of achievement test data. Two of the newly introduced extended indices were found to be very effective for purposes of identifying persons who consistently use an erroneous rule in attempting to solve signed-number arithmetic problems. The potential importance of this result is briefly discussed.