Investigating an invariant item ordering for polytomously scored items

This article discusses the concept of an invariant item ordering (IIO) for polytom-ously scored items and proposes methods for investigating an IIO in real test data. Method manifest IIO is proposed for assessing whether item response functions intersect. Coefficient HT is defined for polytomously scored items. Given that an IIO holds, coefficient HTexpresses the accuracy of the item ordering. Method manifest IIO and coefficient HT are used together to analyze a real data set. Topics for future research are discussed. Keywords coefficient HT, invariant item ordering, item response function for polytomous items, item step response function, polytomous item response theory models In several measurement applications, it is convenient that the items have the same order with respect to difficulty or attractiveness for all respondents. Such an ordering facilitates the interpretation and the comparability of respondents ’ measurement results. An item ordering that is the same for all respondents is called an invariant item ordering (IIO; Sijtsma & Junker, 1996). Before we define an IIO, we first men-tion several measurement applications in which an IIO proves useful. First, many intelligence tests present the items to children in the order according to ascending difficulty (Bleichrodt, Drenth, Zaal, & Resing, 1987; Wechsler, 1999). One reason for this presentation order is to comfort children and prevent them fro