A Note on the -Scoring Method Adapted for Polytomous Test Items.

An approach to scoring tests with binary items, referred to as -scoring method, was previously developed as a classical analog to basic models in item response theory (IRT) for binary items. As some tests include polytomous items, this study offers an approach to -scoring of such items and parallels the results with those obtained under the graded response model (GRM) for ordered polytomous items in the framework of IRT. The proposed design of using -scoring with "virtual" binary items generated from polytomous items provides (a) ability scores that are consistent with their GRM counterparts and (b) item category response functions analogous to those obtained under the GRM. This approach provides a unified framework for -scoring and psychometric analysis of tests with binary and/or polytomous items that can be efficient in different scenarios of educational and psychological assessment.