Robustness of Lord’s Formulas for Item Difficulty and Discrimination Conversions Between Classical and Item Response Theory Models

Abstract

Lord (1980) proposed formulas that provide direct relationships between IRT discrimination and difficulty parameters and conventional item statistics. The purpose of the present study was to determine the robustness of the formulas beyond the initial and restrictive conditions identified by Lord. Simulation and real achievement data were employed. Results from the simulation study indicate that the item discrimination parameters were recovered quite well for low to moderately discriminating items regardless of ability distribution, and the difficulty parameters were recovered quite well for the range typically found for achievement tests. Results of the real data were consistent with those found for the simulation study.