An Investigation of the Nature and Consequence of the Relationship between IRT Difficulty and Discrimination

The focus of this paper is on the empirical relationship between item difficulty and item discrimination. Two studies—an empirical investigation and a simulation study—were conducted to examine the association between item difficulty and item discrimination under classical test theory and item response theory (IRT), and the effects of the association on various quantities of interest. Results from the empirical investigation show that item difficulty and item discrimination are negatively correlated under classical test theory, mostly negatively correlated under the two-parameter logistic model, and mostly positively correlated under the three-parameter logistic model; the magnitude of the correlation varied over the different data sets. Results from the simulation study reveal that a failure to incorporate the correlation between item difficulty and item discrimination in IRT simulations may provide the investigator with inaccurate values of important quantities of interest, and may lead to incorrect operational decisions. Implications to practice and future directions are discussed.