A comparison of classical test theory and item response theory methods for equating number-right scored to formula scored assessments

Two common methods for scoring assessments are formula scoring and number-right scoring. The purpose of this research was to investigate seven different methods for equating these two types of assessments. The three classical methods compared included two applications of Tucker's linear method and the unsmoothed, chained equipercentile equating. The IRT methods used the 1-, 2-, and 3-parameter logistic models and the multiple choice models.;These seven equating methods were compared in both real and simulated data studies. The real data study used SAT data that was gathered under formula-scoring directions. The multiple-choice model was then used to impute responses for omitted responses to simulate data for an assessment designed to follow number-right scoring directions. The simulation study applied the multiple-choice model to simulate data representative of both types of assessments. The equating method with the least absolute bias between the equated score on the simulation study and that on the real data study was the Tucker linear method.