| Abstract: | A procedure is presented for obtaining maximum likelihood trait estimates from number-correct (NC) scores for the three-parameter logistic model. The procedure produces an NC score to trait estimate conversion table, which can be used when the hand scoring of tests is desired or when item response pattern (IP) scoring is unacceptable for other (e.g., political) reasons. Simulated data are produced for four 20-item and four 40-item tests of varying difficulties. These data indicate that the NC scoring procedure produces trait estimates that are tau-equivalent to the IP trait estimates (i.e., they are expected to have the same mean for all groups of examinees), but the NC trait estimates have higher standard errors of measurement than IP trait estimates. Data for six real achievement tests verify that the NC trait estimates are quite similar to the IP trait estimates but have higher empirical standard errors than IP trait estimates, particularly for low-scoring examinees. Analyses in the estimated true score metric confirm the conclusions made in the trait metric. |
