In a course in elementary statistics for psychology students using criterion-referenced achievement tests, the total test score, based on dichotomously scored items, was used for classifying students into those who passed and those who failed. The score on a test is considered as depending on a latent variable; it is assumed that the students can be dichotomized into the categories "mastery" (with scores on the latent variable above a cutting score), and "no mastery" (with scores below the cutting score on the latent variable). Two problems are considered: (a) How many students are classified incorrectly? Using the binomial error model a procedure is described for computing the classification proportions: p(mastery, passed), p(mastery, failed), p(no mastery, passed), and p(no mastery, failed), (b) What is the optimal cutting score on a test? Using a loss function a procedure for computing the optimal curring score is described.
|Publication status||Published - 1977|
Mellenbergh, G. J., Koppelaar, H., & van der Linden, W. J. (1977). Dichotomous decisions based on dichotomously scored items: a case study. Statistica Neerlandica, 31(4), 161-169. https://doi.org/10.1111/j.1467-9574.1977.tb00763.x