Nonparametric estimation of the plausibility functions of the distractors of vocabulary test items

Abstract

The Level II Vocabulary Subtest of the Iowa Tests of Basic Skills was analyzed using a two-stage latent trait approach and an empirical dataset of 2,356 examinees. First, each of the 43 multiplechoice test items was scored dichotomously; then, assuming the (two-parameter) normal ogive model the item parameters were estimated. The operating characteristics of the correct answer and of the three distractors were estimated using a nonparametric approach called the simple sum procedure of the conditional probability density function approach combined with the normal approach method. Differential information was provided by the distractors, and these operating characteristics were named the plausibility functions of the distractors. The operating characteristic of the correct answer of each item estimated by assuming the normal ogive model was compared with the nonparagnetrically estimated operating characteristic for model validation. It was concluded that the nonparametric approach leads to efficient estimation of the latent trait. Index terms: distractors, item response theory, latent trait models, multiple-choice test items, nonparametric estimation, plausibility functions of distractors.