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

The Level II Vocabulary Subtest of the IowaTests of Basic Skills was analyzed using a two-stagelatent trait approach and an empirical datasetof 2,356 examinees. First, each of the 43 multiplechoicetest items was scored dichotomously; then,assuming the (two-parameter) normal ogive modelthe item parameters were estimated. The operatingcharacteristics of the correct answer and of thethree distractors were estimated using a nonparametricapproach called the simple sum procedureof the conditional probability densityfunction approach combined with the normalapproach method. Differential information wasprovided by the distractors, and these operatingcharacteristics were named the plausibility functionsof the distractors. The operating characteristicof the correct answer of each item estimated byassuming the normal ogive model was comparedwith the nonparagnetrically estimated operatingcharacteristic for model validation. It was concludedthat the nonparametric approach leads toefficient estimation of the latent trait. Indexterms: distractors, item response theory, latent traitmodels, multiple-choice test items, nonparametric estimation,plausibility functions of distractors.