In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

Samejima hypothesized that non-monotonically increasing item response functions (IRFs) of ability might occur for multiple-choice items (referred to here as "Samejima items") if low ability test takers with some, though incomplete, knowledge or skill are drawn to a particularly attractive distractor, while very low ability test takers…

A formal framework is presented for determining which of the distractors of multiple-choice test items has a small probability of being chosen by a typical examinee. The framework is based on a procedure similar to an indifference zone formulation of a ranking and election problem. (Author/BW)

A modified beta binomial model is presented for use in analyzing random guessing multiple choice tests and taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented.…

Two basic issues are discussed that involve the Carver model of the relationship between test score and knowledge. The first of these concerns different types of tests which have different probabilities of obtaining the correct answer due to guessing. A derivation is shown which places different test types "on-a-par"--meaning that two tests are…

On well-constructed multiple-choice tests, the most serious threat to measurement is not variation in item discrimination, but the guessing behavior that may be adopted by some students. Ways of ameliorating the effects of guessing are discussed, especially for problems in latent trait models. A new item response model, including an item parameter…

This document contains three papers from the Methodology Project of the Center for the Study of Evaluation. Methods for characterizing test accuracy are reported in the first two papers. "Bounds on the K Out of N Reliability of a Test, and an Exact Test for Hierarchically Related Items" describes and illustrates how an extension of a…

The Answer-Until-Correct (AUC) procedure has been proposed in order to increase the reliability of multiple-choice items. A model for examinees' behavior when they must respond to each item until they answer it correctly is presented. An expression for the reliability of AUC items, as a function of the characteristics of the item and the scoring…

In multiple-choice items the response probability on an item may be viewed as the result of two distinct latent processes--a cognitive process to solve the problem, and another random process that leads to the choice of a certain alternative (the process of giving the actual response). An incomplete latent class model is formulated that describes…

Selection of items for analogy tests according to the Rasch item probability of "goodness of fit" to the model is compared with three commonly used item selection criteria: item discrimination, item difficulty, and item-ability correlation. Word, picture, symbol and number analogies in multiple choice format were administered to several…

A nonparametric multicategorical model for multiple-choice data is proposed as an extension of the binary spline model of J. O. Ramsay and M. Abrahamowicz (1989). Results of two Monte Carlo studies illustrate the model, which approximates probability functions by rational splines. (SLD)

This pamphlet reprints three papers and an invited discussion of them, read at a Division 5 Symposium at the 1975 American Psychological Association Convention. The first paper describes a Bayesian tailored testing process and shows how it demonstrates the importance of using test items with high discrimination, low guessing probability, and a…