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Wilcox, Rand R. – Educational and Psychological Measurement, 2006

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

Descriptors: Nonparametric Statistics, Mathematical Models, Regression (Statistics), Probability

Peer reviewed

Wilcox, Rand R. – Educational and Psychological Measurement, 1982

Results in the engineering literature on "k out of n system reliability" can be used to characterize tests based on estimates of the probability of correctly determining whether the examinee knows the correct response. In particular, the minimum number of distractors required for multiple-choice tests can be empirically determined.…

Descriptors: Achievement Tests, Mathematical Models, Multiple Choice Tests, Test Format

Peer reviewed

Wilcox, Rand R. – Educational and Psychological Measurement, 1981

The paper considers the problem of selecting the t best of k normal populations and simultaneously determining whether the selected populations have a mean larger than a known standard. Illustrations are given for selecting the t best of k examinees when the binomial error model applies. (Author)

Descriptors: Competitive Selection, Criterion Referenced Tests, Decision Making, Mathematical Models

Peer reviewed

Wilcox, Rand R. – Educational and Psychological Measurement, 1981

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)

Descriptors: Mathematical Models, Multiple Choice Tests, Probability, Test Items

Peer reviewed

Wilcox, Rand R. – Educational and Psychological Measurement, 1980

Technical problems in achievement testing associated with using latent structure models to estimate the probability of guessing correct responses by examinees is studied; also the lack of problems associated with using Wilcox's formula score. Maximum likelihood estimates are derived which may be applied when items are hierarchically related.…

Descriptors: Guessing (Tests), Item Analysis, Mathematical Models, Maximum Likelihood Statistics

Peer reviewed

Wilcox, Rand R. – Educational and Psychological Measurement, 1979

Wilcox has described three probability models which characterize a single test item in terms of a population of examinees (ED 156 718). This note indicates indicates that similar models can be derived which characterize a single examinee in terms of an item domain. A numerical illustration is given. (Author/JKS)

Descriptors: Achievement Tests, Item Analysis, Mathematical Models, Probability