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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, 1983

When comparing k normal populations an investigator might want to know the probability that the population with the largest population mean will have the largest sample mean. This paper describes and illustrates methods of approximating this probability when the variances are unknown and possibly unequal. (Author/BW)

Descriptors: Data Analysis, Hypothesis Testing, Mathematical Formulas, Probability

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, 1979

In many situations in education and psychology it is desired to select from k binomial populations the one having the largest probability of success. This paper describes a two-stage procedure for accomplishing this goal. (Author/CTM)

Descriptors: Probability, Sampling, Statistical Analysis

Peer reviewed

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

The classical estimate of a binomial probability function is to estimate its mean in the usual manner and to substitute the results in the appropriate expression. Two alternative estimation procedures are described and examined. Emphasis is given to the single administration estimate of the mastery test reliability. (Author/CTM)

Descriptors: Cutting Scores, Mastery Tests, Probability, Scores

Peer reviewed

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

A problem of considerable importance in certain educational settings is determining how many items to include on a mastery test. Applying ranking and selection procedures, a solution is given which includes as a special case all existing single-stage, non-Bayesian solutions based on a strong true-score model. (Author/JKS)

Descriptors: Criterion Referenced Tests, Mastery Tests, Nonparametric Statistics, Probability

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