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Wilcox, Rand R.; Serang, Sarfaraz – Educational and Psychological Measurement, 2017
The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and "p" values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have…
Descriptors: Hypothesis Testing, Bayesian Statistics, Computation, Effect Size
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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
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Wilcox, Rand R. – Educational and Psychological Measurement, 2006
For two random variables, X and Y, let D = X - Y, and let theta[subscript x], theta[subscript y], and theta[subscript d] be the corresponding medians. It is known that the Wilcoxon-Mann-Whitney test and its modern extensions do not test H[subscript o] : theta[subscript x] = theta[subscript y], but rather, they test H[subscript o] : theta[subscript…
Descriptors: Scores, Inferences, Comparative Analysis, Statistical Analysis
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Wilcox, Rand R. – Educational and Psychological Measurement, 2005
It is known that nonnormality, a heteroscedastic error term, or a nonlinear association can create serious practical problems when using the conventional analysis of covariance (ANCOVA) method. This article describes a simple ANCOVA method that allows heteroscedasticity, nonnormality, nonlinearity, and multiple covariates. When standard…
Descriptors: Statistical Analysis, Error of Measurement, Measurement Techniques
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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
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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
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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
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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
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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
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Wilcox, Rand R. – Educational and Psychological Measurement, 1983
This article provides unbiased estimates of the proportion of items in an item domain that an examinee would answer correctly if every item were attempted, when a closed sequential testing procedure is used. (Author)
Descriptors: Estimation (Mathematics), Psychometrics, Scores, Sequential Approach
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Wilcox, Rand R. – Educational and Psychological Measurement, 1997
Some results on how the Alexander-Govern heteroscedastic analysis of variance (ANOVA) procedure (R. Alexander and D. Govern, 1994) performs under nonnormality are presented. This method can provide poor control of Type I errors in some cases, and in some situations power decreases as differences among the means get large. (SLD)
Descriptors: Analysis of Variance, Error of Measurement, Power (Statistics), Statistical Distributions
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Wilcox, Rand R. – Educational and Psychological Measurement, 1980
When analyzing a squared multiple correlation coefficient, an investigator may be interested in determining whether it is above or below a known constant, rather than testing the null hypothesis. This paper gives the sample sizes required for answering this question when indifference zone formulation of the problem is used. (Author/BW)
Descriptors: Correlation, Hypothesis Testing, Sampling
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Wilcox, Rand R. – Educational and Psychological Measurement, 1979
For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. Several different methods of approximating the maximum likelihood estimate were investigated, and it was found that the Newton-Raphson method should be used when it yields admissable…
Descriptors: Criterion Referenced Tests, Maximum Likelihood Statistics, Measurement, Monte Carlo Methods
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Wilcox, Rand R. – Educational and Psychological Measurement, 1982
When determining criterion-referenced test length, problems of guessing are shown to be more serious than expected. A new method of scoring is presented that corrects for guessing without assuming that guessing is random. Empirical investigations of the procedure are examined. Test length can be substantially reduced. (Author/CM)
Descriptors: Criterion Referenced Tests, Guessing (Tests), Multiple Choice Tests, Scoring
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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
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