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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
Peer reviewed 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 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 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
Peer reviewed 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 Peer reviewed
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
Peer reviewed Peer reviewed
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
Peer reviewed Peer reviewed
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
Peer reviewed Peer reviewed
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
Peer reviewed 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 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 Peer reviewed
Wilcox, Rand R. – Educational and Psychological Measurement, 1980
Using three sets of real data, a comparison of four discrete discriminate analysis procedures is made using the actual versus the optimal error rate. The kernel method gives the most accurate results in all three cases. (Author/RL)
Descriptors: Achievement Tests, Comparative Analysis, Discriminant Analysis, Error of Measurement
Peer reviewed 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 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