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Garner, Mary; Engelhard, George, Jr. – 1997
This paper considers the following questions: (1) what is the relationship between the method of paired comparisons and Rasch measurement theory? (2) what is the relationship between the method of paired comparisons and graph theory? and (3) what can graph theory contribute to the understanding of Rasch measurement theory? It is specifically shown…
Descriptors: Comparative Analysis, Estimation (Mathematics), Graphs, Item Response Theory
Lix, Lisa M.; Keselman, H. J. – 1995
Tests of mean equality proposed by Alexander and Govern (1994) and Tsakok (1978) were compared to the well-known procedures of Brown and Forsythe (1974), James (1951), and Welch (1951) for their ability to limit the number of Type I errors in one-way designs where the underlying distributions were nonnormal, variances were nonhomogeneous, and…
Descriptors: Comparative Analysis, Estimation (Mathematics), Foreign Countries, Least Squares Statistics

Wilcox, Rand R. – Psychometrika, 1992
A method of comparing one-step M-estimates of location for heavy tailed distributions is proposed and investigated. Simulations indicate that the new procedure provides good control over Type I errors and has more power than do some other methods for dealing with heavy tailed distributions. (SLD)
Descriptors: Comparative Analysis, Estimation (Mathematics), Experimental Groups, Mathematical Models

Tate, Richard L. – Journal of Educational Measurement, 1995
Robustness of the school-level item response theoretic (IRT) model to violations of distributional assumptions was studied in a computer simulation. In situations where school-level precision might be acceptable for real school comparisons, expected a posteriori estimates of school ability were robust over a range of violations and conditions.…
Descriptors: Comparative Analysis, Computer Simulation, Estimation (Mathematics), Item Response Theory

Kolen, Michael J. – Journal of Educational Measurement, 1991
Estimation/smoothing methods that are flexible enough to fit a wide variety of test score distributions are reviewed: kernel method, strong true-score model-based method, and method that uses polynomial log-linear models. Applications of these methods include describing/comparing test score distributions, estimating norms, and estimating…
Descriptors: Comparative Analysis, Equated Scores, Equations (Mathematics), Estimation (Mathematics)

Kirisci, Levent; Hsu, Tse-Chi – 1995
The main goal of this study was to assess how sensitive unidimensional parameter estimates derived from BILOG were when the unidimensionality assumption was violated and the underlying ability distribution was not multivariate normal. A multidimensional three-parameter logistic distribution that was a straightforward generalization of the…
Descriptors: Ability, Comparative Analysis, Correlation, Difficulty Level
Beasley, T. Mark; Leitner, Dennis W. – 1993
The L statistic of E. B. Page (1963) tests the agreement of a single group of judges with an a priori ordering of alternative treatments. This paper extends the two group test of D. W. Leitner and C. M. Dayton (1976), an extension of the L test, to analyze difference in consensus between two unequally sized groups of judges. Exact critical values…
Descriptors: Comparative Analysis, Equations (Mathematics), Estimation (Mathematics), Evaluators
Seong, Tae-Je; And Others – 1997
This study was designed to compare the accuracy of three commonly used ability estimation procedures under the graded response model. The three methods, maximum likelihood (ML), expected a posteriori (EAP), and maximum a posteriori (MAP), were compared using a recovery study design for two sample sizes, two underlying ability distributions, and…
Descriptors: Ability, Comparative Analysis, Difficulty Level, Estimation (Mathematics)

Wilcox, Rand R. – Psychometrika, 1993
Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)
Descriptors: Comparative Analysis, Computer Simulation, Equations (Mathematics), Estimation (Mathematics)

Parshall, Cynthia G.; Kromrey, Jeffrey D. – Educational and Psychological Measurement, 1996
Power and Type I error rates were estimated for contingency tables with small sample sizes for the following four types of tests: (1) Pearson's chi-square; (2) chi-square with Yates's continuity correction; (3) the likelihood ratio test; and (4) Fisher's Exact Test. Various marginal distributions, sample sizes, and effect sizes were examined. (SLD)
Descriptors: Chi Square, Comparative Analysis, Effect Size, Estimation (Mathematics)
Wang, Yuh-Yin Wu; Schafer, William D. – 1993
This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…
Descriptors: Comparative Analysis, Computer Simulation, Equations (Mathematics), Estimation (Mathematics)

Swaminathan, Hariharan; Rogers, H. Jane – Journal of Educational Measurement, 1990
A logistic regression model for characterizing differential item functioning (DIF) between two groups is presented. A distinction is drawn between uniform and nonuniform DIF in terms of model parameters. A statistic for testing the hypotheses of no DIF is developed, and simulation studies compare it with the Mantel-Haenszel procedure. (Author/TJH)
Descriptors: Comparative Analysis, Computer Simulation, Equations (Mathematics), Estimation (Mathematics)
Olejnik, Stephen; Algina, James – 1987
The purpose of this study was to develop a single procedure for comparing population variances which could be used for distribution forms. Bootstrap methodology was used to estimate the variability of the sample variance statistic when the population distribution was normal, platykurtic and leptokurtic. The data for the study were generated and…
Descriptors: Comparative Analysis, Estimation (Mathematics), Measurement Techniques, Monte Carlo Methods
Zeng, Lingjia – 1991
Large sample standard errors of linear equating for the single-group design are derived without making the normality assumption. Two general methods based on the delta method of M. Kendall and A. Stuart (1977) are described. One method uses the exact partial derivatives, and the other uses numerical derivatives. Simulation using the beta-binomial…
Descriptors: Comparative Analysis, Computer Simulation, Equated Scores, Equations (Mathematics)
Kim, Seock-Ho; And Others – 1992
Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…
Descriptors: Ability, Bayesian Statistics, Comparative Analysis, Equations (Mathematics)
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