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Bang Quan Zheng; Peter M. Bentler – Structural Equation Modeling: A Multidisciplinary Journal, 2025
This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…
Descriptors: Monte Carlo Methods, Structural Equation Models, Goodness of Fit, Robustness (Statistics)
Sengul Avsar, Asiye; Tavsancil, Ezel – Educational Sciences: Theory and Practice, 2017
This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…
Descriptors: Test Items, Psychometrics, Nonparametric Statistics, Item Response Theory
Reid, Jerry B.; Roberts, Dennis M. – 1978
Comparisons of corresponding values of phi and kappa coefficients were made for 270 instances of data generated by a Monte Carlo technique to simulate a test-retest situation. Data were generated for distributions with the same mean but three different levels of standard deviation, standard error of measurement and cutting score. Ten samples of…
Descriptors: Comparative Analysis, Correlation, Criterion Referenced Tests, Cutting Scores

Gilmer, Jerry S.; Feldt, Leonard S. – 1982
The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the…
Descriptors: Educational Testing, Error of Measurement, Mathematical Formulas, Mathematical Models
Samejima, Fumiko – 1990
Because the test information function and its two modified formulas provide useful information, the reliability coefficient of a test is no longer necessary in modern mental test theory. Yet it is interesting to know how to predict the coefficient using the test information function and its modifications, tailored for each separate population of…
Descriptors: Ability Identification, Elementary Secondary Education, Equations (Mathematics), Error of Measurement

Huck, Schuyler W.; And Others – Educational and Psychological Measurement, 1981
Believing that examinee-by-item interaction should be conceptualized as true score variability rather than as a result of errors of measurement, Lu proposed a modification of Hoyt's analysis of variance reliability procedure. Via a computer simulation study, it is shown that Lu's approach does not separate interaction from error. (Author/RL)
Descriptors: Analysis of Variance, Comparative Analysis, Computer Programs, Difficulty Level
Ackerman, Terry A.; Evans, John A. – 1992
The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…
Descriptors: Comparative Analysis, Equations (Mathematics), Error of Measurement, Item Bias

Kim, Jwa K.; Nicewander, W. Alan – Psychometrika, 1993
Bias, standard error, and reliability of five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. Results indicate that estimates based on Bayesian modal, expected a posteriori, and weighted likelihood estimators were reasonably unbiased with relatively small standard…
Descriptors: Ability, Bayesian Statistics, Equations (Mathematics), Error of Measurement
Lei, Pui-Wa; Koehly, Laura M. – Journal of Experimental Education, 2003
Classification studies are important for practitioners who need to identify individuals for specialized treatment or intervention. When interventions are irreversible or misclassifications are costly, information about the proficiency of different classification procedures becomes invaluable. This study furnishes information about the relative…
Descriptors: Monte Carlo Methods, Classification, Discriminant Analysis, Regression (Statistics)
Patience, Wayne M.; Reckase, Mark D. – 1979
An experiment was performed with computer-generated data to investigate some of the operational characteristics of tailored testing as they are related to various provisions of the computer program and item pool. With respect to the computer program, two characteristics were varied: the size of the step of increase or decrease in item difficulty…
Descriptors: Adaptive Testing, Computer Assisted Testing, Difficulty Level, Error of Measurement