This Monte Carlo simulation studied the relative power of 8 tests for sphericity in randomized block designs where sample size was small (10, 15, 20, and 30) and population covariance matrices of dimension-to-sample size ratio approached 1.0. The locally best invariant test demonstrated substantial power to detect departures from sphericity. (SLD)

Investigated Type I error rates of the likelihood-ratio test for the detection of differential item functioning (DIF) using Monte Carlo simulations under the graded-response model. Type I error rates were within theoretically expected values for all six combinations of sample sizes and ability-matching conditions at each of the nominal alpha…

The bias and relative efficiency of two alternative estimators of optimal weights in meta-analysis were assessed through Monte Carlo simulation, defining the standardized mean differences as the effect-size index. The estimator proposed by L. Hedges and I. Olkin (1985) was more efficient than that of J. Hunter and F. Schmidt (1990). (SLD)

A Monte Carlo simulation study investigated the effects on 10 structural equation modeling fit indexes of sample size, estimation method, and model specification. Some fit indexes did not appear to be comparable, and it was apparent that estimation method strongly influenced almost all fit indexes examined, especially for misspecified models. (SLD)

Assessed five procedures for estimating a common risk difference in a set of independent 2 x 2 tables through Monte Carlo simulation in terms of bias, efficiency, confidence level adjustment, and statistical power. The maximum likelihood estimator showed best performance, followed closely by the Cochran (W. Cochran, 1954) and Mantel-Haenszel (N.…

In this study we investigated the effects of the average signed area (ASA) between the item characteristic curves of the reference and focal groups and three test purification procedures on the uniform differential item functioning (DIF) detection via the Mantel-Haenszel (M-H) method through Monte Carlo simulations. The results showed that ASA,…

This paper reports a set of Monte Carlo simulations designed to evaluate the main claims made by Laufer and Nation about the Lexical Frequency Profile (LFP). Laufer and Nation claim that the LFP is a sensitive and reliable tool for assessing productive vocabulary in L2 speakers, and they suggest it might have a serious role to play in diagnostic…

When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited.…

This study focused on the robustness of unidimensional item response theory (UIRT) models in computerized classification testing against violation of the unidimensionality assumption. The study addressed whether UIRT models remain acceptable under various testing conditions and dimensionality strengths. Monte Carlo simulation techniques were used…

Many measures found in educational research are ordered categorical response variables that are empirical realizations of an underlying normally distributed variate. These ordered categorical variables are commonly referred to as Likert or rating scale data. Regression models are commonly fit using these ordered categorical variables as the…

These results indicate that in deciding on the data-gathering design to be used in seeking norm information, attention should be given to item characteristics and test length with particular attention paid to the range of biserial correlations between item response and ability. (Author)

Type I error rates for the likelihood ratio test for detecting differential item functioning (DIF) were investigated using Monte Carlo simulations. Type I error rates for the two-parameter model were within theoretically expected values at each alpha level, but those for the three-parameter model were not. (SLD)

Developed an item response model for characterizing test-compromise that enables the estimation of item preview and score-gain distributions. In the approach, models parameters and posterior distributions are estimated by Markov Chain Monte Carlo procedures. Simulation study results suggest that when at least some test items are known to be…

Statistical properties of person fit indices are reviewed as indicators of the extent to which a person's score pattern is in agreement with a measurement model. Distribution of a fit index and ability-free fit evaluation are discussed. The null distribution was simulated for a test of 20 items. (SLD)

A Monte Carlo study compared performance of linear and logistic mixed-model analyses of simulated community trials having specific event rates, intraclass correlations, and degrees of freedom. Results indicate that in studies with adequate denominator degrees of freedom, the researcher may use either method of analysis, with certain cautions. (SLD)