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Man, Kaiwen; Schumacker, Randall; Morell, Monica; Wang, Yurou – Educational and Psychological Measurement, 2022
While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…
Descriptors: Hierarchical Linear Modeling, Statistical Distributions, Statistical Bias, Computation
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Olvera Astivia, Oscar Lorenzo; Kroc, Edward; Zumbo, Bruno D. – Educational and Psychological Measurement, 2020
Simulations concerning the distributional assumptions of coefficient alpha are contradictory. To provide a more principled theoretical framework, this article relies on the Fréchet-Hoeffding bounds, in order to showcase that the distribution of the items play a role on the estimation of correlations and covariances. More specifically, these bounds…
Descriptors: Test Items, Test Reliability, Computation, Correlation
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Olvera Astivia, Oscar L.; Kroc, Edward – Educational and Psychological Measurement, 2019
Within the context of moderated multiple regression, mean centering is recommended both to simplify the interpretation of the coefficients and to reduce the problem of multicollinearity. For almost 30 years, theoreticians and applied researchers have advocated for centering as an effective way to reduce the correlation between variables and thus…
Descriptors: Multiple Regression Analysis, Computation, Correlation, Statistical Distributions
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Nam, Yeji; Hong, Sehee – Educational and Psychological Measurement, 2021
This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…
Descriptors: Probability, Models, Statistical Analysis, Statistical Distributions
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Ranger, Jochen; Kuhn, Jörg Tobias; Ortner, Tuulia M. – Educational and Psychological Measurement, 2020
The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels--one for the responses and one for the response times--that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a…
Descriptors: Reaction Time, Tests, Statistical Distributions, Models
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Green, Samuel; Xu, Yuning; Thompson, Marilyn S. – Educational and Psychological Measurement, 2018
Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The…
Descriptors: Factor Analysis, Accuracy, Statistical Distributions, Comparative Analysis
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Trafimow, David – Educational and Psychological Measurement, 2018
Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the…
Descriptors: Statistical Analysis, Correlation, Experiments, Effect Size
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Preston, Kathleen Suzanne Johnson; Reise, Steven Paul – Educational and Psychological Measurement, 2014
The nominal response model (NRM), a much understudied polytomous item response theory (IRT) model, provides researchers the unique opportunity to evaluate within-item category distinctions. Polytomous IRT models, such as the NRM, are frequently applied to psychological assessments representing constructs that are unlikely to be normally…
Descriptors: Item Response Theory, Computation, Models, Accuracy
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Finch, Holmes; Edwards, Julianne M. – Educational and Psychological Measurement, 2016
Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…
Descriptors: Item Response Theory, Computation, Nonparametric Statistics, Bayesian Statistics
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Padilla, Miguel A.; Divers, Jasmin – Educational and Psychological Measurement, 2013
The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…
Descriptors: Sampling, Statistical Inference, Computation, Statistical Analysis
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Paek, Insu; Park, Hyun-Jeong; Cai, Li; Chi, Eunlim – Educational and Psychological Measurement, 2014
Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…
Descriptors: Item Response Theory, Comparative Analysis, Test Items, Equated Scores
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Seo, Dong Gi; Weiss, David J. – Educational and Psychological Measurement, 2013
The usefulness of the l[subscript z] person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating ? showed that the distributions of l[subscript z] were not consistent with its theoretical distribution, resulting in general overfit to the item response…
Descriptors: Achievement Tests, College Students, Goodness of Fit, Item Response Theory
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Chan, Wai – Educational and Psychological Measurement, 2009
A typical question in multiple regression analysis is to determine if a set of predictors gives the same degree of predictor power in two different populations. Olkin and Finn (1995) proposed two asymptotic-based methods for testing the equality of two population squared multiple correlations, [rho][superscript 2][subscript 1] and…
Descriptors: Multiple Regression Analysis, Intervals, Correlation, Computation
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Fidler, Fiona; Thompson, Bruce – Educational and Psychological Measurement, 2001
Illustrates the computation of confidence intervals for effect sizes for some analysis of variance applications and shows how the use of intervals involving noncentral distributions is made practical by new software. (SLD)
Descriptors: Analysis of Variance, Computation, Computer Software, Effect Size