Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT.…

In random-effects meta-analysis the between-study variance ([tau][superscript 2]) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating [tau][superscript 2] and the overall effect and produce confidence intervals…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

The purpose of this study was to explore the degree of grain size of the attributes and the sample sizes that can support accurate parameter recovery with the General Diagnostic Model (GDM) for a large-scale international assessment. In this resampling study, bootstrap samples were obtained from the 2003 Grade 8 TIMSS in Mathematics at varying…

Children (N = 157) 4 to 8 years old participated 1 time (single) or 4 times (repeated) in an interactive event. Across each condition, half were questioned a week later about the only or a specific occurrence of the event ("depth first") and then about what usually happens. Half were prompted in the reverse order ("breadth first"). Children with…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Students often enter biology programs deficient in the math and computational skills that would enhance their attainment of a deeper understanding of the discipline. To address some of these concerns, I developed a series of spreadsheet simulation exercises that focus on some of the mathematical foundations of scientific inquiry and the benefits…

A Monte Carlo simulation approach was taken to investigate the effect of sample size on a variety of latent growth models. A fully balanced experimental design was implemented, with samples drawn from multivariate normal populations specified to represent 12 unique growth models. The models varied factorially by crossing number of time points,…

Two-stage sampling procedures for comparing two population means when variances are heterogeneous have been developed by D. G. Chapman (1950) and B. K. Ghosh (1975). Both procedures assume sampling from populations that are normally distributed. The present study reports on the effect that sampling from non-normal distributions has on Type I error…

When the results of a series of independent studies are combined, it is useful to quantitatively estimate the magnitude of the effects. Several methods for estimating effect size are compared in this paper. Glass' estimator and the uniformly minimum variance unbiased estimator are based on the ratio of the sample mean difference and the pooled…

In the process of fitting a quantitative synthesis model, the assumption of homogeneous effect size variation is assessed via omnibus test statistics. Graphical representations of data on techniques for teaching composition skills are used to help determine the extent to which sample estimates deviate from modeled population estimates. (TJH)

A simulation study compared the performance of the Mann-Whitney "U" test, Student's "t" test, and the alternate (separate variance) "t" test for two mutually independent random samples from normal distributions, with both one-tailed and two-tailed alternatives. Type I error probabilities were computed with equal and…

Using computer simulated data, the Type I error rate and statistical power were empirically estimated for several pairwise multiple comparison strategies for situations where population variances differ. Focus was on comparing modified Bonferroni procedures with Dunnett's solutions, and determining whether or not J. P. Shaffer's suggestion of…