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…

The standard deviation (SD) of a random sample is defined as the square-root of the sample variance, which is the "mean" squared deviation of the sample observations from the sample mean. Here, we interpret the sample SD as the square-root of twice the mean square of all pairwise half deviations between any two sample observations. This…

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,…

Sixteen tables are presented for critical values of the larger of two sample correlation coefficients from two independent samples, given the sample size and the value of the smaller correlation. These tables allow quick assessment of significance without requiring calculation of the test statistic. (SLD)

The problem of chance model modifications under varying levels of sample size, model size, and severity of misspecification in confirmatory factor analysis models was examined through Monte Carlo simulations. Findings suggest that practitioners should exercise caution when interpreting modified models unless sample size is quite large. (SLD)

Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch's approximate degrees of freedom test, and James's second order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a…

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…