Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's…

The purpose of this study was to evaluate the combined effects of reduced equating sample size and shortened anchor test length on item response theory (IRT)-based linking and equating results. Data from two independent operational forms of a large-scale testing program were used to establish the baseline results for evaluating the results from…

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Many studies have been conducted to evaluate the performance of DIF detection methods, when two groups have different ability distributions. Such studies typically have demonstrated factors that are associated with inflation of Type I error rates in DIF detection, such as mean ability differences. However, no study has examined how the direction…

Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near…

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of…

Previous research implementing stratification on the propensity score has generally relied on using five strata, based on prior theoretical groundwork and minimal empirical evidence as to the suitability of quintiles to adequately reduce bias in all cases and across all sample sizes. This study investigates bias reduction across varying number of…

In the presence of test speededness, the parameter estimates of item response theory models can be poorly estimated due to conditional dependencies among items, particularly for end-of-test items (i.e., speeded items). This article conducted a systematic comparison of five-item calibration procedures--a two-parameter logistic (2PL) model, a…

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…

In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…

Using exogenous characteristics to identify endogenous subgroups, the approach discussed in this method note creates symmetric subsets within treatment and control groups, allowing the analysis to take advantage of an experimental design. In order to maintain treatment--control symmetry, however, prior work has posited that it is necessary to use…

The Non-Equivalent groups with Anchor Test equating (NEAT) design is a widely used equating design in large scale testing that involves two groups that do not have to be of equal ability. One group P gets form X and a group of items A and the other group Q gets form Y and the same group of items A. One of the most commonly used equating methods in…

Differential item functioning (DIF) analysis is a key component in the evaluation of the fairness and validity of educational tests. The goal of this project was to review the status of ETS DIF analysis procedures, focusing on three aspects: (a) the nature and stringency of the statistical rules used to flag items, (b) the minimum sample size…