Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based…

This article develops new closed-form variance expressions for power analyses for commonly used difference-in-differences (DID) and comparative interrupted time series (CITS) panel data estimators. The main contribution is to incorporate variation in treatment timing into the analysis. The power formulas also account for other key design features…

This article describes an extension to the use of heteroskedastic ordered probit (HETOP) models to estimate latent distributional parameters from grouped, ordered-categorical data by pooling across multiple waves of data. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level. We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that aggregate linkages can be validated both…

This study compared five common multilevel software packages via Monte Carlo simulation: HLM 7, M"plus" 7.4, R (lme4 V1.1-12), Stata 14.1, and SAS 9.4 to determine how the programs differ in estimation accuracy and speed, as well as convergence, when modeling multiple randomly varying slopes of different magnitudes. Simulated data…

The hierarchical network model (HNM) is a framework introduced by Sweet, Thomas, and Junker for modeling interventions and other covariate effects on ensembles of social networks, such as what would be found in randomized controlled trials in education research. In this article, we develop calculations for the power to detect an intervention…

Designs that facilitate inferences concerning both the total and indirect effects of a treatment potentially offer a more holistic description of interventions because they can complement "what works" questions with the comprehensive study of the causal connections implied by substantive theories. Mapping the sensitivity of designs to…

Research designs involving cluster randomization are becoming increasingly important in educational and behavioral research. Many of these designs involve two levels of clustering or nesting (students within classes and classes within schools). Researchers would like to compute effect size indexes based on the standardized mean difference to…

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…

This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…

The impact of uncertainty about item parameters on test information functions is investigated. The information function of a test is one of the most important tools in item response theory (IRT). Inaccuracy in the estimation of test information can have substantial consequences on data analyses based on IRT. In this article, the major part (called…

We derive an estimator of the standardized value which, under the standard assumptions of normality and homoscedasticity, is more efficient than the established (asymptotically efficient) estimator and discuss its gains for small samples. (Contains 1 table and 3 figures.)

The Mantel-Haenszel (MH) and logistic regression (LR) differential item functioning (DIF) procedures have inflated Type I error rates when there are large mean group differences, short tests, and large sample sizes.When there are large group differences in mean score, groups matched on the observed number-correct score differ on true score,…

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations found that standard errors derived without the normality assumption were more accurate than those derived with the normality assumption in a large sample with moderately skewed score distributions. (SLD)

This article describes a new, unified framework for linear equating in a non-equivalent groups anchor test (NEAT) design. The authors focus on three methods for linear equating in the NEAT design--Tucker, Levine observed-score, and chain--and develop a common parameterization that shows that each particular equating method is a special case of the…