Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

The development of new statistical models for the meta-analysis of diagnostic test accuracy studies is still an ongoing field of research, especially with respect to summary receiver operating characteristic (ROC) curves. In the recently published updated version of the "Cochrane Handbook for Systematic Reviews of Diagnostic Test…

Real data are unlikely to be exactly normally distributed. Ignoring non-normality will cause misleading and unreliable parameter estimates, standard error estimates, and model fit statistics. For non-normal data, researchers have proposed a distributionally-weighted least squares (DLS) estimator to combines the normal theory based generalized…

Over the past ten years, propensity score methods have made an important contribution to improving generalizations from studies that do not select samples randomly from a population of inference. However, these methods require assumptions and recent work has considered the role of bounding approaches that provide a range of treatment impact…

Bayesian inference for structural equation models (SEMs) is increasingly popular in social and psychological sciences owing to its flexibility to adapt to more complex models and the ability to include prior information if available. However, there are two major hurdles in using the traditional Bayesian SEM in practice: (1) the information nested…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

Classical automated test assembly (ATA) methods assume fixed and known coefficients for the constraints and the objective function. This hypothesis is not true for the estimates of item response theory parameters, which are crucial elements in test assembly classical models. To account for uncertainty in ATA, we propose a chance-constrained…