This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple…

Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are…

This study builds on the simulation framework of a recent paper by Stanley and Doucouliagos ("Research Synthesis Methods" 2023;14;515--519). S&D use simulations to make the argument that meta-analyses using partial correlation coefficients (PCCs) should employ a "suboptimal" estimator of the PCC standard error when…

Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against…

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a…

Cognitive diagnosis models (CDMs) are the statistical framework for cognitive diagnostic assessment in education and psychology. They generally assume that subjects' latent attributes are dichotomous--mastery or nonmastery, which seems quite deterministic. As an alternative to dichotomous attribute mastery, attention is drawn to the use of a…

In meta-analysis, effect sizes often need to be converted into a common metric. For this purpose conversion formulas have been constructed; some are exact, others are approximations whose accuracy has not yet been systematically tested. We performed Monte Carlo simulations where samples with pre-specified population correlations between the…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

Equity Indexed Annuities (EIAs) are controversial financial products because the payoffs to investors are based on formulas that are supposedly too complex for average investors to understand. This brief describes how Monte Carlo simulation can provide insight into the true risk and return of an EIA. This approach can be used as a project…

Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…

This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed…