\[ \def\Pr{{\text{Pr}}} \def\E{{\text{E}}} \def\Var{{\text{Var}}} \def\Cov{{\text{Cov}}} \def\cor{{\text{cor}}} \def\bm{\mathbf} \def\bs{\boldsymbol} \] In Tipton and Pustejovsky (2015), we examined several different small-sample approximations for cluster-robust Wald test statistics, which are like \(F\) statistics but based on cluster-robust variance estimators.

Meta-analyses of educational research findings frequently involve statistically dependent effect size estimates. Meta-analysts have often addressed dependence issues using ad hoc approaches that involve modifying the data to conform to the …

Sample size and statistical power are important factors to consider when planning a research synthesis. Power analysis methods have been developed for fixed effect or random effects models, but until recently these methods were limited to simple data …

Cross-classified random effects modeling (CCREM) is a common approach for analyzing cross-classified data in education. However, when the focus of a study is on the regression coefficients at level one rather than on the random effects, ordinary …

Power for Meta-Analysis of Dependent Effects

In my 2018 paper with Beth Tipton, published in the Journal of Business and Economic Statistics, we considered how to do cluster-robust variance estimation in fixed effects models estimated by weighted (or unweighted) least squares. We were recently alerted that Theorem 2 in the paper is incorrect as stated. It turns out, the conditions in the original version of the theorem are too general. A more limited version of the Theorem does actually hold, but only for models estimated using ordinary (unweighted) least squares, under a working model that assumes independent, homoskedastic errors. In this post, I'll give the revised theorem, following the notation and setup of the previous post (so better read that first, or what follows won't make much sense!).

Meta-analytic models for dependent effect sizes have grown increasingly sophisticated over the last few decades, which has created challenges for a priori power calculations. We introduce power approximations for tests of average effect sizes based …

__Purpose__: Speech-language pathologists (SLPs) typically examine narrative performance when completing a comprehensive language assessment. However, there is significant variability in the methodologies used to evaluate narration. The primary aims …

In my 2018 paper with Beth Tipton, published in the Journal of Business and Economic Statistics, we considered how to do cluster-robust variance estimation in fixed effects models estimated by weighted (or unweighted) least squares. A careful reader recently alerted us to a problem with Theorem 2 in the paper, which concerns a computational short cut for a certain cluster-robust variance estimator in models with cluster-specific fixed effects. The theorem is incorrect as stated, and we are currently working on issuing a correction for the published version of the paper. In the interim, this post details the problem with Theorem 2. I'll first review the CR2 variance estimator, then describe the assertion of the theorem, and then provide a numerical counter-example demonstrating that the assertion is not correct as stated.

Single-case experimental designs (SCEDs) are used to study the effects of interventions on the behavior of individual cases, by making comparisons between repeated measurements of an outcome under different conditions. In research areas where SCEDs …

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