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Statistical Power Analysis for Univariate Meta-Analysis: A Three-Level Model

Statistical power analysis has long been a requirement for researchers seeking funding from the Institute of Education Sciences (IES). As in all individual studies, power analysis is also important when conducting meta-analytic review studies to ensure that the study has sufficient ability to detect an overall treatment effect of interest across a large group of related studies. For example, suppose a meta-analytic review determines that a school intervention significantly improves student performance and has good power to detect that effect, then, researchers will have more confidence in further investing in, developing, and recommending the specific intervention for extensive usage. Calculating statistical power can also inform researchers as they design studies. For instance, power analysis can inform the necessary number of studies needed in their sample to detect an effect across all of those studies in a meta-analysis. This study extends prior research on power analysis for univariate meta-analysis and adds new aspects that facilitate the calculations of statistical power.

A three-level model in meta-analysis considers heterogeneity across research groups

There are a few common approaches to conduct meta-analysis. However, recent realizations suggest that the same authors often publish several studies in a certain topic, and thus may be represented many times in the meta-analysis. To address this issue, approaches to calculating statistical power in these studies should account for the repeated representation of the same study teams. Thus, in our study, we formally introduce methodology that adds third level units in the meta-analysis.

In the proposed three-level meta-analysis, the effect sizes are nested within studies, which in turn are nested within research groups of investigators (see the illustrative figure). Specifically, in this illustration, one effect size (e.g., ES 1) is extracted from each study (e.g., Study 1) and several studies (e.g., Study 1 to Study i) are linked to a research group (e.g., Research Group 1) because they are conducted by the same authors. The variance between these third level units (i.e., research groups) may influence the power of the meta-analysis. Consequently, the proposed three-level model takes into account the between-study (second level) and the between-research group (third level) variances and produces more accurate power estimates.

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Experimental Design and Statistical Power for Cluster Randomized Cost-Effectiveness Trials

Cluster randomized trials (CRTs) are commonly used to evaluate educational effectiveness. Recently there has been greater emphasis on using these trials to explore cost-effectiveness. However, methods for establishing the power of cluster randomized cost-effectiveness trials (CRCETs) are limited. This study developed power computation formulas and statistical software to help researchers design two- and three-level CRCETs.

Why are cost-effectiveness analysis and statistical power for CRCETs important?

Policymakers and administrators commonly strive to identify interventions that have maximal effectiveness for a given budget or aim to achieve a target improvement in effectiveness at the lowest possible cost (Levin et al., 2017). Evaluations without a credible cost analysis can lead to misleading judgments regarding the relative benefits of alternative strategies for achieving a particular goal. CRCETs link the cost of implementing an intervention to its effect and thus help researchers and policymakers adjudicate the degree to which an intervention is cost-effective. One key consideration when designing CRCETs is statistical power analysis. It allows researchers to determine the conditions needed to guarantee a strong chance (e.g., power > 0.80) of correctly detecting whether an intervention is cost-effective.

How to compute statistical power when designing CRCETs?

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Conjuring power from a theory of change: The PWRD method for trials with anticipated variation in effects

Timothy Lycurgus, Ben B. Hansen, and Mark White

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Many efficacy trials are conducted only after careful vetting in national funding competitions. As part of these competitions, applications must justify the intervention’s theory of change: how and why do the desired improvements in outcomes occur? In scenarios with repeated measurements on participants, some of the measurements may be more likely to manifest a treatment effect than others; the theory of change may provide guidance as to which of those observations are most likely to be affected by the treatment.

Figure 1:
Power for the various methods across increasing effect sizes when the theory of change is correct.  

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Design and Analytic Features for Reducing Biases in Skill-Building Intervention Impact Forecasts

Daniela Alvarez-Vargas, Sirui Wan, Lynn S. Fuchs, Alice Klein, & Drew H. Bailey

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Despite policy relevance, long term evaluations of educational interventions are rare relative to the amount of end of treatment evaluations. A common approach to this problem is to use statistical models to forecast the long-term effects of an intervention based on the estimated shorter term effects. Such forecasts typically rely on the correlation between children’s early skills (e.g., preschool numeracy) and medium-term outcomes (e.g., 1st grade math achievement), calculated from longitudinal data available outside the evaluation. This approach sometimes over- or under-predicts the longer-term effects of early academic interventions, raising concerns about how best to forecast the long-term effects of such interventions. The present paper provides a methodological approach to assessing the types of research design and analysis specifications that may reduce biases in such forecasts.

What did we do?

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Between-School Variation in Students’ Achievement, Motivation, Affect, and Learning Strategies: Results from 81 Countries for Planning Cluster-Randomized Trials in Education

Martin Brunner, Uli Keller, Marina Wenger, Antoine Fischbach & Oliver Lüdtke

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Does an educational intervention work?

When planning an evaluation, researchers should ensure that it has enough statistical power to detect the expected intervention effect. The minimally detectable effect size, or MDES, is the smallest true effect size a study is well positioned to detect. If the MDES is too large, researchers may erroneously conclude that their intervention does not work even when it does. If the MDES is too small, that is not a problem per se, but it may mean increased cost to conduct the study.  The sample size, along with several other factors, known as design parameters, go into calculating the MDES. Researchers must estimate these design parameters. This paper provides an empirical bases for estimating design parameters in 81 countries across various outcomes.

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