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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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A Bayesian Power Analysis Procedure Considering Uncertainty in Effect Size Estimates from a Meta-analysis.

Han Du1, Lijuan Wang1

  • 1a University of Notre Dame.

Multivariate Behavioral Research
|August 4, 2016
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Summary

This study introduces a Bayesian power analysis to account for effect size uncertainty in meta-analyses. This method provides a more reliable estimation of sample size, improving research design and power assurance.

Keywords:
Bayesian methodseffect size estimatesmeta-analysispower analysissample size determinationuncertainty

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Area of Science:

  • Statistics
  • Biostatistics
  • Meta-analysis

Background:

  • Conventional frequentist power analysis often overlooks uncertainty in effect size estimates.
  • This oversight can lead to significant variability in calculated sample sizes.
  • Addressing this uncertainty is crucial for robust study design.

Purpose of the Study:

  • To propose a hybrid Bayesian power analysis procedure.
  • To model and incorporate uncertainty in effect size estimates from meta-analyses.
  • To enhance the accuracy and reliability of prospective power analyses.

Main Methods:

  • Utilized observed effect sizes and prior distributions to derive posterior distributions.
  • Simulated effect sizes from posterior distributions to calculate individual power values.
  • Developed a power assurance curve by analyzing power distributions across various sample sizes.

Main Results:

  • The Bayesian approach effectively models uncertainty in effect size.
  • Generated power distributions and power assurance curves for given sample sizes.
  • Demonstrated advantages over conventional frequentist methods in two meta-analysis examples (standardized mean differences and Pearson's correlations).

Conclusions:

  • The proposed hybrid Bayesian power analysis offers a more robust method for determining sample sizes.
  • It accounts for effect size uncertainty, leading to more reliable power estimations.
  • This procedure enhances prospective power analysis in meta-analytic research.