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Multilevel meta-analysis of single-case experimental designs using robust variance estimation.

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Synthesizing single-case experimental designs (SCEDs) requires robust methods. Multilevel meta-analysis with robust variance estimation (RVE) accurately estimates log response ratios, while ordinary least squares with RVE best estimates Tau effect sizes.

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Area of Science:

  • Behavioral science research
  • Psychological research methodology

Background:

  • Single-case experimental designs (SCEDs) are crucial for evaluating interventions on individual behaviors.
  • Synthesizing results from multiple SCED studies necessitates advanced statistical methods.
  • Accurate sampling variances for effect size estimates in SCEDs can be compromised by data auto-correlation.

Purpose of the Study:

  • To evaluate the performance of different statistical methods for synthesizing SCEDs under auto-correlation.
  • To compare multilevel meta-analysis (MLMA) with robust variance estimation (RVE) against ordinary least squares (OLS) with RVE.
  • To assess various effect size metrics within these synthesis frameworks.

Main Methods:

  • A Monte Carlo simulation was employed to mimic real data series characteristics.
  • The study simulated data with auto-correlation to test synthesis methods.
  • Performance was evaluated based on bias, accuracy, and confidence interval coverage for different effect size estimators.

Main Results:

  • MLMA combined with RVE demonstrated appropriate bias, accuracy, and confidence interval coverage for log response ratios.
  • OLS estimator corrected with RVE showed superior performance for estimating overall average Tau effect sizes.
  • Meta-analysis of within-case standardized mean differences was inadequately handled by all tested methods.

Conclusions:

  • MLMA with RVE is a reliable method for synthesizing SCEDs when estimating log response ratios.
  • OLS with RVE offers the best approach for synthesizing Tau effect sizes from SCED data.
  • Further development is needed for robust meta-analysis of within-case standardized mean differences in SCED research.