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<p>For the meta-analysis of single-case experimental design (SCED) studies, multilevel models can be used. Prior research evaluating this approach mainly looked at inferences about the overall treatment effect. Despite their importance, variance parameters received much less attention. Moreover, findings regarding variance parameter estimation are inconsistent. This study aims to fill these gaps by systematically studying variance estimates under realistic conditions and using different analysis strategies. We found that analyzing raw data or effect size data gives similar results. Standardization can induce substantial bias in the variance estimates, but this bias is reduced by applying Hedges’ small sample correction factor. We also observed that using the SCED counterpart of the sampling variance formula used for standardized mean differences in combination with Hedges’ correction factor leads to distorted results. Finally, we found that a parametric bootstrap procedure can further reduce the bias and mean squared error in the variance estimates, whereas various nonparametric bootstrapping methods fail to improve the estimates.</p>

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Variance Estimation in Single-Case Data Meta-Analysis: Bootstrapping to the Rescue?

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Wim Van den Noortgate,
  • Mariola Moeyaert

摘要

For the meta-analysis of single-case experimental design (SCED) studies, multilevel models can be used. Prior research evaluating this approach mainly looked at inferences about the overall treatment effect. Despite their importance, variance parameters received much less attention. Moreover, findings regarding variance parameter estimation are inconsistent. This study aims to fill these gaps by systematically studying variance estimates under realistic conditions and using different analysis strategies. We found that analyzing raw data or effect size data gives similar results. Standardization can induce substantial bias in the variance estimates, but this bias is reduced by applying Hedges’ small sample correction factor. We also observed that using the SCED counterpart of the sampling variance formula used for standardized mean differences in combination with Hedges’ correction factor leads to distorted results. Finally, we found that a parametric bootstrap procedure can further reduce the bias and mean squared error in the variance estimates, whereas various nonparametric bootstrapping methods fail to improve the estimates.