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A randomization test wrapper for synthesizing single-case experiments using multilevel models: A Monte Carlo

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Summary
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A new randomization test (RT) wrapper for multilevel models (MLMs) improves treatment effect evaluation in single-case research. This nonparametric approach offers superior power for multiple-baseline designs with few cases and controls Type I error for bimodal data.

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Area of Science:

  • Behavioral Science
  • Statistics
  • Research Methodology

Background:

  • Multilevel models (MLMs) are used in single-case research for multiple-baseline designs (MBDs).
  • Traditional MLMs have statistical assumptions often violated in single-case data.
  • This limits the reliable synthesis of group data in MBDs.

Purpose of the Study:

  • To introduce a nonparametric solution to overcome MLM limitations in single-case research.
  • To present a randomization test (RT) wrapper for MLMs in MBDs.
  • To evaluate the performance of the RT wrapper against parametric MLMs.

Main Methods:

  • Developed a randomization test (RT) wrapper for multilevel models (MLMs).
  • Conducted a simulation study manipulating key data characteristics (cases, observations, variability, distribution, autocorrelation, effect size).
  • Compared the RT wrapper's Type I error rate and power against traditional parametric MLMs.

Main Results:

  • The RT wrapper demonstrated superior statistical power compared to parametric tests for MBDs with fewer than five cases.
  • The RT wrapper maintained controlled Type I error rates for bimodal data.
  • Traditional parametric MLMs showed uncontrolled Type I error rates for bimodal data.

Conclusions:

  • The RT wrapper offers a robust, nonparametric alternative for analyzing group data in MBDs.
  • This method enhances the validity of treatment effect evaluation in single-case research, especially with limited cases or complex data distributions.
  • The RT wrapper addresses critical limitations of traditional MLMs in single-case research settings.