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This study introduces a Bayes factor approach for multiway analysis of variance (ANOVA), offering graded evidence for effects or invariances. Researchers can now quantify evidence using this hierarchical modeling method in statistical software.

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Area of Science:

  • Statistics
  • Psychological Methods
  • Quantitative Psychology

Background:

  • Traditional multiway analysis of variance (ANOVA) often relies on null hypothesis significance testing.
  • There is a need for methods that provide graded evidence for both effects and their absence.

Purpose of the Study:

  • To present a Bayes factor approach for multiway analysis of variance (ANOVA).
  • To enable researchers to quantify the evidence for or against effects and invariances within complex designs.

Main Methods:

  • Conceptualizing ANOVA as a hierarchical model with clustered levels within factors.
  • Developing Bayes factors for fixed and random effects, accommodating within-subjects, between-subjects, and mixed designs.
  • Discussing model construction, comparison strategies, and providing a practical example.

Main Results:

  • The Bayes factor approach allows for graded evidence, moving beyond dichotomous significance testing.
  • Demonstrated the computation of Bayes factors using the BayesFactor package in R and the JASP statistical package.
  • The method is comprehensive, covering various ANOVA designs and effect types.

Conclusions:

  • The Bayes factor approach offers a robust alternative for multiway ANOVA, providing nuanced interpretations of data.
  • This method enhances statistical inference by quantifying evidence for effects and invariances.
  • Implementation in R and JASP makes this advanced statistical technique accessible to researchers.