Specialty › Bayesian

Repeated-measures ANOVA (Bayes factor)

Bayesian repeated-measures ANOVA: Bayes factor for a within-subject effect, with the subject factor treated as random.

What is Repeated-measures ANOVA (Bayes factor)?

BF₁₀ compares the model response ~ condition + subject against the subject-only null, both with subject as a random factor — so the evidence concerns the within-subject condition effect, with between-subject variability absorbed either way.

Default JZS priors on the fixed effect (r-scale selectable). The BF is estimated by sampling, so a small Monte-Carlo error percentage is attached.

When should I use Repeated-measures ANOVA (Bayes factor)?

  • The Bayesian twin of the classical RM-ANOVA: quantify evidence for or against a condition effect, including support for the null.

What data does it need?

Response (numeric) + within factor + subject ID + prior r-scale.

What does it report?

BF₁₀ / BF₀₁ with Jeffreys interpretation, posterior medians + 95% CrIs for the condition effects.

What does it assume?

  • Normal residuals, compound symmetry via the random subject intercept.
  • Each subject observed in every condition (balanced designs behave best).

How do I interpret the result?

BF₁₀ = 5 → data are 5× more likely under a condition effect than under none. BF near 1 means the experiment was uninformative, not that the null is true.

See also

References

  • Rouder, Morey, Speckman & Province (2012). Default Bayes factors for ANOVA designs. JMP 56.