Specialty › Bayesian

One-way ANOVA (Bayes factor)

Bayesian one-way ANOVA with the JZS prior weighs the evidence for a difference between group means.

What is One-way ANOVA (Bayes factor)?

Same BF framework as Bayesian linear regression, applied to one-way ANOVA: BF₁₀ compares the model with the factor against the intercept-only null. Posterior medians + credible intervals give per-group offsets from the grand mean.

Bayesian ANOVA differs from frequentist in two practical ways: (1) it can quantify evidence *for* no group difference (BF < 1/3), and (2) the credible intervals are interpreted as 'there's a 95% posterior probability the true offset is in this range' — a probability statement about the parameter, not the procedure.

When should I use One-way ANOVA (Bayes factor)?

  • Group-comparison studies where you'd want to support 'groups are equivalent' as a positive finding.
  • Replication studies — quantifying evidence for or against a previously reported effect.

What data does it need?

Response + factor (k ≥ 2 levels) + r-scale prior.

What does it report?

BF₁₀ of factor vs intercept-only + posterior median + 95% CrI for each group offset + grand-mean posterior.

How do I interpret the result?

The pattern of credible intervals reveals which groups drive the model preference; non-overlapping CrIs roughly correspond to meaningful pairwise differences.

See also

References

  • Rouder et al. (2012). Default Bayes factors for ANOVA designs.