Bayesian ANOVA (BIC Bayes Factor)

The BIC-approximated Bayesian ANOVA compares a model with group means against an intercept-only model using BF10 = exp((BIC0 − BIC1)/2), which corresponds to a unit-information prior.

BIC 근사 베이즈 분산분석은 집단 평균 모형과 절편만 있는 모형의 BIC 차이로 BF10 = exp((BIC0 − BIC1)/2)를 구해 집단 차이의 증거를 평가하는 방법이다.

Is there evidence for or against differences among several group means, beyond a p value?

여러 집단 평균에 차이가 있다는(또는 없다는) 증거를 p값 말고 어떻게 보일 수 있나요?

The Bayes factor is approximated from the difference in the Bayesian information criterion between the null model and the group model. It expresses how much more likely the data are under group differences than under equal means, but it differs from the default JZS Bayes factor computed with a Cauchy prior on effects.

When to use Bayesian ANOVA (BIC Bayes Factor)

• You want a quick Bayes factor for a one-way design
• You need evidence for equal means as well as against
• Only standard model-fit output is available

When to use something else

• You need the default JZS Bayes factor; use a Rouder-style Bayesian ANOVA instead
• Variances differ strongly across groups; use Welch's ANOVA instead

Assumptions and requirements

• Independent observations
• Normally distributed residuals
• Equal variances across groups
• Large enough sample for the BIC approximation

What the analysis reports

• BF10 and BF01
• BIC of null and group models
• Posterior probability of H1 under equal prior odds
• Classical F, p and η² for comparison

How to report it

A Bayesian one-way ANOVA (BIC approximation) gave BF10 = [value] for the effect of [group], F([df1], [df2]) = [value], η² = [value].

Related methods

• One way ANOVA
• Bayesian t Test (Bayes Factor)

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