Bayesian t Test (Bayes Factor)

The Bayesian t test compares two group means with a Bayes factor that weighs evidence for a difference against no difference, using a Cauchy prior on standardized effect size (JZS prior).

베이즈 t 검정은 표준화 효과크기에 Cauchy 사전분포(JZS)를 두고, 두 집단 평균 차이가 있다는 가설과 없다는 가설에 대한 증거를 베이즈 인자로 비교하는 방법이다.

How can I quantify evidence that two groups do not differ, rather than just failing to reject the null?

두 집단에 차이가 없다는 증거를 수치로 보이려면 어떻게 해야 하나요?

The JZS Bayes factor BF10 is the ratio of how well the data are predicted by a model with a Cauchy-distributed effect size versus a model with zero effect. Values above 1 favour a difference and values below 1 favour the null, so it can express evidence for no difference.

When to use Bayesian t Test (Bayes Factor)

• You want to state evidence for the null hypothesis
• You want a continuous measure of evidence rather than a significance decision
• You plan to monitor evidence as data accumulate

When to use something else

• Group variances differ markedly and samples are unequal; use Welch's t test or a Bayesian model with unequal variances instead
• You have more than two groups; use a Bayesian ANOVA instead

Assumptions and requirements

• Observations are independent
• Outcome is approximately normal within groups
• Equal variances across the two groups

What the analysis reports

• BF10 and BF01
• t statistic
• Posterior median and credible interval of effect size δ
• Posterior probability of H1 under equal prior odds

How to report it

A Bayesian independent-samples t test (Cauchy prior r = [value]) gave BF10 = [value], with posterior δ = [value], 95% CrI [[value], [value]].

Related methods

• Independent Samples t test
• Bayesian ANOVA (BIC Bayes Factor)

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