The visualization shows a Bayesian two-sample *t* test, for simplicity the variance is assumed to be known. It illustrates both Bayesian estimation via the posterior distribution for the effect, and Bayesian hypothesis testing via Bayes factor. The frequentist p-value is also shown. The null hypothesis, H_{0} is that the effect δ = 0, and the alternative H_{1}: δ ≠ 0, just like a two-tailed *t* test. You can use the sliders to vary the observed effect (Cohen's d), sample size (*n* per group) and the prior on δ.

The **prior **on the effect is a scaled unit-information prior. The black, and red circle on the curves represents the likelihood of 0 under the prior and posterior. Their likelihood ratio is the Savage-Dickey density ratio, which I use here as to compute Bayes factor. The ** p-value** is the traditional

Check out Alexander Etz's blog series "Understanding Bayes" for a really good introduction to Bayes factor. Fabian Dablander also wrote a really good post, "Bayesian statistics: why and how", which introduces Bayesian inference in general. If you're interesting in an easy way to perform a Bayesian *t* test check out JASP, or BayesFactor if you use R.

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