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, H0 is that the effect δ = 0, and the alternative H1: 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.

Settings

Observed effect (d = 1)
Sample size (n = 10)
SD of prior (σδ = 0.3)

About the visualization

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 p-value for a two-sample t test with known variance (i.e. a Z test). HDI is the posterior highest density interval, which in this case is analogous a credible interval. And CI is the traditional frequentist confidence interval.

Learn more

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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If you enjoy my work, or maybe even use it in your own teaching, please consider supporting me on Patreon. My visualizations will always be free to use, but you can show your support by donating a dollar or two for every new visualization I create.

Suggestions, errors, and bugs

Have any suggestion? Or found any bugs? Send them to me, my contact info can be found here.