A Bayesian analysis reports how much the data should move your belief — a Bayes factor, or a posterior distribution with an interval — rather than a p-value that only says whether a result is surprising under a null. Magic Stat computes the JZS Bayes factor and the posterior for the standard designs.
The default output is a Bayes factor: the evidence in the data for one hypothesis against another, on a scale where 1 is no evidence and larger values favour the alternative. For the t-test family this is the JZS factor (Rouder et al. 2009), computed by numerical integration with a Cauchy prior on the effect size. For correlation there is an exact factor; for one-way ANOVA and contingency the factor is the BIC approximation.
Alongside the factor, Magic Stat estimates the posterior distribution of the effect by direct sampling from the conjugate model — no MCMC — and summarises it with the highest-density interval (HDI), a ROPE decision and the probability of direction. A robustness plot shows how the Bayes factor moves as the prior width changes, so you can see whether the conclusion depends on that choice.
This is accessible Bayesian statistics, not a general Bayesian modelling language. There is no prior on every parameter, no hierarchical structure you design yourself, and the factor for ANOVA and contingency is approximate. If your question needs a bespoke Bayesian model, Stan or JASP's more general modules are the right tools.
Modes: two-sample t · paired t · one-sample t · one-way ANOVA (factor + pairwise) · Pearson correlation · linear regression (one or multiple predictors) · repeated measures (2+ time points) · contingency (BIC approximation).
Prior: JZS Cauchy prior on the effect size, widened or narrowed through the prior scale.
Posterior summary: 95% HDI by default, ROPE width selectable, probability of direction reported.
The data are about five times more likely under the alternative than under the null. The app labels it with the Jeffreys scale (anecdotal, moderate, strong, very strong, decisive). It is evidence, not a decision — the threshold is yours, and the ROPE gives a practical answer instead.
For the t family (JZS) it is computed by numerical integration of the exact model, and for correlation it is exact. For one-way ANOVA and contingency tables it is the BIC approximation (Wagenmakers 2007) — useful and honest, but approximate, and the app says so on the results.
For these conjugate designs the posterior can be sampled directly, which is fast and deterministic. A general-purpose sampler is what you need for hierarchical or bespoke models, and those are outside this module — Stan or JASP are the tools there.
They answer different questions. A p-value addresses whether the data are surprising under the null; a Bayes factor compares two hypotheses and can favour the null. Where a reviewer demands a p-value, the frequentist tests elsewhere in the app provide it.
Yes. The computations run locally; the only automatic signal is an anonymous installation counter.