Bayes factor (BF₁₀) as an addition
In brief
The Bayes factor BF₁₀ compares how well two assumptions predict the data: H₁ (there is a difference, a change, a relationship) against H₀ (there is none). BF₁₀ = 8 means: the data are about 8 times more likely under H₁ than under H₀. Unlike the p value it can also express evidence for H₀.
Where it appears
By default nowhere. Under "Settings" → "Show Bayes factors", a collapsed line "Bayes factor" appears below the result for the t test (two groups), the before/after comparison and the Pearson correlation. The APA line then gets "BF₁₀ = …". There is no Bayes factor for Spearman and Kendall. The Welch result and all other numbers stay unchanged.
Reading it
- From BF₁₀ > 1 it favors H₁; below 1 it favors H₀ - the reciprocal BF₀₁ is then shown (BF₀₁ = 5 means: the data are about 5 times more likely under H₀ than under H₁).
- Classification after Lee and Wagenmakers (2013): 1-3 anecdotal, 3-10 moderate, 10-30 strong, 30-100 very strong, above 100 extreme. These are rules of thumb, not cut-offs.
- A BF₁₀ close to 1 means the data favor neither side. That is different from "no effect".
The Bayes factor depends on the prior, that is, on which effect sizes H₁ considers plausible. The default (see below) is widely used; anyone needing another prior has to set it in JASP or R. It replaces neither the effect size nor the confidence interval.
t(38) = 2.51, p = .016, d = 0.79, 95% CI [0.15, 1.42], BF₁₀ = 3.4
For specialists
t test: JZS Bayes factor after Rouder et al. (2009), two-sided; Cauchy prior on the effect size δ with scale r = √2/2 (default in JASP and BayesFactor, "medium"). For two groups it uses the Student t (equal variances), not Welch. The integral over the mixing variance g is solved numerically (Gauss-Legendre over ln g). Correlation: Ly, Verhagen and Wagenmakers (2016), stretched beta prior on ρ with κ = 1 (uniform, as in JASP), exact density of r with ₂F₁. The R package BayesFactor (correlationBF) uses a narrower prior by default (rscale = 1/3); with rscale = 1 it agrees. Checked against R: scripts/bayes-erwartet.R.