Specialty › Bayesian

Correlation (Bayes factor)

The JZS Bayes factor weighs the evidence for and against a non-zero Pearson correlation.

What is Correlation (Bayes factor)?

Same idea as bayes_ttest, applied to the correlation ρ. BF₁₀ quantifies whether the data favour 'ρ ≠ 0' over 'ρ = 0'. The prior on ρ is a stretched beta — concentrated near 0 by default, widening with the r-scale parameter.

Pair with the frequentist Pearson r when you want both perspectives in the same report. They typically agree directionally; the BF flags when the frequentist 'significant at p = 0.04' result is actually only anecdotal evidence (BF₁₀ ~ 1–3) — the kind of case that fails to replicate.

When should I use Correlation (Bayes factor)?

Same as Pearson correlation, when you want a Bayesian framing.
Replication settings where you need to quantify evidence either way.

What data does it need?

Two numeric columns + prior r-scale.

What does it report?

BF₁₀ + sample r + posterior median + 95% CrI on ρ + Jeffreys-scale verbal label.

What does it assume?

Independent paired observations.
Approximately bivariate normal (the JZS prior is on Fisher-z scale).

How do I interpret the result?

Compare BF₁₀ and the frequentist p side-by-side: BF₁₀ > 10 with p < 0.01 is solid; BF₁₀ ~ 1–3 with p ~ 0.05 is the marginal case where the frequentist result is misleadingly 'significant'.