Reading a Bayes Factor

Info sheet · Statistics for Psychology & Neuroscience

Author

Andrew Bell

Published

August 13, 2026

Info sheet 0.2 (draft) · Prerequisites: NHST vs Bayesian inference · Give feedback ↗

Working notes for the author — not shown to students once collapsed; remove before publishing.

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What you’ll get from this sheet

The single number a Bayesian analysis reports — and how to read it. By the end you should be able to:

  1. Interpret a Bayes factor as a ratio of evidence.
  2. Use the strength conventions without treating them as a bright line.

A Bayes factor (BF) is a ratio: BF₁₀ = 10 means the data are ten times more likely under the model with an effect than under the model without one. BF₁₀ = 0.2 means the reverse (5× more likely under the null). Unlike a p‑value it’s symmetric — it can evidence a null as readily as an effect — and it’s a continuous measure, not a yes/no verdict.

A ratio of evidence

A Bayes factor is simply a ratio of how well two models predicted the data. Write BF₁₀ for the alternative (an effect) over the null (no effect): a BF₁₀ of 10 says the observed data are ten times more likely under the model with an effect than under the model without one. A BF₁₀ of 0.2 says the opposite — the data are five times more likely under the null (equivalently BF₀₁ = 5). That symmetry is the crucial difference from a p‑value: a Bayes factor can pile up evidence for a null just as readily as against it, which NHST simply can’t do.

Drag the Bayes factor and see where it lands on the conventional evidence scale — in both directions:

At BF₁₀ = 1 (the centre) the data don’t favour either model — perfectly ambiguous. Slide right and the evidence tips toward an effect; slide left, past 1, and it tips toward the null (that’s what BF₀₁ tracks). The labels — anecdotal (1–3), moderate (3–10), strong (10–30), very strong (30–100), extreme (>100) — are handy shorthand, but the deeper point is that a Bayes factor is a continuous measure of evidence, not a bright‑line decision like p < .05. It invites the richer question — which hypotheses, or which predictors, does the data support, and by how much? — rather than merely is anything significant?

See it in code

library(BayesFactor)
bf <- ttestBF(group_a, group_b)   # Bayes factor for a two-group difference
bf                                 # prints BF10; 1/bf gives BF01

# extract the number:
extractBF(bf)$bf

One study reports BF₁₀ = 0.25; another reports BF₁₀ = 1.1. Do they say the same thing (“no significant effect”)?

No — and that’s the power of the Bayes factor. BF₁₀ = 0.25 means the data are 4× more likely under the null (BF₀₁ = 4) — moderate, positive evidence for no effect. BF₁₀ = 1.1 means the data are essentially uninformative — they barely distinguish the two hypotheses, so the study is inconclusive and needs more data. A p‑value would lump both together as “non‑significant”; the Bayes factor tells them apart — evidence for the null versus no evidence either way.

The evidence labels (anecdotal / moderate / strong) are conventions, not laws — don’t turn “BF > 3” into a new p < .05 bright line; report the number and let readers judge. A Bayes factor also depends on the prior you place on the effect, so state it. And keep the two subscripts straight: BF₁₀ is evidence for the alternative over the null; BF₀₁ = 1/BF₁₀ is the reverse — reporting the wrong one flips your conclusion.

Where this shows up next

The same number appears in Bayesian ANOVA and regression, where it compares whole models. See Chapter (Bayesian Methods).