Categorical › Contingency / proportions

Contingency table (Bayes factor)

The Bayesian contingency test quantifies evidence for association between two categorical variables as a Bayes factor (BF₁₀), using an independent-multinomial model.

What is Contingency table (Bayes factor)?

Instead of a p-value, the Bayes factor compares the marginal likelihood of an association model against independence. BF₁₀ > 1 favours association; BF₁₀ < 1 favours independence — evidence for the null is expressible, unlike in the frequentist test.

Uses Gunel & Dickey (1974) priors with the independent-multinomial sampling plan (row totals fixed); prior concentration 1 is the default.

When should I use Contingency table (Bayes factor)?

  • Anywhere you'd run a chi-square test but want graded evidence, including evidence for independence.

What data does it need?

Two categorical columns + prior concentration.

What does it report?

BF₁₀ with a Jeffreys-style evidence label, the contingency table, and the frequentist χ² for reference.

What does it assume?

  • Independent observations.
  • Sampling plan matches the fixed-margin assumption (rows).

How do I interpret the result?

BF₁₀ ≥ 3 / 10 / 30 / 100: moderate / strong / very strong / extreme evidence for association; reciprocals support independence.

See also

References

  • Gunel & Dickey (1974). Bayes factors for independence in contingency tables. Biometrika 61.
  • Jamil et al. (2017). Default Gunel-Dickey Bayes factors. BRM 49.