Summary: This article considers Bayesian \(p\)-values for testing independence in \(2 \times 2\) contingency tables with cell counts observed from the two independent binomial sampling scheme and the multinomial sampling scheme. From the frequentist perspective, Fisher’s \(p\)-value \((p_F)\) is the most commonly used \(p\)-value but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, M. J. Bayarri and J. O. Berger [J. Am. Stat. Assoc. 95, No. 452, 1127–1142 (2000; Zbl 1004.62022)] first proposed the partial posterior predictive \(p\)-value \((p_{PPOST})\), which can avoid the double use of the data that occurs in another Bayesian \(p\)-value proposed by I. Guttman [J. R. Stat. Soc., Ser. B 29, 83–100 (1967; Zbl 0158.37305)] and D. B. Rubin [Ann. Stat. 12, 1151–1172 (1984; Zbl 0555.62010)], called the posterior predictive \(p\)-value \((p_{POST})\). The subjective and objective Bayesian \(p\)-values in terms of \(p_{POST}\) and \(p_{PPOST}\) are derived under the beta prior and the (noninformative) Jeffreys prior, respectively. Numerical comparisons among \(p_F, p_{POST}\), and \(p_{PPOST}\) reveal that \(p_{PPOST}\) performs much better than \(p_F\) and \(p_{POST}\) for small to moderate sample sizes from the frequentist perspective.