we investigate small, moderate and large-sample performances of frequentist confidence intervals (FCIs) and Bayesian credible intervals (BCIs) under three criteria. For a set values for the model parameters, 10,000 $3\times2$ bilateral data tables are generated from the product of trinomial distributions under a balanced design. The essence of these criteria rely on the principle that good FCIs (Wald FCIs described in Appendix 1 of the Supplementary Web Materials) or good HPD BCIs should have their true coverage close to or preferably larger than the nominal value. Indeed, FCIs and BCIs with deflated true coverage are recommended against. Lengths of the intervals must also be considered. We use the three following criteria:

-   the expected true coverage probability (ETCP) of the interval $\big(\widehat{\Delta}_L,
    \widehat{\Delta}_U\big)$ for $\Delta$, $P\big(\widehat{\Delta}_L\leq
    \Delta\leq\widehat{\Delta}_U\big)$, in repeated sampling;

-   the expected width (EWCI) of the interval of $\big(\widehat
    {\Delta}_L, \widehat{\Delta}_U\big)$ for $\Delta$, $\widehat{\Delta}_U-\widehat{\Delta}_L$, in repeated sampling; and

-   the expected mean square error (MSE) that reflects a compromise between bias and precision, in repeated sampling.

Although these criteria are defined in terms of $\Delta$, we also examine the behaviors of these criteria for $(\gamma,\lambda_0,\lambda_1)$ as well. For the case of the MSE, we go further by adding the 