Table 9: Posterior predictive summaries for the sample correlation coefficient r pred for the replicated data associated with each of the two-dimensional beta binomial models.

Model Mean Std. Dev. 95% Interval Bayesian p-value
First model 0.412 0.152 (0.097, 0.688) 0.037
Second model 0.284 0.163 (0.043, 0.589) 0.005
Third model 0.246 0.159 (0.070, 0.547) 0.002