run_simulations(sample_size = c(40,50,60),
+sample_prob = c(0.5,0.5),
+prob0 = c(0.1,0.2,0.3,0.4),
+prob1 = c(0.6,0.2,0.1,0.1),
+niter = 100)
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Running 100 iterations on 3 sample sizes. Progress: ■■■■■■■■■■■ …
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Running 100 iterations on 3 sample sizes. Progress: ■■■■■■■■■■■■■■■■■■■■■ …
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: cannot compute exact p-value with ties
+#> Warning: Chi-squared approximation may be incorrect
+#> Warning: Chi-squared approximation may be incorrect
+#> $sample_size_40
+#> # A tibble: 100 × 14
+#> wilcox fisher chi_sq_false chi_sq_true lrm kruskal coinasymp run
+#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
+#> 1 0.000695 3.07e-4 0.00134 0.00134 3.10e-4 6.60e-4 6.60e-4 1
+#> 2 0.00250 6.91e-3 0.0107 0.0107 1.57e-3 2.39e-3 2.39e-3 2
+#> 3 0.000618 4.54e-3 0.00684 0.00684 2.78e-4 5.87e-4 5.87e-4 3
+#> 4 0.00596 2.47e-2 0.0231 0.0231 3.55e-3 5.71e-3 5.71e-3 4
+#> 5 0.307 5.04e-1 0.512 0.512 2.97e-1 3.00e-1 3.00e-1 5
+#> 6 0.0463 1.38e-1 0.136 0.136 3.64e-2 4.47e-2 4.47e-2 6
+#> 7 0.000486 2.05e-3 0.00540 0.00540 2.29e-4 4.60e-4 4.60e-4 7
+#> 8 0.00724 3.11e-2 0.0315 0.0315 5.07e-3 6.94e-3 6.94e-3 8
+#> 9 0.00420 2.22e-2 0.0235 0.0235 2.61e-3 4.01e-3 4.01e-3 9
+#> 10 0.00000169 7.49e-7 0.0000144 0.0000144 7.43e-8 1.57e-6 1.57e-6 10
+#> # ℹ 90 more rows
+#> # ℹ 6 more variables: y <list>, x <list>, n_null <int>, n_intervene <dbl>,
+#> # sample_size <dbl>, K <int>
+#>
+#> $sample_size_50
+#> # A tibble: 100 × 14
+#> wilcox fisher chi_sq_false chi_sq_true lrm kruskal coinasymp run
+#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
+#> 1 0.00000473 2.27e-5 0.0000592 0.0000592 4.87e-7 4.51e-6 4.51e-6 1
+#> 2 0.00000729 1.31e-5 0.0000585 0.0000585 1.42e-6 6.95e-6 6.95e-6 2
+#> 3 0.00154 4.67e-3 0.00734 0.00734 1.04e-3 1.48e-3 1.48e-3 3
+#> 4 0.00167 3.20e-4 0.000481 0.000481 5.13e-4 1.62e-3 1.62e-3 4
+#> 5 0.00758 4.24e-2 0.0501 0.0501 5.95e-3 7.35e-3 7.35e-3 5
+#> 6 0.0000209 2.80e-5 0.000113 0.000113 3.03e-6 2.00e-5 2.00e-5 6
+#> 7 0.00000461 3.81e-6 0.0000425 0.0000425 7.76e-7 4.39e-6 4.39e-6 7
+#> 8 0.0000269 1.32e-4 0.000328 0.000328 6.86e-6 2.58e-5 2.58e-5 8
+#> 9 0.0000278 7.29e-5 0.000262 0.000262 8.94e-6 2.65e-5 2.65e-5 9
+#> 10 0.000000146 7.69e-8 0.00000138 0.00000138 4.25e-9 1.38e-7 1.38e-7 10
+#> # ℹ 90 more rows
+#> # ℹ 6 more variables: y <list>, x <list>, n_null <int>, n_intervene <dbl>,
+#> # sample_size <dbl>, K <int>
+#>
+#> $sample_size_60
+#> # A tibble: 100 × 14
+#> wilcox fisher chi_sq_false chi_sq_true lrm kruskal coinasymp run
+#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
+#> 1 0.0000174 1.02e-4 0.000238 0.000238 5.11e-6 1.68e-5 1.68e-5 1
+#> 2 0.00000137 1.15e-7 0.00000118 0.00000118 2.56e-7 1.32e-6 1.32e-6 2
+#> 3 0.0000437 1.97e-4 0.000474 0.000474 1.91e-5 4.23e-5 4.23e-5 3
+#> 4 0.0000683 2.87e-4 0.000460 0.000460 2.32e-5 6.60e-5 6.60e-5 4
+#> 5 0.000119 5.54e-4 0.00109 0.00109 6.31e-5 1.15e-4 1.15e-4 5
+#> 6 0.0000110 6.09e-5 0.000104 0.000104 2.43e-6 1.06e-5 1.06e-5 6
+#> 7 0.000000277 1.57e-7 0.00000160 0.00000160 1.74e-8 2.66e-7 2.66e-7 7
+#> 8 0.0000141 1.17e-4 0.000214 0.000214 3.92e-6 1.36e-5 1.36e-5 8
+#> 9 0.000000209 7.16e-8 0.000000823 0.000000823 1.37e-8 2.01e-7 2.01e-7 9
+#> 10 0.000000522 7.52e-7 0.00000421 0.00000421 5.16e-8 5.01e-7 5.01e-7 10
+#> # ℹ 90 more rows
+#> # ℹ 6 more variables: y <list>, x <list>, n_null <int>, n_intervene <dbl>,
+#> # sample_size <dbl>, K <int>
+#>
+
+
+