Evaluation of Analysis of means, Wald, and Log-likelihood ratio tests in comparing independent proportions

In this study, in experiments where groups are compared based on a binary variable, the Analysis of Means (ANOM), Wald, and Log-Likelihood Ratio tests for proportions were compared under comprehensive experimental conditions in terms of type I error rate and test power. As a result of 50,000 simulations, it was observed that the type I error rate for ANOM stayed within the 4.00% to 6.00% range under all experimental conditions. For the LR test, the type I error rate was negatively affected by small sample sizes (n=10, sometimes n=20). For the Wald test, the type I error rate generally fell outside the 4.00%-6.00% limits and was quite irregular. In terms of test power, ANOM and the LR test were similar, although ANOM performed slightly better. Considering both type I error rate and test power together, ANOM was found to be considerably superior to the other two tests.