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

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Bibliographic Details
Title: Evaluation of Analysis of means, Wald, and Log-likelihood ratio tests in comparing independent proportions
Authors: YİĞİT, SONER
Source: International Journal of Science and Research Archive. 16:1180-1187
Publisher Information: GSC Online Press, 2025.
Publication Year: 2025
Subject Terms: ANOM, Type I Error, Test Power, Monte Carlo Simulation, Binary Outcome
Description: 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.
Document Type: Article
ISSN: 2582-8185
DOI: 10.30574/ijsra.2025.16.1.2094
DOI: 10.5281/zenodo.17233446
DOI: 10.5281/zenodo.17233445
Rights: CC BY
Accession Number: edsair.doi.dedup.....d44aa1db1f78f1acbaffc64648d30207
Database: OpenAIRE
Description
Abstract: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.
ISSN:25828185
DOI:10.30574/ijsra.2025.16.1.2094