Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods
The comparison of two paired binomial proportions is a topic of interest in statistics, with important applications in medicine. There are different methods in the statistical literature to solve this problem, and the McNemar test is the best known of all of them. The problem has been solved from a...
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MDPI AG
2024-01-01
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| Online Access: | https://www.mdpi.com/2227-7390/12/2/190 |
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| author | José Antonio Roldán-Nofuentes Tulsi Sagar Sheth José Fernando Vera-Vera |
| author_facet | José Antonio Roldán-Nofuentes Tulsi Sagar Sheth José Fernando Vera-Vera |
| author_sort | José Antonio Roldán-Nofuentes |
| collection | DOAJ |
| description | The comparison of two paired binomial proportions is a topic of interest in statistics, with important applications in medicine. There are different methods in the statistical literature to solve this problem, and the McNemar test is the best known of all of them. The problem has been solved from a conditioned perspective, only considering the discordant pairs, and from an unconditioned perspective, considering all of the observed values. This manuscript reviews the existing methods to solve the hypothesis test of equality for the two paired proportions and proposes new methods. Monte Carlo simulation methods were carried out to study the asymptotic behaviour of the methods studied, giving some general rules of application depending on the sample size. In general terms, the Wald test, the likelihood-ratio test, and two tests based on association measures in 2 × 2 tables can always be applied, whatever the sample size is, and if the sample size is large, then the McNemar test without a continuity correction and the modified Wald test can also be applied. The results have been applied to a real example on the diagnosis of coronary heart disease. |
| first_indexed | 2024-03-08T10:42:39Z |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T10:42:39Z |
| publishDate | 2024-01-01 |
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| spelling | doaj.art-c9fdde72ab1d47a2804afe4054c50f972024-01-26T17:31:02ZengMDPI AGMathematics2227-73902024-01-0112219010.3390/math12020190Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 MethodsJosé Antonio Roldán-Nofuentes0Tulsi Sagar Sheth1José Fernando Vera-Vera2Department of Statistics and Operations Research, School of Medicine, University of Granada, 18016 Granada, SpainDepartment of Statistics and Operations Research, School of Medicine, University of Granada, 18016 Granada, SpainDepartment of Statistics and Operations Research, Faculty of Sciences, University of Granada, Fuentenueva s/n, 18071 Granada, SpainThe comparison of two paired binomial proportions is a topic of interest in statistics, with important applications in medicine. There are different methods in the statistical literature to solve this problem, and the McNemar test is the best known of all of them. The problem has been solved from a conditioned perspective, only considering the discordant pairs, and from an unconditioned perspective, considering all of the observed values. This manuscript reviews the existing methods to solve the hypothesis test of equality for the two paired proportions and proposes new methods. Monte Carlo simulation methods were carried out to study the asymptotic behaviour of the methods studied, giving some general rules of application depending on the sample size. In general terms, the Wald test, the likelihood-ratio test, and two tests based on association measures in 2 × 2 tables can always be applied, whatever the sample size is, and if the sample size is large, then the McNemar test without a continuity correction and the modified Wald test can also be applied. The results have been applied to a real example on the diagnosis of coronary heart disease.https://www.mdpi.com/2227-7390/12/2/190hypothesis testpaired binomial proportionspowersample sizetype I error rate |
| spellingShingle | José Antonio Roldán-Nofuentes Tulsi Sagar Sheth José Fernando Vera-Vera Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods Mathematics hypothesis test paired binomial proportions power sample size type I error rate |
| title | Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods |
| title_full | Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods |
| title_fullStr | Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods |
| title_full_unstemmed | Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods |
| title_short | Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods |
| title_sort | hypothesis test to compare two paired binomial proportions assessment of 24 methods |
| topic | hypothesis test paired binomial proportions power sample size type I error rate |
| url | https://www.mdpi.com/2227-7390/12/2/190 |
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