Hypothesis Test to Compare Two Paired Binomial Proportions: Assessment of 24 Methods

José Antonio Roldán-Nofuentes (), Tulsi Sagar Sheth and José Fernando Vera-Vera
Additional contact information
José Antonio Roldán-Nofuentes: Department of Statistics and Operations Research, School of Medicine, University of Granada, 18016 Granada, Spain
Tulsi Sagar Sheth: Department of Statistics and Operations Research, School of Medicine, University of Granada, 18016 Granada, Spain
José Fernando Vera-Vera: Department of Statistics and Operations Research, Faculty of Sciences, University of Granada, Fuentenueva s/n, 18071 Granada, Spain

Mathematics, 2024, vol. 12, issue 2, 1-23

Abstract: 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.

Keywords: hypothesis test; paired binomial proportions; power; sample size; type I error rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/2/190/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/2/190/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:2:p:190-:d:1314317

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().