Martín Andrés, A.; Álvarez Hernández, M. Comment on: “An improved score interval with a modified midpoint for a binomial proportion”. (English) Zbl 1510.62151 J. Stat. Comput. Simulation 86, No. 2, 388-393 (2016). Summary: W. Yu et al. [ibid. 84, No. 5, 1022–1038 (2014; Zbl 1453.62428)] propose a novel confidence interval (CI) for a binomial proportion by modifying the midpoint of the score interval. This CI is competitive with the various commonly used methods. At the same time, we [the authors, J. Appl. Stat. 41, No. 7, 1516–1529 (2014; Zbl 1514.62742)] analyse the performance of 29 asymptotic two-tailed CI for a proportion. The CI they selected is based on the arcsin transformation (when this is applied to the data increased by 0.5), although they also refer to the good behaviour of the classical methods of score and Agresti and Coull (which may be preferred in certain circumstances). The aim of this commentary is to compare the four methods referred to previously. The conclusion (for the classic error \(\alpha\) of 5%) is that with a small sample size (\( \leq 80\)) the method that should be used is that of Yu et al.; for a large sample size (\(n \geq 100\)), the four methods perform in a similar way, with a slight advantage for the Agresti and Coull method. In any case the Agresti and Coull method does not perform badly and tends to be conservative. The program which determines these four intervals are available from the address http://www.ugr.es/local/bioest/Z_LINEAR_K.EXE. MSC: 62F25 Parametric tolerance and confidence regions 62-08 Computational methods for problems pertaining to statistics Keywords:arcsin transformation; adjusted Wald interval; binomial distribution; confidence interval; Wilson score interval Citations:Zbl 1453.62428; Zbl 1514.62742 Software:Z_LINEAR_K PDFBibTeX XMLCite \textit{A. Martín Andrés} and \textit{M. Álvarez Hernández}, J. Stat. Comput. Simulation 86, No. 2, 388--393 (2016; Zbl 1510.62151) Full Text: DOI References: [1] Agresti A, Coull BA. Approximate is better than ‘exact’ for interval estimation of binomial proportions. Amer Statist. 1998;52(2):119-126. 10.2307/2685469[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · doi:10.2307/2685469 [2] Yu W, Guo X, Xu W. An improved score interval with a modified midpoint for a binomial proportion. J Stat Comput and Simul. 2014;84(5):1022-1038. 10.1080/00949655.2012.738211 doi: 10.1080/00949655.2012.738211[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1453.62428 · doi:10.1080/00949655.2012.738211 [3] Martín Andrés A, Álvarez Hernández M. Two-tailed asymptotic inferences for a proportion. J Appl Stat. 2014;41(7):1516-1529. 10.1080/ 02664763.2014.881783 doi: 10.1080/02664763.2014.881783[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1514.62742 · doi:10.1080/ [4] Upton GJG. A comparison of alternative tests for the 2 × 2 comparative trial. J R Stat Soc A. 1982;145(1):86-105. 10.2307/2981423 doi: 10.2307/2981423[Crossref], [Web of Science ®], [Google Scholar] · doi:10.2307/2981423 [5] Martín Andrés A, Silva Mato A. Choosing the optimal unconditioned test for comparing two independent proportions. Comput Statist Data Anal. 1994;17:555-574. doi: 10.1016/0167-9473(94)90148-1[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0937.62534 [6] Chen LA, Hung HN, Chen CR. Maximum average-power (MAP) tests. Comm Statist Theory Methods. 2007;36:2237-2249. 10.1080/03610920701215480 doi: 10.1080/03610920701215480[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1124.62007 · doi:10.1080/03610920701215480 [7] Martín Andrés A, Álvarez Hernández M. Two-tailed approximate confidence intervals for the ratio of proportions. Stat Comput. 2014;24:65-75. 10.1007/s11222-012-9353-5 doi: 10.1007/s11222-012-9353-5[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1325.62061 · doi:10.1007/s11222-012-9353-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.