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Comment on: “An improved score interval with a modified midpoint for a binomial proportion”. (English) Zbl 1510.62151

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

Software:

Z_LINEAR_K
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References:

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