In defence of score intervals for proportions and their differences

Newcombe, Robert Gordon ORCID: https://orcid.org/0000-0003-4400-8867 and Nurminen, Markku 2011. In defence of score intervals for proportions and their differences. Communications in Statistics - Theory and Methods 40 (7) , pp. 1271-1282. 10.1080/03610920903576580

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Abstract

A recent article (Santner et al., 200723. Santner , T. J. , Pradhan , V. , Senchaudhuri , P. , Mehta , C. R. , Tamhane , A. ( 2007 ). Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions . Computat. Statist. Data Anal. 51 : 5791 – 5799. asserted that a score interval for a difference of independent binomial proportions (Miettinen and Nurminen, 198511. Miettinen , O. , Nurminen , M. ( 1985 ). Comparative analysis of two rates . Statist. Med. 4 : 213 – 226. may have inadequate coverage. We re-visit the properties of score intervals for binomial proportions and their differences. Published data indicate these methods produce mean coverage slightly above the nominal confidence level 1 − α. We argue it is appropriate to align mean rather than minimum coverage with 1 − α, based on a moving average representation of the coverage probability. The poor coverage properties claimed by Santner et al. (200723. Santner , T. J. , Pradhan , V. , Senchaudhuri , P. , Mehta , C. R. , Tamhane , A. ( 2007 ). Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions . Computat. Statist. Data Anal. 51 : 5791 – 5799. actually relate to an inferior version of the score interval (Mee, 19849. Mee , R. W. ( 1984 ). Confidence bounds for the difference between two probabilities . Biometrics 40 : 1175 – 1176 .

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Medicine
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Confidence interval ; Coverage ; Proportion ; Exact ; Score
Publisher:	Taylor & Francis
ISSN:	0361-0926
Last Modified:	21 Oct 2022 09:47
URI:	https://orca.cardiff.ac.uk/id/eprint/37692

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