New confidence intervals for the difference between two proportions in two-sample correlated binary data

Research output: Contribution to journalArticle

Abstract

Asymptotic confidence intervals for the difference between two proportions have been well developed in two-sample correlated binary data. But, the coverage probabilities of such asymptotic confidence intervals are much smaller than the nominal level in small samples, because the asymptotic confidence intervals rely on the large sample theory. The aim of this paper is to construct new confidence intervals whose performance is better than the existing confidence intervals in small samples. Assuming the beta-binomial model, we derive the Edgeworth expansion of the studentized test statistic. Then, we propose new confidence intervals by eliminating the skewness in the Edgeworth expansion. We conduct simulation studies to compare the new confidence intervals with the existing confidence intervals.

Original languageEnglish
Pages (from-to)175-183
Number of pages9
JournalJournal of the Korean Statistical Society
Volume37
Issue number2
DOIs
Publication statusPublished - 2008 Jun 1

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Correlated Binary Data
Confidence interval
Proportion
Edgeworth Expansion
Small Sample
Beta-binomial Model
Large Sample Theory
Coverage Probability
Skewness
Test Statistic
Categorical or nominal
Simulation Study

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

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abstract = "Asymptotic confidence intervals for the difference between two proportions have been well developed in two-sample correlated binary data. But, the coverage probabilities of such asymptotic confidence intervals are much smaller than the nominal level in small samples, because the asymptotic confidence intervals rely on the large sample theory. The aim of this paper is to construct new confidence intervals whose performance is better than the existing confidence intervals in small samples. Assuming the beta-binomial model, we derive the Edgeworth expansion of the studentized test statistic. Then, we propose new confidence intervals by eliminating the skewness in the Edgeworth expansion. We conduct simulation studies to compare the new confidence intervals with the existing confidence intervals.",
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AB - Asymptotic confidence intervals for the difference between two proportions have been well developed in two-sample correlated binary data. But, the coverage probabilities of such asymptotic confidence intervals are much smaller than the nominal level in small samples, because the asymptotic confidence intervals rely on the large sample theory. The aim of this paper is to construct new confidence intervals whose performance is better than the existing confidence intervals in small samples. Assuming the beta-binomial model, we derive the Edgeworth expansion of the studentized test statistic. Then, we propose new confidence intervals by eliminating the skewness in the Edgeworth expansion. We conduct simulation studies to compare the new confidence intervals with the existing confidence intervals.

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