JSM 2004 - Toronto

Abstract #300629

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Activity Number: 110
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #300629
Title: The Effect of Dependence on Confidence Intervals for a Population Proportion
Author(s): Weiwen Miao*+ and Joseph L. Gastwirth
Companies: Macalester College and George Washington University
Address: 1600 Grand Ave, St. Paul, MN, 55105,
Keywords: confidence Interval ; dependent observation ; coverage probability ; jury discrimination ; expected length
Abstract:

The binomial model is widely used in statistical applications. Usually, the success probability, p, and its associated confidence interval are estimated from a random sample. Thus, the observations are independent and identically distributed. Motivated by a legal case where grand jurors could serve on consecutive years, this paper shows that when the observations are dependent, even slightly, the coverage probabilities of the usual confidence intervals can deviate noticeably from their nominal level. Several modified confidence intervals that incorporate the dependence structure are proposed and examined. Our results show that the modified Wilson, Agresti-Coull, and Jeffreys confidence intervals perform well and can be recommended for general use.

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