Advances and Applications in Statistics
Volume 58, Issue 1, Pages 35 - 43
(September 2019) http://dx.doi.org/10.17654/AS058010035 |
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A COMPARISON OF CONFIDENCE INTERVALS FOR A PROPORTION AND CRITERIA FOR THEIR APPLICATION
Hortensia Reyes-Cervantes, Félix Almendra-Arao and Marcos Morales-Cortés
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Abstract: The confidence interval for a proportion more used in practice is the Wald interval, apparently because of its simplicity. However, it is known that the coverage probability of this interval has an absolutely pathological behavior, for this reason general statistics textbook recommend it for use only under certain criteria. However, these criteria are deficient for its application and not trustworthy for this interval. Additionally, several alternative confidence intervals to the Wald interval are also known. Among them, we highlight the Agresti-Coull, Wilson and Arcsine. In this work, we analyze performance of these outstanding alternative intervals for a wide range of parameter values: and Comparison was made in terms of the above criteria, average coverage probability by default, average coverage probability due to excess and expected mean length. |
Keywords and phrases: confidence interval, proportion, coverage probability, expected length, Wald, Wilson, Agresti-Coull, Arcsine.
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