14 Exact Average Coverage Probabilities and Confidence Coefficients of Intervals for a Risk Difference

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For a confidence interval of a parameter in the binomial distribution, the coverage probability is a variable function of the parameter. The confidence coefficient is the infimum of the coverage probabilities and is an important behavior of the confidence interval. However, the exact confidence coefficient and average coverage probability of interval for two independent binomial distributions have not been accurately derived in the literature. In this study, we propose methodologies for calculating the exact confidence coefficients and average coverage probabilities of confidence intervals for a difference of the binomial proportions. Therefore, using these methodologies, we illustrate the performance of existing intervals and provide recommendations.

Binomial distribution

Confidence coefficient

Confidence interval

Coverage probability

Difference of proportions

Risk difference 

Biometrics Section