Abstract
The Wald interval is easy to calculate; it is often used as the confidence interval for binomial proportions. However, when using this confidence interval, the actual coverage probability often falls under the nominal coverage probability in small cases. On the other hand, several confidence intervals where the actual cover age probability does not fall under the nominal coverage probability are suggested. In this study, we intro-duce five exact confidence intervals where the actual coverage probability does not fall under the nominal coverage probability and we calculate the expected length of the confidence intervals and compare/verify the accuracy of the coverage probabilities. Further, we examined the characteristics of these five exact confidence intervals at length. Coverage probability of Sterne was significantly closer to 0.95 than the other confidence intervals and stable. Its expected Length are not scattered in the width compared with the other methods. As a result, we found that the quality of the confidence interval based on the Sterne test is its availability for small samples.
Highlights
Studies on confidence intervals for binomial probability not to fall under the nominal coverage proportions have been performed since a long time probability at all times, but it has been indicated that ago and continue to be performed
We intro-duce five exact confidence intervals where the actual coverage probability does not fall under the nominal coverage probability and we calculate the expected length of the confidence intervals and compare/verify the accuracy of the coverage probabilities
This study introduces five exact confidence intervals where the actual coverage probability does not fall under the nominal coverage probability; we calculate the expected length of the confidence interval and compare/verify the accuracy of the coverage probabilities
Summary
The confidence interval is a method for the actual coverage. Several other exact methods have been addition, new confidence intervals have been suggested. When using these new confidence method of Clopper and Pearson (1934) This method intervals, the actual coverage probability often falls is easy to understand and program. Several confidence intervals that uses the likelihood ratio test statistic on the where the actual coverage probability does not fall binomial distribution test. This study introduces five exact confidence intervals where the actual coverage probability does not fall under the nominal coverage probability; we calculate the expected length of the confidence interval and compare/verify the accuracy of the coverage probabilities. We define the attained LR p-value as Equation 3:
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