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# The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution

DOI link for The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution

The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution book

# The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution

DOI link for The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution

The 1 × 2 $ 1\times 2 $ Table and the Binomial Distribution book

## ABSTRACT

This chapter presents the H. Blaker exact interval as an approach to reduce the conservatism of the Clopper-Pearson exact interval. Blaker focused on confidence intervals but formulated the problems in terms of preference functions and confidence curves such that both hypothesis tests and confidence intervals can be derived within the same framework. The chapter discusses the recommendations in more detail and summarize the merits of the different methods. An elegant solution was proposed by Blaker, who sought to improve exact inference in discrete distributions, including the binomial, negative binomial, hypergeometric, and Poisson distributions. The Wald interval is in widespread use, partly because it is the default confidence interval for the binomial probability in most statistical software packages. The practical problem with too low coverage is that the Wald interval will include the true binomial probability less often than the nominal level specifies.