The Wald Confidence Interval for a Binomial p as an Illuminating “Bad” Example

Abstract

When teaching we usually not only demonstrate/discuss how a certain method works, but, not less important, why it works. In contrast, the Wald confidence interval for a binomial p constitutes an excellent example of a case where we might be interested in why a method does not work. It has been in use for many years and, sadly enough, it is still to be found in many textbooks in mathematical statistics/statistics. The reasons for not using this interval are plentiful and this fact gives us a good opportunity to discuss all of its deficiencies and draw conclusions which are of more general interest. We will mostly use already known results and bring them together in a manner appropriate to the teaching situation. The main purpose of this article is to show how to stimulate students to take a more critical view of simplifications and approximations. We primarily aim for master’s students who previously have been confronted with the Wilson (score) interval, but parts of the presentation may as well be suitable for bachelor’s students.

KEYWORDS:

• Correlation
• Coverage probability
• Score statistic
• Skewness
• Wald statistic

Acknowledgments

The author thanks three referees, an associate editor, and the editor for encouraging and helpful comments, which have substantially improved the article.

Disclosure Statement

The author reports there are no competing interests to declare.