Brody and Jamie’s Colleague: The Difference in Confidence Interval Estimators and Estimates

In an ever-increasing data-driven world, understanding and describing uncertainty around statistical results have become increasingly more important. Although describing uncertainty can take many forms, recent statements from professional associations (e.g., American Statistical Association) have suggested an increased use of confidence intervals. The calculation of a confidence interval (CI) is fairly straightforward, but the interpretation of a frequentist CI is not. This paper presents a case that demonstrates a potentially important connection among the CI estimator, estimate, and the coverage probability to gain a deep understanding of the meaning of the word confident in the interpretation of a CI. The case provides evidence of the connections among the coverage probability, long-run interpretation of a CI, and the interpretation of a CI that may support robust knowledge.