ABSTRACT
The Wilson score interval has been the main vehicle for this approach. This chapter might employs more precise ‘Clopper-Pearson’ inverted Binomial calculations, but since the Wilson interval aligns closely with the Clopper-Pearson, and is easier to calculate, the benefits of the approximation outweigh small costs of ultimate precision. The chapter computes and plots Wilson distributions. These are analogues of the Normal distribution for this interval. It uses the same method to compute logit-Wilson, continuity-corrected Wilson and Clopper-Pearson distributions. The ‘logit-Wilson’ regression method estimates variance using the Wilson interval on this logit scale. Gauss’s method of least squares regression over variance, on which our method is based, assumes variance is approximately Normal. The lower bound tail area appears slightly larger, indicating that even the continuity-corrected Wilson interval might obtain Type I errors. The Wilson score interval is a member of a class of confidence intervals characterising expected variation about an observed Binomial proportion.
