Introduction
In a previous post I talked about estimating a binomial proportion, including for rare events. The reason I wrote that was for background to this post. Here, we’ll again be looking at estimating proportions - and can include rare events - but with an added wrinkle: A population that is finite.
In the Binomial case, every observation is assumed to be independent and have a fixed probability of the outcome of interest (a “success” or a “failure”).
Introduction
The common approach
Common Approach: The math
Why the common approach is bad
Alternatives
Alternative 1: Wilson and Agresi-Coull intervals
Wilson interval: The math
Alternative 2: Bayesian method
Comparisons
Summary
Introduction
Estimating a proportion gets covered in virtually every introductory statistics course, so why would I be writing a post about it? There are three reasons:
One of my goals with these posts is to explain some basic statistical concepts.
Introduction
Should you use a two-tailed test or a one-tailed test (or similarly, a confidence interval or 1-sided confidence bound)? For those just learning statistics, or who have had only a little training in the subject, this question comes up fairly often. And there is some conflicting information and advice out there. Most often I’ve seen comments critical of one-sided methods, such as:
The short answer is: Never use one tailed tests.
The slides for my Introduction to Spatial Data (geared for non-Statisticians) can be found here:
https://jelsema.github.io/presentations/2019-intro-spatial/intro_spatial.html#1