A statistical inference course based on p-values

TL;DR

This paper proposes a novel approach to teaching statistical inference centered on p-values, ensuring valid inference across all sample sizes, contrasting with traditional methods that focus on large-sample approximations.

Contribution

It introduces an alternative curriculum for statistical inference courses built around p-values, emphasizing validity for all sample sizes and including computational details and examples.

Findings

Provides a comprehensive course outline and illustrative examples.

Demonstrates provably valid inference for small and large samples.

Offers computational methods for p-value-based inference.

Abstract

Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach to teaching this course, built around p-values, emphasizing provably valid inference for all sample sizes. Details about computation and marginalization are also provided, with several illustrative examples, along with a course outline.