Fundamentals of p-values: Introduction

TL;DR

This paper introduces the fundamental concept of p-values in statistical hypothesis testing, focusing on their basic properties and the notion of p-functions within a simplified discrete framework.

Contribution

It provides an accessible explanation of p-values and introduces the concept of p-functions, laying groundwork for further exploration of the general case.

Findings

Clarifies the concept of p-values using basic probability theory

Introduces the notion of p-functions as a foundation for p-values

Restricts analysis to discrete cases without zero-probability outcomes

Abstract

We explain the concept of p-values presupposing only rudimentary probability theory. We also use the occasion to introduce the notion of p-function, so that p-values are values of a p-function. The explanation is restricted to the discrete case with no outcomes of zero probability. We are going to address the general case elsewhere.