The p-value from a fuzzy point of view

TL;DR

This paper introduces a fuzzy set perspective on p-values, proposing new membership functions to interpret significance levels more flexibly and applying this approach to compare binomial proportions.

Contribution

It presents a novel fuzzy membership function framework for p-values, moving beyond arbitrary significance thresholds and enhancing interpretation of statistical measures.

Findings

New fuzzy membership functions for p-values

Application to compare binomial proportions

Assessment of confidence interval precision

Abstract

The purpose of the paper is to provide a new way of seeing the p-value in terms of a fuzzy membership function. According to the ASAs statement, we aim at removing the arbitrary choice of the significance level and at demonstrating that the p-value can be profitably interpreted from a fuzzy point of view. In particular, we propose a new class of membership functions by viewing the p-value as a function of the null hypothesis and we apply our approach to compare two independent binomial proportions. The proposed membership functions can also be employed to assess the precision of confidence intervals and the power of statistical tests.