Fisher’s significance test: A gentle introduction

Abstract

The p-value is often misunderstood and, for example, misinterpreted as a probability for the correctness of the null hypothesis. The aim of this article is to first explain the definition of the p-value. Determining the p-value requires knowledge of a probability function. How an appropriate statistical model is selected and how the p-value is determined using this model, the null hypothesis and the empirical data is explained using the t-distribution. When interpreting the p-value obtained in this way, two incompatible statistical schools of thought are confronted: the orthodox Neyman-Pearson hypothesis test, which amounts to a decision between the null hypothesis and a complementary alternative hypothesis, and Fisher’s significance test, in which no alternative hypothesis is formulated and in which the smaller the p-value, the greater the evidence against the null hypothesis. The amount ends with some critical remarks about the handling of p-values.

Keywords

• statistical models
• statistical data interpretation
• data analysis