# There are no alternative hypotheses in tests of null hypotheses

## TL;DR

This paper clarifies that null hypothesis testing involves only one hypothesis, not two, and explains how this misconception has led to misinterpretations in statistical methods.

## Contribution

The paper identifies a fundamental misconception in NHST teaching and introduces dual hypotheses statistical testing as a distinct procedure.

## Key findings

- Null hypothesis statistical testing does not involve an alternative hypothesis.
- Procedures with power analysis and type-II thresholds are part of a different inferential framework.
- The confusion stems from applying Aristotle's excluded middle to empirical science.

## Abstract

Null hypothesis statistical testing (NHST) is typically taught by first posing a null hypothesis and an alternative hypothesis. This conception is sadly erroneous as there is no alternative hypothesis in the NHST. This misconception generated erroneous interpretations of the NHST procedures, and the fallacies that were deduced from this misconception attracted much attention in deterring the use of NHST. Herein, it is reminded that there is just one hypothesis in these procedures. Additionally, procedures accompanied by a power analysis and a threshold for type-II errors are actually a different inferential procedure that could be called dual hypotheses statistical testing (DHST). The source of confusions in teaching NHST may be found in Aristotle's axiom of excluded middle. In empirical sciences, in addition to the falsity or veracity of assertions, we must consider the inconclusiveness of observations, which is what is rejected by the NHST.