AUTHOR=Cousineau Denis 

TITLE=There are no alternative hypotheses in tests of null hypotheses

JOURNAL=Frontiers in Psychology

VOLUME=Volume 16 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2025.1708313

DOI=10.3389/fpsyg.2025.1708313

ISSN=1664-1078

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.