A historical criticism of null hypothesis testing is that a null hypothesis cannot be correct in the first place. The reason that many nulls cannot be correct is that what makes a null hypothesis a null hypothesis is its infinite precision. Only an infinitely precise hypothesis can be used to generate an infinitely precise prediction, such as t will be zero. It is around that infinitely precise prediction that we would construct a probability density function. If you are thinking, I just want to know if the difference is significant, and if you mean important, a null hypothesis test will never tell you that. Although we should know from the start when our nulls cannot be correct, there is still reason to test them: to see if we can confidently decide on the direction of a difference. In this editorial, I explore when nulls can and cannot be correct and summarize the field of directional decisions. Ronald Fisher made directional decisions. To John Tukey, the only reason to test a null was to decide on direction. And it is not a matter of using one-tailed tests. Before you submit your P values to a journal, read this editorial and rethink what you have written. The question is one of direction.
"Editorial, Your Null Hypothesis Must Be False: Test It Anyway,"
Georgia Journal of Science, Vol. 78, No. 3, Article 1.
Available at: https://digitalcommons.gaacademy.org/gjs/vol78/iss3/1