Testing “Small,” not Null, Hypotheses: Classical and Bayesian Approaches

Given the many attacks on it, null hypothesis testing should be dead. The brief argument is as follows: The null hypothesis is that some parameter (usually a difference between groups on some outcome variable) is exactly equal to zero. This is never true. Therefore, we can always reject a null hypothesis without collecting any data, let alone doing any statistical analyses. If we insist on collecting data, we will either (correctly) reject the null hypothesis, or (incorrectly, due to lack of power) fail to reject the null hypothesis.