ABSTRACT
We expose fallacies in the arguments of critics of null hypothesis significance testing who go too far in arguing that we should abandon significance tests altogether. Beginning with statistics containing sampling or measurement error, significance tests provide prima facie evidence for the validity of statistical hypotheses, which may be overturned by further evidence in practical forms of reasoning involving defeasible or dialogical logics. For example, low power may defeat acceptance of the null hypothesis. On the other hand, we support recommendations to report point estimates and confidence intervals of parameters, and believe that the null hypothesis to be tested should be the value of the parameter given by a theory or prior knowledge. We also use a Wittgensteinian argument to question the coherence of concepts of subjective degree of belief underlying subjective Bayesian alternatives to significance testing.
