Understanding Statistical Testing

Statistical hypothesis testing is common in research, but aconventional understanding sometimes leads to mistaken application andmisinterpretation. The logic of hypothesis testing presented in this article providesfor a clearer understanding, application, and interpretation. Key conclusions are that(a) the magnitude of an estimate on its raw scale (i.e., not calibrated by the standarderror) is irrelevant to statistical testing; (b) which statistical hypotheses are testedcannot generally be known a priori; (c) if an estimate falls in a hypothesized set ofvalues, that hypothesis does not require testing; (d) if an estimate does not fall in ahypothesized set, that hypothesis requires testing; (e) the point in a hypothesized setthat produces the largest p value is used for testing; and (f) statistically significantresults constitute evidence, but insignificant results do not and must not beinterpreted as evidence for or against the hypothesis being tested