Statistical Hypothesis Tests and Statistical Power in Pure and Applied Science

The process of statistical hypothesis testing is often used in science in attempts to separate real effects from random variation. However, as commonly used and interpreted, statistical hypothesis tests often lead to illogical conclusions, particularly when the null hypothesis is not rejected. These illogical conclusions occur to some extent in basic science, where their source can at least be understood in terms of the values inherent in such science. They arise much more often in applied science, where the inherent values of basic science seldom match the values associated with the applied situations. The paper presents examples from both basic and applied science. It then proposes that every statistical hypothesis test could be more logically interpreted if its statistical power were estimated and considered in the interpretation. Scientific journals should establish requirements for power estimates to accompany results of all statistical hypothesis tests.