Concept of power in statistical testing of hypothesis

A major part of the application of statistical inference is in the testing of hypothesis. Retrospectives of intriguing dialogs on the role of hypothesis testing in clinical trials can be found in an early article by Cutler et al. (1966). Before we tap into the not so unfamiliar territory of the idea of using statistical testing to evaluate a new form of treatment in clinical trials (see Sundaresan et al. (1981)), and refer the article by Robert et al. (2021) to readers as a reference point for single-case study design and to those with interests in a recent practical primer on power calculations for such design, a light conversation on the logic of statistical testing of hypothesis may be necessary to bring in the topic on how one may see “power” of a test in relation to measuring the quality of the test.