Calculation of Statistical Power and Sample Size

Power analysis and sample size calculation are intensely debated topics in medical research. With increasing pressure on researchers, medical journals are demanding a priori power analysis or sample size calculation as an imperative part of a well-designed study. Consequently, study authors feel compelled to embed power estimations in studies, making power analysis and sample size calculation increasingly common in recent years. Despite the increasing popularity of power estimations, research has found that in almost 50% of cases, there is inadequate reporting of how the power/sample size was calculated. When performing power estimations, it is important to distinguish a priori power analysis from post hoc power analysis. While a priori power analysis represents the gold standard for studies such as randomized clinical controlled trials, post hoc power analysis is commonly conducted in negative trials (i.e., accepting the null hypothesis) without a priori sample size calculation. There is a large repertoire of arguments against post hoc power analysis that increasingly raise doubts about their validity. Instead, confidence intervals are becoming more important, especially for negative studies, as they provide a better transparency of the presented data. This chapter covers basic knowledge about a priori and post hoc power analysis/sample size calculation along with the fundamental statistical background knowledge. The translation of a priori sample size calculation, as a fundamental element of a well-structured and well-powered study, into clinical research is elaborated in this chapter using typical scenarios and a step-by-step guide.