Statistical analysis: sample size and power estimations

Abstract

### Key points Medical research sets out to form conclusions applicable to populations with data obtained from randomized samples drawn from those populations. Larger sample sizes should lead to more reliable conclusions. Sample size and power considerations should therefore be part of the routine planning and interpretation of all clinical research.1 The purpose of this article is to outline the issues involved and to describe the rationale behind sample size and power calculations. Research has significant costs in terms of organizational outlay and staffing, and also the potential costs to patients and subjects. Patients in clinical trials may be subjected to the risks of receiving potentially useless or harmful new treatments, or of not receiving a beneficial new treatment if they are assigned to a control arm. Consequently, there is a strong ethical justification for researchers to ensure that the data they collect are sufficient and of adequate quality such as to maximize the likelihood of the research contributing to practically useful conclusions. There are two main ways in which the conclusions from an interventional clinical trial may be incorrect when applied to the population as a whole. These are called type I and II …