Education And Debate

Estimating sample sizes for binary, ordered categorical, and continuous outcomes in two group comparisons

BMJ 1995; 311 doi: (Published 28 October 1995) Cite this as: BMJ 1995;311:1145

This article has a correction. Please see:

  1. M J Campbell, reader in medical statistics,a,
  2. S A Julious, statistician programmera,
  3. D G Altman, headb
  1. aMedical Statistics and Computing, University of Southampton, Southampton General Hospital, Southampton SO16 6YD
  2. bMedical Statistics Laboratory, Imperial Cancer Research Fund, PO Box 123, London WC2A 3PX
  1. Correspondence to: Dr Campbell.
  • Accepted 21 July 1995

Sample size calculations are now mandatory for many research protocols, but the ones useful in common situations are not all easily accessible. This paper outlines the ways of calculating sample sizes in two group studies for binary, ordered categorical, and continuous outcomes. Formulas and worked examples are given. Maximum power is usually achieved by having equal numbers in the two groups. However, this is not always possible and calculations for unequal group sizes are given.

A sample size calculation is now almost mandatory in research protocols and to justify the size of clinical trials in papers.1 Nevertheless, one of the most common faults in papers reporting clinical trials is in fact a lack of justification of the sample size, and it is a major concern that important therapeutic effects are being missed because of inadequately sized studies.2 A recent paper has concluded “the reporting of statistical power and sample size needs to be improved.”3 Recent articles in the BMJ have described the basis of sample size calculations,4 5 and explained the fundamental concepts of statistical significance (alpha), effect size ((delta)), and power (1-ß). A nomogram for sample size calculations for continuous data is also available.6 However, there have been some recent developments in the theory of sample size calculations, which are likely to prove useful, and the purpose of this paper is to make available a collection of formulas and examples for a variety of situations likely to be encountered in practice. In particular, situations not dealt with in previous articles are two group comparisons with unequal sample sizes, and sample sizes for ordered categorical outcomes (for example categories better, same, or worse). The paper describes sample size calculations, and provides tables, for studies comparing two groups of individuals that have outcome variables that are …

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