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Practice Statistics Notes

Analysis of continuous data from small samples

BMJ 2009; 338 doi: https://doi.org/10.1136/bmj.a3166 (Published 06 April 2009) Cite this as: BMJ 2009;338:a3166
  1. J Martin Bland, professor of health statistics 1,
  2. Douglas G Altman, professor of statistics in medicine2
  1. 1Department of Health Sciences, University of York, York YO10 5DD
  2. 2Centre for Statistics in Medicine, University of Oxford, Wolfson College Annexe, Oxford OX2 6UD
  1. Correspondence to: Professor Bland mb55{at}york.ac.uk

    Studies with small numbers of measurements are rare in the modern BMJ, but they used to be common and remain plentiful in specialist clinical journals. Their analysis is often more problematic than that for large samples.

    Parametric methods, including t tests, correlation, and regression, require the assumption that the data follow a normal distribution and that variances are uniform between groups or across ranges.1 In small samples these assumptions are particularly important, so this setting seems ideal for rank (non-parametric) methods, which make no assumptions about the distribution of the data; they use the rank order of observations rather than the measurements themselves.1 Unfortunately, rank methods are least effective in small samples. Indeed, for very small samples, they cannot yield a significant result whatever the data. For example, when using the Mann-Witney test for comparing two samples of …

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