Statistics Notes

Standard deviations and standard errors

BMJ 2005; 331 doi: http://dx.doi.org/10.1136/bmj.331.7521.903 (Published 13 October 2005)
Cite this as: BMJ 2005;331:903

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  1. Douglas G Altman (doug.altman@cancer.org.uk), professor of statistics in medicine1,
  2. J Martin Bland, professor of health statistics2
  1. 1 Cancer Research UK/NHS Centre for Statistics in Medicine, Wolfson College, Oxford OX2 6UD
  2. 2 Department of Health Sciences, University of York, York YO10 5DD
  1. Correspondence to: Prof Altman

    The terms “standard error” and “standard deviation” are often confused.1 The contrast between these two terms reflects the important distinction between data description and inference, one that all researchers should appreciate.

    The standard deviation (often SD) is a measure of variability. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn. For data with a normal distribution,2 about 95% of individuals will have values within 2 standard deviations of the mean, the other 5% being equally scattered above and below these limits. Contrary to popular misconception, the standard deviation is a valid measure of variability regardless of the distribution. About 95% of observations of any distribution usually fall within the 2 standard …

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