BMJ  2005;331:903 (15 October), doi:10.1136/bmj.331.7521.903

Education and debate

Statistics Notes

Standard deviations and standard errors

Douglas G Altman, professor of statistics in medicine1, J Martin Bland, professor of health statistics2

1 Cancer Research UK/NHS Centre for Statistics in Medicine, Wolfson College, Oxford OX2 6UD, 2 Department of Health Sciences, University of York, York YO10 5DD

Correspondence to: Prof Altman doug.altman@cancer.org.uk

The first 150 words of the full text of this article appear below.

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 deviation limits, though those outside may all be at one end. We may choose a different summary statistic, however, when . . . [Full text of this article]


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Rapid Responses:

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A standard error?
Stephen J Senn
bmj.com, 18 Oct 2005 [Full text]
Usually it is advisible to avoid "usually" in statistics
Jo R Goedhuys
bmj.com, 21 Oct 2005 [Full text]
Standard error refers to standard error of mean
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