It is rare in the literature to see it recognised that a standard deviation, or variance,of values in a dataset is, just as the mean is, an estimate of a population value.It can be salutory to see how wide the confidence interval around these estimates arefor small datasets

Computational background

Ignore this next bit if you don't like equations!

The CI around an observed SD

The formula for CI around an observed SD in R code is from:

SD * sqrt(n - 1) / sqrt(qchisq(1 - ((1 - ci) / 2), n - 1))


SD * sqrt(n - 1) / sqrt(qchisq((1 - ci) / 2, n - 1))

Typesetting that with MathJax is not beautiful but is:

$$SD * \sqrt{\frac{n-1}{qchisq((1 - (1 - ci) / 2), (n-1)}}$$


$$SD * \sqrt{\frac{n-1}{qchisq((1 - ci) / 2, (n-1)}}$$

where 'qchisq(p, df)' is the quantile of the chisquare function for that df (degrees of freedom, i.e. n - 1)

Next please ...

Unless you are very familiar with it, please now go to the 'Background' tab and read the information there.

App created by Chris Evans PSYCTC.org

Last updated 21.iii.24.

Licenced under a Creative Commons, Attribution Licence-ShareAlike Please respect that and put an acknowledgement and link back to here if re-using anything from here.

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