# Pooled standard deviation

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**Pooled standard deviation** is a way to find a better estimate of the true standard deviation given several different samples taken in different circumstances where the mean may vary between samples but the true standard deviation (precision) is assumed to remain the same. It is calculated by

or with simpler notation,

where s_{p} is the pooled standard deviation, *n _{i}* is the sample size of the

*i'*th sample,

*s*is the standard deviation of the

_{i}*i*'th sample, and

*k*is the number of samples being combined.

*n*−1 is used instead of

*n*for the same reason it may be used in calculating standard deviations from samples.

## External links Edit

Definitions

- http://www.iupac.org/goldbook/P04758.pdf
- http://www.isixsigma.com/dictionary/Pooled_Standard_Deviation-295.htm

Uses

- Cohen's
*d*(effect size) - http://web.psych.utoronto.ca/~psy379/Stats%20PPT.pdf - also referring to Cohen's
*d*(on page 6) - http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1473027

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