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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Unbiased standard deviation in summarize |

Date |
Fri, 16 Nov 2012 22:52:38 +0000 |

The formula used by -summarize- is documented. Even if it weren't experiment would show that the SD is calculated as the square root of the variance, itself calculated with a divisor of (n - 1). . set obs 7 obs was 0, now 7 . gen y = _n . su y Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- y | 7 4 2.160247 1 7 . mata ------------------------------------------------- mata (type end to exit) --------------------------------------------- : y = 1::7 : sqrt(mean((y :- mean(y)):^2)) 2 : sqrt(sum((y :- mean(y)):^2)/6) 2.160246899 Although a divisor of (n - 1) does give an unbiased estimate of variance, its square root is _not_ an unbiased estimate of SD, and you would need to program a correction factor yourself. : n = 7 : sqrt(2 / (n - 1)) * exp(lngamma(n / 2)) / exp(lngamma((n - 1)/2)) .9593687887 This is not quite what is given at http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation It's also documented everywhere that Stata is called "Stata". Nick On Fri, Nov 16, 2012 at 10:00 PM, Daniel Almar de Sneijder <dasneijder@gmail.com> wrote: > Hello STATA, > > First of all, my initial guess is that the computed standard deviation in > STATA does not correct for possible biases. However I am not sure as I > havent found any good documentation on this issue. My questions are: > > 1. Does anybody know whether the standard deviations, computed with the > command summarize, are unbiased? > > 2. If so, how can I correct for this? * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Unbiased standard deviation in summarize***From:*Nick Cox <njcoxstata@gmail.com>

**References**:**st: Unbiased standard deviation in summarize***From:*Daniel Almar de Sneijder <dasneijder@gmail.com>

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