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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 23:12:56 +0000 |

Note that that example correction factor was only for normal distributions. Nick On Fri, Nov 16, 2012 at 10:52 PM, Nick Cox <njcoxstata@gmail.com> wrote: > 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/

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

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

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