Timeline for Standard deviation of standard deviation
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14 events
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| Jan 14, 2021 at 16:57 | comment | added | equaeghe | @JeremyDorner: First bring the outside ratio of Gamma functions inside. Then you get $s\cdot\sqrt{\frac{\frac{n-1}{2}\cdot\Gamma(\frac{n-1}{2})^2}{\Gamma(\frac{n}{2})^2}-1}$. Apply Stirling's approximation <en.wikipedia.org/wiki/Gamma_function#Stirling's_formula> to both Gamma function values and simplify. | |
| Jan 13, 2021 at 10:06 | comment | added | Jeremy Dorner | @equaeghe bit of a long shot, but is there a derivation for that? I tried applying Stirling's approximation but wasn't able to derive it. | |
| Jul 18, 2019 at 5:01 | comment | added | Syrtis Major | For those who want a simple form, $s/\sqrt{2(n-1)}$ is a good approximation at a few percent level. | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Feb 4, 2017 at 16:18 | comment | added | Harvey Motulsky | Probably worth pointing out that s (computed in @Macro's answer is sometimes referred to as the standard error of the sample standard deviation. | |
| Nov 3, 2016 at 18:57 | comment | added | equaeghe | The Gamma function is hard to calculate for non-small values of $n$. Applying Stirling's approximation, I get $s\cdot\sqrt{\mathrm{e}\cdot(1-\frac{1}{n})^{n-1}-1}$, which is computationally feasible as well as a bit more compact expression-wise. | |
| Aug 9, 2016 at 19:10 | comment | added | danijar | Did you forget to square the distances in the first formula? | |
| May 29, 2012 at 2:39 | history | edited | Macro | CC BY-SA 3.0 |
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| May 17, 2012 at 16:40 | vote | accept | CommunityBot | moved from User.Id=88 by developer User.Id=4454 | |
| May 16, 2012 at 21:55 | comment | added | whuber♦ | +1 It's nice to see not only a better reply come along after almost two years, but a reply that provides more useful detail than the references elsewhere in this thread. | |
| May 16, 2012 at 17:05 | history | edited | Macro | CC BY-SA 3.0 |
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| May 16, 2012 at 11:08 | history | edited | Macro | CC BY-SA 3.0 |
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| May 16, 2012 at 1:23 | history | edited | Macro | CC BY-SA 3.0 |
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| May 16, 2012 at 0:20 | history | answered | Macro | CC BY-SA 3.0 |