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This question already has an answer here:

I have data on exchange rates, where I have calculated the mean and the standard deviation of the payoff. I am able to run a regression (payoff regressed on a constant) and get the standard error of the sample mean.

Is it possible to either do the same with the standard deviation or calculate from a formular and get the standard error of the standard deviation?

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marked as duplicate by Glen_b Mar 29 '17 at 10:53

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    $\begingroup$ This post gives two versions of the variance of the sample variance (which is not what you asked but is related to it and at least the result in that case is relatively simple). You'll note that it depends on the fourth moment (which you won't know). If you're prepared to make some distributional assumption (in many common cases this will specify the fourth moment; otherwise it will be a function of the parameters you estimate) you may be able to get further ... ctd $\endgroup$ – Glen_b Mar 29 '17 at 10:42
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    $\begingroup$ ctd... (e.g. under normality, we have a result for the standard error of the standard deviation here) and if you're not, Wikipedia has an approximately unbiased result that involves excess kurtosis here -- as we might expect from its appearance in the variance of the variance (note that this assumes excess kurtosis is known, not estimated -- but in very large samples may be of use with sample values)...ctd $\endgroup$ – Glen_b Mar 29 '17 at 10:42
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    $\begingroup$ ctd... while this post shows how to get an asymptotic formula for the standard error of the standard deviation from that variance-of-the-variance result I pointed to in the first link. $\endgroup$ – Glen_b Mar 29 '17 at 10:51
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    $\begingroup$ Note that details of exactly how to implement that in Excel are off topic here, but presumably the explicit formulas in those last two links will be of some potential help to you. (I would not assume your variable is normal) $\endgroup$ – Glen_b Mar 29 '17 at 10:54