This question asks about a way to calculate the standard deviation of a standard deviation. The answer with most votes derives a formula for an unbiased estimator of $\text{SD}[s]$, which confuses me a bit, since $\text{SD}[s]$ denotes the standard deviation of the sample standard deviation. But then, what would an estimator for the standard deviation of the standard deviation be?
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$\begingroup$ Because the sample standard deviation for a fixed sample size $n$ is a fixed multiple of the standard deviation, the result is self-evident. $\endgroup$– whuber ♦Commented Mar 7, 2022 at 21:25
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$\begingroup$ I'm not sure I understand. As you note the linked questions ask about the standard deviation of $s$, the sample standard deviation. Are you asking what the standard deviation of $\sigma$ is? In a typical frequentist perspective $\sigma$ is a fixed value. Therefore the variance and standard deviation are both 0. Can you clarify your question? $\endgroup$– David L ThiessenCommented Mar 8, 2022 at 2:54
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