# What is the definition of this statistic?

For a data set that is Gaussian distributed, $$\sigma$$ defines the standard-deviation of the distribution. My question is, what is the correct indention or terminology for the following: $$\frac{\sigma}{\sqrt{2N-2}} \text{.}$$

My interpretation is that it is the "error" in the standard deviation, $$\sigma$$. Is this a correct way to view this?

• To help you clarify your question, note that this is not quite a statistic because it's not a function of the data alone (sigma can't be computed from the data, only estimated). Second, where did this quantity arise? – RMurphy Jul 7 '19 at 17:49

It's important to distinguish between the true population value of a parameter of a statistical distribution and the estimate of that value obtained from a sample of size $$N$$. The symbol $$\sigma$$ is conventionally used to represent the population standard deviation, the square root of the population variance $$\sigma^2$$. A sample estimate of the variance is conventionally represented as $$s^2$$ and a sample estimate of the standard deviation as $$s$$.
This question shows the formula for the standard error of estimates of the variance, $$s^2$$, when sampling from a normal distribution. The answer to that question shows a way to convert such standard error estimates of $$s^2$$ to standard error estimates of $$s$$ that holds in the limit of large sample sizes for sampling from any of a large class of distributions. A bit of math shows that if you replace $$\sigma$$ in your formula with $$s$$ you have the corresponding formula for the standard error of the sample standard deviation in the case of a normal distribution.