What is a sigma?
In particle physics, sigma denotes "significance", not standard deviation. Technically what we're quoting as "sigmas" are "z-values", where z=Phi^{-1}(1 - p), where Phi^{-1} is the inverse CDF of the Normal distribution and p is the p-value of the experimental result. So, 7 sigma is defined to be the level of significance (for an arbitrary distribution) corresponding to the same quantile as 7 standard deviations out in a Normal distribution.
In other words, "z sigma" means: That a result like this occurs as a statistical fluke, is just as likely as a standard-normal distributed variable giving a value above z.
(The author is a stats professor at CMU.)
Quoting: "The plot shows the first 50 simulations. In the first simulation I picked some distribution {F_1}. Let {\theta_1} be the median of {F_1}. I generated {n=100} observations from {F_1} and then constructed the interval. The confidence interval is the first vertical line. The true value is the dot. For the second simulation, I chose a different distribution {F_2}. Then I generated the data and constructed the interval. I did this many times, each time using a different distribution with a different true median. The blue interval shows the one time that the confidence interval did not trap the median. I did this 10,000 times (only 50 are shown). The interval covered the true value 94.33 % of the time. I wanted to show this plot because, when some texts show confidence interval simulations like this they use the same distribution for each trial. This is unnecessary and it gives the false impression that you need to repeat the same experiment in order to discuss coverage."
Nitpick: this is still a standard deviation in some (potentially very contrived and nonlinear) coordinate system. (As a simple example, a log-normal distribution might have a mean of 1 and a standard deviation effectively of multiplying or dividing by 2. Edit: also, multidimensional stuff might have to be shoehorned into a polar coordinate system.) But in practice you'd never bother to construct such a coordinate system, so that's more a mathematical artifact than anything useful.
Anyway, as I mentioned elsewhere, the motivation for calling it sigma is that, by construction, it maps onto the quantiles of the standard Normal distribution. So an N-sigma result will have the same p-value as N standard deviations in a Normal distribution. So you can associate "sigmas" with "standard deviations of the Normal distribution". Perhaps this is what you are trying to say, but it does not make sigma a standard deviation in any statistical sense, i.e. it is not necessarily related to the variance of the relevant distribution.
> In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.[1]
https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rul...
The "Simple English Wikipedia" is a really underrated resource for understanding jargon outside your field.