For what it's worth, sigma is chosen for this purpose specifically to evoke the notion of "standard deviations". But quoting the std dev. directly is useless, since the distribution is unspecified. So we "convert" the statistical significance to the corresponding number of standard deviations of the Normal distribution, since that is a familiar distribution. If you like, it's another way of stating p-values, which physicists prefer because ours can have lots of zeros :)
cshimmin|3 years ago