5 ms·
What is a sigma?
by neals 5y ago
What is a sigma?
- jstx1 5y ago1 sigma = 1 standard deviation
- throw0101a 5y agoA unit used in statistics: > 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/Standard_deviation https://en.wikipedia.org/wiki/Standard_deviation
- tempay 5y agoThis page is likely more approachable: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule#Table_of_numerical_values https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rul...
- sundarurfriend 5y agoI thought you were going to link to https://simple.wikipedia.org/wiki/Standard_deviation https://simple.wikipedia.org/wiki/Standard_deviation The "Simple English Wikipedia" is a really underrated resource for understanding jargon outside your field.
- cshimmin 5y agoI work in this field (different experiment); despite the downvotes this is a reasonable question. Reposting my comment from above, since there is confusion here (the other sibling comments are incorrect). 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.
- jxm262 5y agooh wow, thanks for pointing this out :)
- cshimmin 5y agoFor 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 :)
- yccs27 5y agoThis is the correct answer. 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.
- sgregnt 5y agoI would add: If the null hypothesis is true, then "the result like this... (in this case the null hypothesis is of cause that the standard model is true)
- mike_ivanov 5y agoIf the null hypothesis were true, and the experiment were repeated infinite number of times with a different sample each time then "the result like this or more extreme ...
- Filligree 5y agoWhat's that in Bayesian terms?
- 5y ago
- EVa5I7bHFq9mnYK 5y agoIt's just a way to say something has probability of 0.0000000002% while looking smart.
- WanderPanda 5y agoIt actually is smart to compress this on an exponential scale instead of writing a large number like this :p
- omginternets 5y agoA standard deviation.
- RosanaAnaDana 5y agoA measurement of uncertainty.