#### Is 3sigma the same as 3*1sigma?

Sometime early this year, Jeremy Drake asked this innocuous sounding question in the context of determining the bounds on the amplitude of an absorption line: Is the 3sigma error bar the same length as 3 times the 1sigma error bar?

In other words, if he measured the 99.7% confidence range for his model parameter, would it always be thrice as large as the nominal *1sigma* confidence range? The answer is complicated, and depends on who you ask: Frequentists will say “yes, of course!”, Likelihoodists will say “Maybe, yeah, er, depends”, and Bayesians will say “*sigma*? what’s that?” So I think it would be useful to expound a bit more on this to astronomers, whose mental processes are generally Bayesian but whose computational tools are mostly Frequentist.

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