[blog post] A sigma here, a sigma there…

11 05 2012

Whenever we come across a new result one of the first things we ask is “How many sigma is it?!” It’s a strange question, and one that deserves a good answer. What is a sigma? How do sigmas get (mis)used? How many sigmas is enough?

The name “sigma” refers to the symbol for the standard deviation, σ. When someone says “It’s a one sigma result!” what they really mean is “If you drew a graph and measured a curve that was one standard deviation away from the underling model then this result would sit on that curve.” Or to use a simple analogy, the height distribution for male adults in the USA is 178cm with a standard deviation of 8cm. If a man measured 170cm tall he would be a one sigma deviation from the norm and we could say that he’s a one sigma effect. As you can probably guess, saying something is a one sigma effect is not very impressive. We need to know a bit more about sigmas before we can say anything meaningful.

A typical distribution of simulated data with a one sigma band drawn.

A typical distribution of simulated data with a one sigma band drawn.

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