>> * "In statistics, σ refers to an area under the normal distribution defined in terms of standard deviations* that's the default definition in a statistical context
> No, you're quite wrong about that.
It is the default, actually. There are plenty of exceptions to the default, but it certainly is common in the context of experimental physics, the present context.
Quote: "But what does a 5-sigma result mean, and why do particle physicists use this as a benchmark for discoveries?
To answer these questions, we'll have to look at one of the statistician's oldest friends and C-student's worst enemies: the normal distribution or bell curve."
> ... your comments seem to be missing, is that there is no distributional assumption being made ...
Do read some experimental physics -- see what assumptions are made. Here is how a physicist maps a sigma value to a p-value:
> Do read some experimental physics -- see what assumptions are made.
lutusp, the way in which you are using the word "assumption" carries a very high risk that people will misunderstand you. The critical point here is that the physicists are nowhere using the Normal distribution as a modeling assumption. They are not suggesting that the Normal distribution is a reasonable model for any real data generating process in their problem domain. They are simply using it as a scale, like Celsius of Fahrenheit. There's a crucial philosophical distinction there that, even if you get, your readers will not.
> No, you're quite wrong about that.
It is the default, actually. There are plenty of exceptions to the default, but it certainly is common in the context of experimental physics, the present context.
http://physicsbuzz.physicscentral.com/2012/07/does-5-sigma-d...
Quote: "But what does a 5-sigma result mean, and why do particle physicists use this as a benchmark for discoveries?
To answer these questions, we'll have to look at one of the statistician's oldest friends and C-student's worst enemies: the normal distribution or bell curve."
> ... your comments seem to be missing, is that there is no distributional assumption being made ...
Do read some experimental physics -- see what assumptions are made. Here is how a physicist maps a sigma value to a p-value:
http://i.imgur.com/pcjr6cN.gif
If this wasn't a discussion of the analysis of the outcome of a physics experiment, I would be more likely to accept these digressions.