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* "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 cont

* "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. greycat is correct in his/her corrections of what you're saying. In statistics sigma is used to represent one of two things: - a parameter of a probability distribution, typically one which influences the spread of the distribution - a measure of dispersion in an actual data set, which may be an estimator of a parameter in a probability distribution Neither of those things necessarily involve the Gaussian density. In physics it seems that "sigma values" are used as a scale to measure p-values, so that instead of saying 0.0000003, they can just say 5σ. But the critical point here, which your comments seem to be missing, is that there is no distributional assumption being made; there is no implication that the Normal distribution describes any data-generating process, merely that the probability of an equal or more extreme value of a test statistic under some model, is the same as the probability of observing a value more than 5 standard deviations from the mean under a Gaussian model.

lutusp 13y ago
>> * "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. http://physicsbuzz.physicscentral.com/2012/07/does-5-sigma-discovery.html 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 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.
- Myrmornis 13y ago
  > 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.

lutusp 13y ago

>> * "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. http://physicsbuzz.physicscentral.com/2012/07/does-5-sigma-discovery.html 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 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.

Myrmornis 13y ago
> 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.