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No, I think you're wrong. See my comment above. Note that nowhere in the article you link does it say there's an assumption of normality. Doubtless the journali

No, I think you're wrong. See my comment above. Note that nowhere in the article you link does it say there's an assumption of normality. Doubtless the journalist or whoever chose the picture of th normal distribution was a bit confused also. Edit: oh, no, actually I think you're right :). I thought it was referring to the location of the test statistic in its null distribution. But it seems it's a scale for measuring p-values. This explains it clearly: What does "five sigma" mean? It means that the results would occur by chance alone as rarely as a value sampled from a Gaussian distribution would be five standard deviations from the mean. http://www.graphpad.com/www/data-analysis-resource-center/blog/statistical-significance-defined-using-the-five-sigma-standard/ http://www.graphpad.com/www/data-analysis-resource-center/bl...

lutusp 13y ago
All that aside, remember that the context is a nontechnical person asking what 5σ means in statistical analysis in physics. That greatly narrows the possible interpretations. By the way, this same conversation took place after the LHC Higgs anouncement -- the same five-sigma standard for discovery, and the same detailed discussion of what that means. > But it seems it's a scale for measuring p-values. Yes, and that was a point I made in my reply to the OP -- that the context assumed an association with p-values, which in turn assume a normal distribution.
- Myrmornis 13y ago
  Sorry, I'm either not understanding or I still am not convinced you are correct. p-values don't assume a normal distribution. A p-value is the probability of generating an equal or more extreme value of your test statistic under the null hypothesis. Normal distributions are nowhere in sight. The only way that the Normal distribution comes into play is that physicists are measuring the smallness of their p-values by stating a number of standard deviations from the Normal mean that would have the same p-value. I'm finding this discussion helpful by the way. I have worked in applied statistics but not in any fields which use this "sigma" scale or would talk about "sigma values".
  - lutusp 13y ago
    > p-values don't assume a normal distribution. No, not unless a p-value is expressed in terms of sigma as in this case and similar ones. In this case, and commonly in experimental physics, there's a relationship between n-sigma (usually 3σ or 5σ in different circumstances) and how a p-value is acquired from a sigma expression. The p-value is acquired from a sigma value like this: http://i.imgur.com/pcjr6cN.gif http://i.imgur.com/pcjr6cN.gif My point? In experimental physics there's a connection between (a) an expression including an integer and "sigma", (b) a resulting, widely quoted numerical value, and (c) the method for converting one to the other, using a Gaussian distribution as shown. 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." Couldn't have said it better myself. > The only way that the Normal distribution comes into play is that physicists are measuring the smallness of their p-values by stating a number of standard deviations from the Normal mean that would have the same p-value. Hmm. Yes, that's right. That's why I replied as I did in my original post.

lutusp 13y ago

All that aside, remember that the context is a nontechnical person asking what 5σ means in statistical analysis in physics. That greatly narrows the possible interpretations. By the way, this same conversation took place after the LHC Higgs anouncement -- the same five-sigma standard for discovery, and the same detailed discussion of what that means. > But it seems it's a scale for measuring p-values. Yes, and that was a point I made in my reply to the OP -- that the context assumed an association with p-values, which in turn assume a normal distribution.

Myrmornis 13y ago
Sorry, I'm either not understanding or I still am not convinced you are correct. p-values don't assume a normal distribution. A p-value is the probability of generating an equal or more extreme value of your test statistic under the null hypothesis. Normal distributions are nowhere in sight. The only way that the Normal distribution comes into play is that physicists are measuring the smallness of their p-values by stating a number of standard deviations from the Normal mean that would have the same p-value. I'm finding this discussion helpful by the way. I have worked in applied statistics but not in any fields which use this "sigma" scale or would talk about "sigma values".
- lutusp 13y ago
  > p-values don't assume a normal distribution. No, not unless a p-value is expressed in terms of sigma as in this case and similar ones. In this case, and commonly in experimental physics, there's a relationship between n-sigma (usually 3σ or 5σ in different circumstances) and how a p-value is acquired from a sigma expression. The p-value is acquired from a sigma value like this: http://i.imgur.com/pcjr6cN.gif http://i.imgur.com/pcjr6cN.gif My point? In experimental physics there's a connection between (a) an expression including an integer and "sigma", (b) a resulting, widely quoted numerical value, and (c) the method for converting one to the other, using a Gaussian distribution as shown. 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." Couldn't have said it better myself. > The only way that the Normal distribution comes into play is that physicists are measuring the smallness of their p-values by stating a number of standard deviations from the Normal mean that would have the same p-value. Hmm. Yes, that's right. That's why I replied as I did in my original post.