Physics Buzz

> 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

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

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.

Wondering what this is about? These are the long awaited satellite communication logs from flight MH370 with Inmarsat. Basically, the raw data that indicated the likely crash in the Indian Ocean off Australia, and thus gave an area to search. CNN has some info @ http://www.cnn.com/2014/05/27/world/asia/malaysia-missing-plane/index.html

There have been all sorts of theories about the math and data. So we finally have the data and others can peak into it. Although, I suspect we are going to see some crazy new theories now. Here are just some of the links I found while researching the topic and what to do with this raw data:

http://www.duncansteel.com/

http://www.reddit.com/r/MH370/comments/218i36/how_the_satellite_company_inmarsat_tracked_down/

http://physicsbuzz.physicscentral.com/2014/03/how-did-inmarsat-really-find-flight.html

http://aviation.stackexchange.com/questions/2623/how-did-the-aaib-assist-in-locating-mh370

Despite the article's somewhat confusing presentation, compressed sensing isn't primarily about photos. It's a principle that can be used to reconstruct any sort of signal from a small number of measurements. The only requirement is that we can find a representation for that signal that is sparse (every signal maps to some vector of mostly 0s). Luckily, most natural signals have this property (whereas random noise is not sparse in any representation).

The fundamental breakthrough here is that we can acquire signals (photos, recordings, MRI volumetric images, etc...) using a much smaller number of samples than previously thought possible. A useful application: let radiologists accurately image the body in less time. A weird application: Single-pixel cameras (http://physicsbuzz.physicscentral.com/2006/10/single-pixel-camera.html)

With all respect I do not agree with your example for the lhc .
For two reasons primarily:
The first has already been mentioned about various groups and experiments / detectors.
The second, I think is more important. In order to claim discoveries at any of those experiments certain statistical constraints must be met. The 5 sigma rule is by its very nature garnered by repetition and is a necessary because of the nature of quantum mechanics and particle physics. Here is a write up on cern and 5 sigma
http://physicsbuzz.physicscentral.com/2012/07/does-5-sigma-discovery.html?m=1

The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist.

On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive.

Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112.html