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apoorvk
\(\Huge\sigma\) \(\large \text{What is a 'sigma' proof?}\) Three days back, in arguably this millenium's biggest announcement yet from the world of Physics, CERN scientists briefed us about the discovery of a new Boson like particle, stating that they had about a "4.5 sigma proof" of it's discovery. Also, they mentioned that a minimum of 5 sigmas is required for the doubtless confirmation of any fact or theory. What is this ''sigma proof", and what does it signify in layman terms?
Is it only about statistics and analysis of the numbers? I was trying to read up about it in the web, but it became too confusing and complicated for me. (Also, does this 'sigma' thingy, by any cat in hell's chance have any relation with the Six Sigma system that is widely used in QM?)
nice heading haha...im curious about this too...
Perhaps @myininaya would know this.
Or His Majesty, @KingGeorge might be able to help his poor subject on this!
http://en.wikipedia.org/wiki/Statistical_significance#In_terms_of_.CF.83_.28sigma.29
that is a good idea i will post plzz wait
http://asq.org/learn-about-quality/six-sigma/overview/overview.html
@eliassaab - Sir thank you for that link, but I that really need to understand it in layman terms,the wikipedia explanation looks greek to me :S
@Yahoo! - thanks but that link "Six Sigma" which I believe is not related to 'sigma-proofs'. Six sigma is a Quality Management System (QMS) protocol actually.
nice article.. i would like to add one thing .. usually many of the physical phenomenon follow normal distribution which is of bell shape and usually 3 sigma covers overs 99.99 confidence over that phenomenon.. then 5 sigma is like nearly 100% that the particle exist..
So does this have something to with a bell-curve? I am starting to get the picture..
http://www.youtube.com/watch?v=ThP51oPttS0&feature=plcp Sigma is essentially a way of measuring how likely it is that an experiment's results are not chance or erroneous. It increases very very quickly from one sigma level to another. The video explains it completely. :)
@raja99 going by this link (provided by @Limitless ) 3 sigmas would be similar getting a head 8 times in a row, that is one out of 256 possibilities, that is roughly a 255/256, that is roughly 99.6% of error eliminated. Am I right?
Yes, @apoorvk. That's correct. It seems that their video is slightly different and works out to 99.7%.
yeah, approximation probably.. Hmm, so is the relation between that "no. of coins" thingy, and the no. of sigmas kinda linear?
I don't know how to describe the relationship between sigmas. It seems like it's not linear.
Hmm, so it seems too. Anyways, thanks a zillion-trillion, that was a lot of help, now I can 'feel' 'em holy-sigmas. :P
Awesome! Glad to help. :)
Sigma represents standard deviations. In statistics, we look at how confident we can be of a given result, and we represent that data in terms of standard deviations. It can be translated into a percentage certainty that the result is correct. Basically, it is saying that, if the result was incorrect, it would be an outlier, and it is quantifying just how much of an outlier the result would be.
Hmm, okay, so lesser the deviation from the mean result, the more the no. of sigmas right?
Nope, other way around. A sigma represents one standard deviation. So, if it's one sigma, it's one standard deviation. This can be confusing, because you have to be clear what you're talking about. With the CERN result, they're talking about confidence. They're saying that they're confident to a 5 sigma level of certainty that the result is not just background noise. What that means is that if it was background noise, it would be an outlier on the level of 5 standard deviations from the mean. About 68.27% of the values lie within 1 standard deviation of the mean. Similarly, about 95.45% of the values lie within 2 standard deviations of the mean. Nearly all (99.73%) of the values lie within 3 standard deviations of the mean. So, if you have a 3 sigma level of confidence that a result is signal rather than noise, you're saying that basically the odds of the result being background noise are .27%. 5 sigma, of course, is much stronger than this. The result CERN provided claimed 4.9 sigma, which corresponds to 99.999904%. So this is kind of like saying that the odds of the result being inaccurate are .000096%. That's not exactly what it means, but it is an okay way to think about it.
Oh... okay... Hmm.. EUREKA! Great, thanks a billion @nbouscal that seriously helped me to visualize, the picture is even more clear now!! (: Sadly this medal-system.. :\ Please make do with these stars for now -_- \(\Huge \color{gold}{⋆⋆⋆}\) Thanks again! :) :P