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Three sigma rule

6 messages · Salil Sharma, David Winsemius, PIKAL Petr +2 more

David Winsemius
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On May 28, 2011, at 2:12 PM, Salil Sharma wrote:

            

      
      
      
    

        
Can you describe this rule? I get the idea that it might be "private  
language" adopted by the SigxSigma sect.

            

      
      
      
    

        
The quantile function is pretty much "standard operating procedure".

fivenum will return the values that would appear in a box-and-whiskers  
plot.

  
    

      
      
    

  


  


      

    

    
2 days later

    

      
      

        


  

        

      PIKAL Petr
    

    

      
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Hi

r-help-bounces at r-project.org napsal dne 28.05.2011 20:12:33:

            

      
      
      
    

        
in

            

      
      
      
    

        
rule?

            

      
      
      
    

        
percentile

            

      
      
      
    

        
Not sure what you exactly want but you could look at function quantile.

Or you could compute confidence interval for mean by e.g.

            

      
      
      
    

        
function (x, p = 0.95) 
{
    x.na <- na.omit(x)
    mu <- mean(x.na)
    odch <- sd(x.na)
    l <- length(x.na)
    alfa <- (1 - p)/2
    mu.d <- mu - qt(1 - alfa, l - 1) * odch/sqrt(l)
    mu.h <- mu + qt(1 - alfa, l - 1) * odch/sqrt(l)
    return(data.frame(mu.d, mu, mu.h))
}

Regards
Petr

            

      
      
      
    

        

      
      
    

        
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      Bert Gunter
    

    

      
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Folks:

        
On Tue, May 31, 2011 at 8:48 AM, Petr PIKAL <petr.pikal at precheza.cz> wrote:

            

      
      
      
    

        
-- Nor am I, but ...

            

      
      
      
    

        
I'm pretty sure that this is NOT what he wants.

-- Bert

            

      
      
      
    

        

      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Thomas Levine
    

    

      
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I think you really want a normality test. If that's what you want, you
have more options than the three-sigma rule.

http://en.wikipedia.org/wiki/Normality_test

Tom

        
On Tue, May 31, 2011 at 12:31 PM, Bert Gunter <gunter.berton at gene.com> wrote:

            

      
      
      
    

        

      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      David Winsemius
    

    

      
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On May 28, 2011, at 5:12 PM, David Winsemius wrote:

        

            

      
      
      
    

        
Given the mention of the SixSigma package I can perhaps be forgiven  
for jumping to the conclusion that it might be "private language" and  
I still cannot be sure that a corruption of standard statistical  
theory has not been adopted by the SSers.

Looking at Wikipedia I get a different "answer" to the question what  
is the "three sigma rule" than I do by looking at "The American  
Statistician". My hierarchy for probity assigns a higher level of  
confidence to TAS.

	The Three Sigma Rule
Author(s): Friedrich Pukelsheim
Source: The American Statistician, Vol. 48, No. 2 (May, 1994), pp. 88-91
Published by: American Statistical Association
Stable URL: http://www.jstor.org/stable/2684253 .

For a distribution whose density is unimodal (and notice _not_  
assuming symmetry):

Pr( abs( X-mean(X) ) > 3*sd(X) ) < 4/18 < 0.05

It seemed trivial to test this with a normal distribution, so I  
illustrate it with a skewed distribution:

 > X <- rexp(300)
 > sum( abs( X-mean(X) ) > 3*sd(X) )/300
[1] 0.02

            

      
      
      
    

        
Would those percentiles be:

 > 50 -c(68, 95, 99.7)/2
[1] 16.00  2.50  0.15
 > 50 + c(68, 95, 99.7)/2
[1] 84.00 97.50 99.85