Three sigma rule

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

Dear Sir,



I have data, coming from tests, consisting of 300 values. Is there  
a way in
R with which I can confirm this data to 68-95-99.8 rule or three- 
sigma rule?

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

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

I need to look around percentile ranks and prediction intervals for  
this
data. I, however, used SixSigma package and used ss.ci() function,  
which
produced 95% confidence intervals. I still am not certain about  
percentile
ranks conforming to 68-95-99.7 rule for this data.

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

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

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


-- 
David Winsemius, MD
West Hartford, CT

David Winsemius, MD
West Hartford, CT