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