Thanks to Rolph Turner and Jason Turner ...
I guess I was too excited about getting back on the list after an absense of
several years ... I'll be a little more thoughtful about the problem before
posting next time, and a little less trigger-happy with the "Send"
e-mail
button.
Never-the-less, much appreciated.
- Mohamed
-----Original Message-----
From: Rolf Turner [mailto:rolf@math.unb.ca]
Sent: Saturday, November 15, 2003 9:55 AM
To: Mohamed.Abdolell@cancercare.on.ca
Subject: Re: [R] computing a p-value ...
You do not need to simulate data; the available information is
all that you need in order to do the usual ANOVA. Most elementary
statistics texts will tell you how.
The ``standard 1-way ANOVA'' assumes that the population standard
deviations are equal for the various levels. You thus form
SSE by ``pooling'':
SSE = (nA-1)*stdA^2 + ... + (nE-1)*stdE^2
You form the sum of squares for the factor as
SSF = nA*(mA-mBar)^2 + ... + nE*(mE-mBar)^2
where ``mBar'' is the `grand mean'':
mBar = (nA*mA + ... + nE*mE)/n where in turn n = nA + ... + nE
Then form
MSF = SSF/4 and MSE = SSE/(n - 5)
(4 because 4 = 5-1 and the factor has 5 levels).
Finally form Fstat = MSF/MSE. Under the null hypothesis of ``no
factor effect'' the statistic Fstat has an F distribution with 4
numerator and n-5 denominator degrees of freedom.
The p-value would be given in R by
pval <- 1 - pf(Fstat,4,n-5)
Warning: ANOVA is pretty robust to the assumption of a common population
standard deviation UNLESS the design is highly unbalanced, with large
standard deviations corresponding to small sample sizes. So if, for
example, stDC is particularly large and nC is particularly small, then
the Fstat and its p-value are likely to be misleading. In such a case
you should talk face-to-face with a knowledgable statistician about
how to proceed.
cheers,
Rolf Turner
rolf@math.unb.ca
-----Original Message-----
From: Jason Turner [mailto:jasont@indigoindustrial.co.nz]
This should get you started. These methods can be found in most
introductory statistics textbooks.
http://www.itl.nist.gov/div898/handbook/prc/section4/prc47.htm
Cheers
Jason
--
Indigo Industrial Controls Ltd.
http://www.indigoindustrial.co.nz
64-21-343-545
jasont@indigoindustrial.co.nz
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