[R] Cramer-von Mises normality test

Raymond Wan rwan at kuicr.kyoto-u.ac.jp
Wed Jun 14 11:28:33 CEST 2006

Hi Robert,

On Tue, 13 Jun 2006, Robert Powell wrote:
> I've been running some normality tests using the nortest package. For
> some of my datasets the Cramer-von Mises normality test generates an
> extremely high probability (e.g., 1.637e+31) and indicates normality
> when the other tests do not. Is there something I'm misunderstanding
> or potentially a bug in the code?
> Below are the results of the tests and then, below that, I've
> provided that column of the datafile.

 	Well, I can't answer all of your questions, but I did try your 
sample and at least your installation does the same thing as mine.  That 
is, for your sample data, I got the same results.

 	Each test is slightly different and looks for different 
characteristics.  So, it is not unusual for one test to indicate 
normality, but another one doesn't.  Granted, the difference in p-value is 
quite large...

 	I plotted the histogram of your data and to me, it doesn't "look" 
very normal...not very scientific, I know...

 	If you can locate it, I suggest finding the book "Testing for 
Normality" which the Nortest package cites.  It is quite good and might 
explain something to you...unfortunately, neither it nor any source I've 
found gives a simple table that says:  Use test X if you want to see if 
the Y property of the distribution is normal.  (Various tests seems to 
place different emphasis on different things...)


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