Re: Categorical Data Question

On Wed, 30 Aug 2006 17:19:10 GMT, "hanya" <hanya@xxxxxxx> wrote:

Hi, I have a problem here that appears to involve Goodness-of-Fit, but my
textbook does not spell out exactly how to solve this case.

I have data from an experiment for a random variable X, where

X Frequency
0 X0
1 X1
2 X2
...


I have a choice of modelling X as a Poisson or Normal distribution.

A couple of the most important pieces of information are
"How are the numbers generated?" and, alternately,
"What are they being used for?"

Another question is, "Does it really matter?"
If the Poisson mean is very large, that Poisson approaches Normal.
If the counts are very small, you won't have much power for
comparing them, in any fashion.



I'm guessing one should test goodness-of-fit as a Poisson, then choose
normal if it rejects.

Since most procedures expect "normal", and there are a
variety of tests for normality, why not test for "normal"?


If I want to test the Poisson distribution, which
estimate of lambda should I use? Should I use the sample mean, or find the
MLE to use variance data as well?

Then how should I test goodness of fit? Should I use chi-square or
G-square?

I think you are suggesting "Pearson" versus "Likelihood" tests
on the contingency table. They are not usually the best choice.

Hope this helps.


--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.