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RE: st: query on testing uniform distributions


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: query on testing uniform distributions
Date   Tue, 1 Nov 2011 14:08:37 +0000

Good point. 

However, if a uniform model were to be modified, then any more refined model would imply unequal expected frequencies and scaling would then be indicated once more. 

Also, a motivation for Pearson residuals (although I don't think Pearson ever used them) is, as you know, that they can be thought as a decomposition of a chi-square statistic; such a motivation can be useful for some readerships as explaining what was done, even if the test itself is not carried out. 

Nick 
n.j.cox@durham.ac.uk 

Maarten Buis

On Tue, Nov 1, 2011 at 9:53 AM, Nick Cox wrote:
> The expected frequencies here are easy to calculate, so I'd move to
> Pearson residuals, (observed - expected) / sqrt(expected) and also
> plot those against day of year to see what fine structure there is.
> The quantile plot is a good starting point, but needs to be followed
> up.

Just an extra detail on the extra detail: In this case, where the
model is a uniform distribution, the division by sqrt(expected) would
just rescale all residuals by the same number. I would probably look
at the raw residuals, as that way the picture would be exactly the
same, but I would find the scale of the residuals to be easier to
interpret.


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