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st: RE: What does contribution to chi-square mean in tabchii


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: What does contribution to chi-square mean in tabchii
Date   Sat, 29 Nov 2003 11:35:31 -0000

-tabchii- is a user-written command. A version 
which will work in Stata 6 through 8 is 
available from the -tab_chi- package on SSC 
and an earlier version which will work in 
Stata 5 is available from 
http://www.stata.com/users/njc/tab_chi/

I am not sure what kind of answer Don 
wants here. The definition of contribution 
given in the help file is 

(observed frequency - expected frequency)^2 
	/ expected frequency 

and Don clearly understands that. The 
programmer's intent in allowing 
such contributions to be shown was that 
some users like to see that step, perhaps 
even as a check on hand calculations. 
Personally I much prefer to look at 
the (signed) square root of that 

(observed freq - expected freq) 
	/ sqrt(expected frequency) 

given the usual argument that the direction of 
deviation from expectation is often helpful 
in interpretation. These quantities are called Pearson 
residuals in -tabchii- and indeed 
elsewhere. And in turn a refinement 
on that, the adjusted residual, 
has a distribution in the null case
that is closer to Gaussian(0,1). 

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

Donald Spady
 
> Can you please tell me how to interpret the chi-square 
> 'contribution' to
> chi-sqare as used in tabchii.  I find it useful in telling 
> me where the
> total chi-square is coming from but is there more that one 
> can get out of
> it? i.e. say the chi-square (total) is 100 and the 
> contribution of one cell
> is 55, another is 35, another 5 and another 5.  Obviously 
> the first cell's
> chi square counts a lot but can I say anything else, say in 
> regard to cell
> 2's chi-square of 35.  Or is it just an interesting way of 
> getting an
> insight into the data.

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