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Re: st: k-sample tests for differences in proportions


From   Joseph Coveney <jcoveney@bigplanet.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: k-sample tests for differences in proportions
Date   Thu, 06 Nov 2003 15:07:57 +0900

Richard Williams wrote:

--------------------------------------------------------------------------------

Just as a sidelight, I took Joseph's data and ran one of the "right" commands,

xi : logit  degreed i.religion

I got a chi-square of 1.86 with 4 d.f., significant at the .7615 level.

Then, I ran a totally inappropriate horribly flawed Anova,

oneway degreed religion, tabulate

and got an F of 0.46 with df = 4, 295, significant at the .7623 
level.  Fisher's exact test came up with .775.

So, anybody who happened to be using the .7616 level of significance for 
their decision-making would have badly screwed up here if they'd done it 
the wrong way.  For everyone else, the difference between the right and 
wrong approaches is virtually non-existent.

Doing the same things with the different data set generated by May's 
commands, the chi-square was 12.53 with 4 d.f. and the F was 3.19 with df = 
4, 295.  In both cases the level of significance for the test statistic was 
.0138.  Fisher's Exact test came up with .015.

Given that more than one person has probably mishandled a problem like 
this, it is nice to know that there is a good chance they reached the right 
conclusion anyway.

--------------------------------------------------------------------------------

In general, if you wish to use -anova- for binary data, I recommend first 
transforming the dependent variable (logit transformation works well) after 
-collapse-, and then performing weighted -anova- using the inverse of the 
variance as the analytical weight.  The details (formulas) can be found in the 
user's manual for -glogit-.  Actually, -glogit- and -gprobit- produce an ANOVA 
table for you, so it will be much more convenient just to use either of these 
commands for the ANOVA, unless you prefer a different transformation.

Joseph Coveney




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