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


From   Richard Williams <Richard.A.Williams.5@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: k-sample tests for differences in proportions
Date   Wed, 05 Nov 2003 23:01:00 -0500

At 10:37 PM 11/5/2003 +0900, Joseph Coveney wrote:
How about -glm-? See the do-file below for how. The example is artificial,
but it shows how to use -glm- followed by -test- to do exactly what you want.
If you want to adjust for multiple comparisons, Stata can do that, too. -help
test- Also, just as an aside, consider performing logistic regression
(examining odds ratios, using link(logit)) in lieu of testing differences in
proportions.

Joseph Coveney
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.

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Richard Williams, Associate Professor
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