Richard Williams wrote:
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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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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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