On 23 Nov 1999 11:05:51 -0800, [EMAIL PROTECTED] (David
Cross/Psych Dept/TCU) wrote:
> Jin:
>
> Pearson's test is "conditional" only on the sample size (N) being fixed.
> This is the classic test of independence, and also the test of interaction
> in a log-linear model.
- isn't the test in the log-linear model done with a Likelihood
chisquare?
> On Fri, 19 Nov 1999, Jin Kim wrote:
>
> > Dear list members
> >
> > I am a student studying contingency table analysis these days.
> > I have a question about the underlying statistical concept of Pearson
> > chi^2 test.
> > My question is:
> >
> > Does Pearson chi^2 test assume that both row and column margins are
> > fixed?
> >
> > In other words, I wish to know whether Pearson chi^2 test is
> > 'conditional' like Fisher's exact test.
I don't usually worry about definitions like this one --
Does 'conditional' mean exactly the same as 'fixed margins'? The
original theoretical development of Pearson's assumed margins were
fixed.
See F. Yates, 1984, "Tests of significance for 2x2 contingency
tables', Journal Royal Statis. Soc., Ser A, 147:426-449. This is the
same Yates who devised Yates's correction factor in 1934. (See
references in Zar's textbook.) In JRSS, Yates chuckled at the fact
that the assumptions for all three tests were formally the same. What
I don't remember is whether they *have* to be the same, which does
not seem right.
The Pearson test with the Yates correction does a better job of
reproducing Fisher's Exact test; the Pearson test without the
correction does a better job of reproducing what you actually get by
randomization of the fractions on either or both margins -- so,
pragmatically, Pearson's behaves as if it were not on fixed margins,
even though it was created with fixed margins. (I saw at least three
ways to 'develop' the test when I took the relevant course; I don't
think that *all* the ways assumed fixed margins. But, did they?)
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
