----- Original Message -----
From: Donald F. Burrill <[EMAIL PROTECTED]>
To: Wouter Duyck <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Tuesday, December 14, 1999 9:03 AM
Subject: Re: ANOVA with proportions
> On Tue, 14 Dec 1999, Wouter Duyck wrote:
>
> > I have a question. I have n subjects. For each subject, I have a
> > proportion. I want to test if there are some differences in that
> > proportion, depending on some independent variables (e.g. sex) on which
> > the subjects differ.
> >
> > Can I use those proportions as a dependent variable in an ANOVA?
>
> Why not? Proportions are means, after all. Might even be more
> interesting analyses to be pursued, if the proportions represent (or,
> perhaps, conceal?) some repeated measures on the subjects.
My first thought was that this seemed like a rather cavalier misuse of
ANOVA, given that the population distributions are rather far from normal,
and that Bernoulli distributions have a relation between mu and sigma that
ANOVA fails to exploit. However, out of curiosity, I ran the following
simulation twenty times:
MTB > random 10 c11;
SUBC> bernoulli 0.4.
MTB > random 10 c10;
SUBC> bernoulli 0.5.
MTB > random 10 c12;
SUBC> bernoulli 0.6.
MTB > stack c10-c12 c13;
SUBC> subs c14.
MTB > oneway c13 c14
MTB > table c13 c14;
SUBC> chisquare.
and a similar one in which the null hypothesis was true 80 times, and
discovered that the p-values obtained are actually rather close! The main
peculiarity of the distribution of the ANOVA p (if Ho is true) is that it is
very granular at the high end: the value 1.000 appeared several times, as
did several other values. The chisquare test seemed to have slightly more
power, but not by as much as I'd expected.
I still think that chi-square is probably a better choice,and logistic
regression more flexible - but I was surprised how well the screwdriver
drove the nail...
-Robert Dawson
