As I recall, there was an article by Lunney et al that appeared in the
Journal of Educational Measurement that examined the use of ANOVA with "1"
and "0" as the DV. I believe that they concluded that distortion was
minimal when the distributions were within an 80/20 split... I think that
the article was in the early 70s, perhaps 1971.
As Don has noted, proportions are means... which will be symmetrically
distributed when the split is about 50/50. Apparently, the Central Limit
Theorem applies as long as sample size is sufficiently large...
Bill
__________________________________________________________________________
William B. Ware, Professor and Chair Educational Psychology,
CB# 3500 Measurement, and Evaluation
University of North Carolina PHONE (919)-962-7848
Chapel Hill, NC 27599-3500 FAX: (919)-962-1533
http://www.unc.edu/~wbware/ EMAIL: [EMAIL PROTECTED]
__________________________________________________________________________
On Tue, 14 Dec 1999, Robert Dawson wrote:
>
> ----- 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
>
>
>
