Just a reminder that transformations can be used on proportions as a dv to reduce
the skew, important if some values approach 0 or 1. These include arcsine,
probit, and logit. Each needs special treatment when p=0 or p=1. Cohen and Cohen
(2nd ed. of Applied MR/C) has a section on transformations for proportions (pp.
265-270).
Cheers, Dale Berger
William B. Ware wrote:
> 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
> >
> >
> >
