Re: Re: running ANOVA on binary data?
Isaac Dialsingh
from statisticians.
Yet all are correct to some extent.
Isaac
'Pray like if everything depended on God and then work like everything
depended on you'
----- Original Message -----
From: "Harley.Baker" <Harley...@csuci.edu>
Newsgroups: bit.listserv.spssx-l
To: <SPS...@LISTSERV.UGA.EDU>
Sent: Tuesday, August 22, 2006 9:52 PM
Subject: Re: running ANOVA on binary data?
> Robinson,
>
> In general, the difficulty is that ANOVA is not uniformly justified in
such
> situations. This is because dichotomous data have a greater probability of
> violating seriously the ANOVA assumptions than do strictly numeric data.
>
> While the comments from Kevin and Michael about the inadvisability of
ANOVA
> with dichotomous variables are correct, the real issue may not be whether
> the assumptions are violated, but rather the degree to which they are
> violated. In general, the major assumptions of an ANOVA model can be
tested
> to the degree to which they are violated in any particular data set. If
the
> violations are relatively minor, the use of ANOVA may be warranted. I
would
> argue that in such a case, the use of ANOVA is justified statistically
> because the data fit the model. If the use of ANOVA then can be justified
> from an empirical viewpoint (e.g., makes sense in the context of the
> particular research and intended use of the outcomes) I would say to use
> ANOVA.
>
> Harley
>
>
> Dr. Harley Baker
> Associate Professor and Chair, Psychology Program
> Chief Assessment Officer for Academic Affairs
> California State University Channel Islands
> One University Drive
> Camarillo, CA 93012
>
> 805.437.8997 (p)
> 805.437.8951 (f)
>
> harley...@csuci.edu
>
>
>
> > From: Patricia Rego <p.r...@uq.edu.au>
> > Reply-To: Patricia Rego <p.r...@uq.edu.au>
> > Newsgroups: bit.listserv.spssx-l
> > Date: Wed, 23 Aug 2006 11:12:14 +1000
> > To: <SPS...@LISTSERV.UGA.EDU>
> > Conversation: running ANOVA on binary data?
> > Subject: Re: running ANOVA on binary data?
> >
> > And your response, Kevin, is in a much more appropriate tone and more
> > helpful than the previous response to Robinson's query.
> > Patricia
> >
> >
> > -----Original Message-----
> > From: SPSSX(r) Discussion [mailto:SPS...@LISTSERV.UGA.EDU] On Behalf Of
> > Kevin Bladon
> > Sent: Wednesday, 23 August 2006 1:01 AM
> > To: SPS...@LISTSERV.UGA.EDU
> > Subject: Re: running ANOVA on binary data?
> >
> > Robinson,
> >
> > I agree, using ANOVA for a dichotomous response variable violates the
> > assumptions of homogeneity of variances and normally distributed
> > errors. You should definitely look into using logistic regression for
> > this type of analysis.
> >
> > Regards,
> > Kevin Bladon, Ph.D., A.Ag.
> > Resource Analyst
> > Silvacom Ltd.
> > 3825 - 93 Street
> > Edmonton, AB
> > T6E 5K5
> > Phone: 780.462.3238
> > Fax: 780.462.4726
> > E-mail: kevin....@silvacom.com
> > www.silvacom.com
> >
> > "Make every obstacle an opportunity."
> > - Lance Armstrong
> > Cancer survivor and 7 time Tour de
> > France champion (1999-2005)
> >
> >
> > On Aug 21, 2006 12:06, Michael Kruger wrote:
> >
> >> If you are talking about running an ANOVA on a response or dependent
> >> variable that is binary, you really need to take a statistics course.
> >> ANOVA assumes a normally distributed , interval level variable. A
> >> binary
> >> variale is neither of these things!
> >>
> >>>
> >>>
> >>>
> >>>
> >>
> >>
> >> --
> >> Michael Kruger
> >> "A True Prince"
> >> Statistical Analyst
> >> C.S. Mott Center
> >> Dept. of OB/GYN
> >> Wayne State University School of Medicine
> >> (313)-577-1794
> >
> > Hello,
> >
> > I would like to ask if you are aware of any problems (violated
> > assumptions) if you run an ANOVA on binary data (e.g. 0 / 1 coded for
> > answer "no" "yes" or "patient not infected" "patient infected"). How
> > severe are those violations? Would you consider running an ANOVA in this
> > case "common practice" or not recommendable? Does anybody happen to know
> > where this aspect is discussed in literature?
> >
> > Thanks a lot. I really appreciate your help.
> >
> > Sincerely,
> > Robinson Aschoff
> >
> > I hope this hasn`t been asked before a alot. I didn`t found it in the
> > archive though.
> > ----------------------------------------------------------------
> > Felix-Robinson Aschoff
> > Information Management Research Group
> > Department of Informatics
> > University of Zurich
> > Binzmuehlestrasse 14
> > CH-8050 Zurich, Switzerland
> >
> > E-Mail: asc...@ifi.unizh.ch
> > Phone: +41 (0)44 635 6690
> > Fax: +41 (0)44 635 6809
> > Room: 2.D.11
> > http://www.ifi.unizh.ch/im
John Reynolds
interesting. It can arise when there is interest in partitioning the
variation in a binomial random variable into components of variation.
ANOVA decompositions of binary random variables have been much studied
in population genetics (see papers by Cockerham 1971, 1973 and the text
book Genetic Data Analysis II by Bruce Weir for discussions of the
variance of gene frequencies, variance of inbreeding, variance of
heterozygosity, etc). Small and large sample tests and confidence
intervals for these variance components of binary variables have, I
suspect, not been well studied but bootstrapping is probably one
reasonable approach when we're confronted with some data of this type
(binary and hierarchical).
The other approach is via link functions and logistic regression via a
generalised linear model (GLM in the sense of Nelder and McCullagh)
allows us to carry out the analogue of a fixed effects ANOVA on binary
data. A relatively new development by Nelder and colleagues
(Hierarchical Generalised Linear Models or HGLMs) apparently enables us
to carry out the analogue of a mixed model ANOVA (fixed, random,
crossed and nested factors) on binary data. I believe implementation
of this approach might be available in the latest version of GENSTAT.
Other approaches (late 80's and early 90's) include the Generalised
Linear Mixed Models (GLMMs) of Schall (1991) and Breslow and Clayton
(1993) and these have also been implemented in GENSTAT (using its
average information REML algorithm as the "engine").
So the short answer is "Yes, we can run ANOVA on binary data, but the
required tools are either an ordinary ANOVA algorithm supplemented by
the bootstrap, or HGLMs or GLMMs".
Ted Harding
> [good stuff, not duplicated here]
Before we get carried away by this topic (unless of
course we ourselves find it interesting in its own
right amongst ourselves), let me point out somthing.
When I received and read Isaac Dialsingh's message
this morning, I was initially puzzled that I had not
received the earlier messages which Isaac quotes.
Then I looked closely, and found that the entire
thread had originally been posted to the SPSS-L list,
and not to us. The first we heard of it in MedStats
was from Isaac.
Therefore anything we say about it will not go to the
original poster (Robinson Aschoff, asc...@ifi.unizh.ch )
unless we explicitly copy our replies to him -- which
he may not want to see!
However, Isaac does raise on his own account a debatable
point, namely "It is simply amazing at the different
answers we get for a simple question from statisticians.
Yet all are correct to some extent."
Ah well, now it's up to us!
Best wishes to all,
Ted.
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Date: 23-Aug-06 Time: 10:54:51
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