1. If you use a random effects model, you should make Subject the
random factor. I.e., a random intercepts model with 1|Subject. Group
is a fixed effect: You have only 2 groups. Even if you had more than
2 groups, treating Group as random would return a standard deviation,
not a P-value as you wanted. Finally, I doubt you believe the groups
used are meaningless, and only the population of groups is of
interest. Instead you consider them special, so Group is a fixed effect.
2. The number of observations for each Subject is the number of
trials, which you previously indicated were 7 to 10 in the cases listed.
3. If you have no interest in the Subject effect, you can use a fixed
Subject factor instead with glm() instead of glmer() or other mixed
model function. This is a good idea so long as the number of subjects
is, say, less than 10. Otherwise a mixed model would be a better idea.
I suggest you fit all three models to learn about what you're doing:
1) glmer() or equivalent, with cbind(successes, failures) ~ 1|Subject
+ Group; 2) glm() with cbind(successes, failures) ~ Subject + Group;
and 3) lm(p ~ Subject + Group), where p is the proportion success for
a particular subject and group.
Then compare the results. They will probably all 3 give the same
conclusion to the hypothesis question about Group. I would guess the
glmer() P-value will be larger, then the glm() and finally the lm(),
but the last two may reverse. The lm() model may actually perform
fairly well, as the Edgeworth series converges rapidly to normal for
binomial distributions with p within 0.15 to 0.85 and 10+ replicates,
as I stated before.
I'd be interested in seeing the results of these 3 fits myself just
for curiosity.
At 01:21 PM 2/10/2011, array chip wrote:
Robert and Bert, thank you both very much for the response, really
appreciated. I agree that using regular ANOVA (or regular t test)
may not be wise during the normality issue. So I am debating between
generalized linear model using glm(.., family=binomial) or
generalized linear mixed effect model using glmer(...,
family=binomial). I will forward to Robert an offline list email I
sent to Bert about whether using (1|subject) versus (1|group) in
mixed model specification. If using (1|group), both models will give
me the same testing for fixed effects, which is what I am mainly
interested in. So do I really need a mixed model here?
Thanks again
John
From: Bert Gunter <gunter.ber...@gene.com>
To: Robert A LaBudde <r...@lcfltd.com>
Cc: array chip <arrayprof...@yahoo.com>
Sent: Thu, February 10, 2011 10:04:06 AM
Subject: Re: [R] comparing proportions
Robert:
Yes, exactly. In an offlist email exchange, he clarified this for me,
and I suggested exactly what you did, also with the cautions that his
initial ad hoc suggestions were unwise. His subsequent post to R-help
and the sig-mixed-models lists were the result, although he appears to
have specified the model incorrectly in his glmer function (as
(1|Group) instead of (1|subject).
Cheers,
Bert
On Thu, Feb 10, 2011 at 9:55 AM, Robert A LaBudde
<<mailto:r...@lcfltd.com>r...@lcfltd.com> wrote:
> prop.test() is applicable to a binomial experiment in each of two classes.
>
> Your experiment is binomial only at the subject level. You then have
> multiple subjects in each of your groups.
>
> You have a random factor "Subjects" that must be accounted for.
>
> The best way to analyze is a generalized linear mixed model with a binomial
> distribution family and a logit or probit link. You will probably have to
> investigate overdispersion. If you have a small number of subjects, and
> don't care about the among-subject effect, you can model them as fixed
> effects and use glm() instead.
>
> Your original question, I believe, related to doing an ANOVA assuming
> normality. In order for this to work with this kind of proportion problem,
> you generally won't get good results unless the number of replicates per
> subject is 12 or more, and the proportions involved are within
0.15 to 0.85.
> Otherwise you will have biased confidence intervals and significance tests.
>
>
>
> At 07:51 PM 2/9/2011, array chip wrote:
>>
>> Content-type: text/plain
>> Content-disposition: inline
>> Content-length: 2969
>>
>> Hi Bert,
>>
>> Thanks for your reply. If I understand correctly, prop.test() is not
>> suitable to
>> my situation. The input to prop.test() is 2 numbers for each group (# of
>> success
>> and # of trials, for example, groups 1 has 5 success out of 10 trials;
>> group 2
>> has 3 success out of 7 trials; etc. prop.test() tests whether the
>> probability of
>> success is the same across groups.
>>
>> In my case, each group has several subjects and each subject has 2 numbers
>> (#
>> success and # trials). So
>>
>> for group 1:
>> subject 1: 5 success, 10 trials
>> subject 2: 3 success, 8 trials
>> :
>> :
>>
>> for group 2:
>> subject a: 7 success, 9 trials
>> subject b: 6 success, 7 trials
>> :
>> :
>>
>> I want to test whether the probability of success in group 1 is the same
>> as in
>> group 2. It's like comparing 2 groups of samples using t test, what I am
>> uncertain about is that whether regular t test (or non-pamametric test) is
>> still
>> appropriate here when the response variable is actually proportions.
>>
>> I guess prop.test() can not be used with my dataset, or I may be wrong?
>>
>> Thanks
>>
>> John
>>
>>
>>
>>
>>
>>
>>
>> ________________________________
>> From: Bert Gunter <<mailto:gunter.ber...@gene.com>gunter.ber...@gene.com>
>>
>> Sent: Wed, February 9, 2011 3:58:05 PM
>> Subject: Re: [R] comparing proportions
>>
>> 1. Is this a homework problem?
>>
>> 2. ?prop.test
>>
>> 3. If you haven't done so already, get and consult a basic statistical
>> methods book to help you with questions such as this.
>>
>> -- Bert
>>
>>
>> > Hi, I have a dataset that has 2 groups of samples. For each sample, then
>> > response measured is the number of success (no.success) obatined with
>> > the
>> >number
>> > of trials (no.trials). So a porportion of success (prpop.success) can be
>> > computed as no.success/no.trials. Now the objective is to test if there
>> > is a
>> > statistical significant difference in the proportion of success between
>> > the 2
>> > groups of samples (say n1=20, n2=30).
>> >
>> > I can think of 2 ways to do the test:
>> >
>> > 1. regular t test based on the variable prop.success
>> > 2. Mann-Whitney test based on the variable prop.success
>> > 2. do a binomial regression as:
>> > fit<-glm(cbind(no.success,no.trials-no.success) ~ group, data=data,
>> > family=binomial)
>> > anova(fit, test='Chisq')
>> >
>> > My questions is:
>> > 1. Is t test appropriate for comparing 2 groups of proportions?
>> > 2. how about Mann-Whitney non-parametric test?
>> > 3. Among the 3, which technique is more appropriate?
>> > 4. any other technique you can suggest?
>> >
>> > Thank you,
>> >
>> > John
>> >
>> >
>> >
>> > [[alternative HTML version deleted]]
>> >
>> >
>> > ______________________________________________
>> > <mailto:R-help@r-project.org>R-help@r-project.org mailing list
>> >
<https://stat.ethz.ch/mailman/listinfo/r-help>https://stat.ethz.ch/mailman/listinfo/r-help
>> > PLEASE do read the posting guide
>> >
<http://www.R-project.org/posting-guide.html>http://www.R-project.org/posting-guide.html
>> > and provide commented, minimal, self-contained, reproducible code.
>> >
>> >
>>
>>
>>
>> --
>> Bert Gunter
>> Genentech Nonclinical Biostatistics
>>
>>
>>
>>
>> [[alternative HTML version deleted]]
>>
>>
>> ______________________________________________
>> <mailto:R-help@r-project.org>R-help@r-project.org mailing list
>>
<https://stat.ethz.ch/mailman/listinfo/r-help>https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>>
<http://www.R-project.org/posting-guide.html>http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ================================================================
> Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail:
<mailto:r...@lcfltd.com>r...@lcfltd.com
> Least Cost Formulations, Ltd. URL:
<http://lcfltd.com/>http://lcfltd.com/
> 824 Timberlake Drive Tel: 757-467-0954
> Virginia Beach, VA 23464-3239 Fax: 757-467-2947
>
> "Vere scire est per causas scire"
> ================================================================
>
>
--
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
<http://devo.gene.com/groups/devo/depts/ncb/home.shtml>http://devo.gene.com/groups/devo/depts/ncb/home.shtml
================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: r...@lcfltd.com
Least Cost Formulations, Ltd. URL: http://lcfltd.com/
824 Timberlake Drive Tel: 757-467-0954
Virginia Beach, VA 23464-3239 Fax: 757-467-2947
"Vere scire est per causas scire"
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