Hi, I initially posted this to the general R mailing list, but Bert Gunter 
thought this may be a mixed model issue, so suggested me to post here.

I have a dataset that has 2 groups of subjects. For each subject in each group, 
the response measured is the number of success (no.success) obatined with the 
number of trials (no.trials). So a probability of success (prop.success) can be 
computed as no.success/no.trials for each subject in each group. The data may 
look like:

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
:
:

The objective is to test if there is a statistical significant difference in the 
proportion of success between the 2 groups of subjects (say n1=20, n2=30).

Initially, I can think of 3 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
3. do a binomial regression as:
    fit<-glm(cbind(no.success,no.trials-no.success) ~ group, data=data, 
         family=binomial)
    anova(fit, test='Chisq')

Bert Gunter instead thought this may be modeled by a mixed model because there 
is a random subject to subject variability in their probability of success 
within a group. So I specified a mixed model for this data:

4. glmer(prop.success~group+(1|group), weights=no.trials, data=data, 
        family=binomial)

My questions is:
1. Is t test appropriate for comparing 2 groups of proportions?
2. how about Mann-Whitney non-parametric test?
3. Actually, model 3 (binomial regression) and 4 (mixed model) gave me exactly 
the same test for fixed effects, and the variance component for group in model 4 
is very very small (E-133), so is mixed model really necessary here?
4. Among the 4, which technique is more appropriate?
5. any other technique you can suggest?

Thank you,

John


      
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