interactions for paired and unpaired proportions


I would like to compare the effect of a treatment between two groups.

My dataset is summarized in this table:

Each score corresponds to a proportion (namely, the proportion of successes on a given cognitive test).

How would you compare the difference of treatment effects between Group 1 and Group 2, taking into account the within-subject variability? Would you use a logistic regression?

Thanks a lot for your help


TS Contributor
Does this mean that you only have 3 subjects? If not, how large are your groups?

And why is the number of trials different between subjects, and also within subjects?

With kind regards

So far, I have only 3 subjects, but the number of subjects will increase.

The duration of each test is fixed, but the number of trials is determined by the subject (s/he initiates each trial). That's why the number of trials is different between subjects and also within subjects.

Thanks a lot for your help!


TS Contributor
So you have 2 outcome scores for each subject: number of successes pre/post
(or maybe proportion of successes pre/post),. And you have his or her group
membership. Basically, you could use a repeated-measures ("mixed") ANOVA
with time of measurement as within-subjects factor and group memberhip as
between-subjects factor.

With kind regards

The scores pre/post for each subject are proportions (success rates). Would you use ANOVA with proportions?! What about a mixed-effects logistic regression?

Thanks a lot.
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TS Contributor
Yes, the dependent variable is a proportion, and not just a binary response variable.
You do not want to model a subject's cognitive achievement as 400 single yes/no
measurements, I suppose, but as proportion of successful trials (or, perhaps, as number
of sucessful trials - if subjects with low ability tend to initiate less trials, then proportion
will be misleading). But if mixed-effects logistic regression for 250-400 repeated
measurements is more powerful and better interpretable (I don't know), then this
could be an option, of course.

With kind regards



Omega Contributor
Major question, were subjects randomized or not? This will dictate if you need to control for baseline differences. Also, beta-regression may be an option. Was time between test standard and set?

Secondarily, you need to have a protocol written for this (I would imagine), to prevent you from just running analyses until you find something. Given your presentation/question there are likely many areas that may bias future repeatability.