# interactions for paired and unpaired proportions

#### recherche888

##### New Member
Hello,

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

#### Karabiner

##### 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

Karabiner

#### recherche888

##### New Member
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!

#### Karabiner

##### 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

Karabiner

#### recherche888

##### New Member
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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#### Karabiner

##### 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

Karabiner

#### hlsmith

##### Not a robit
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.