A good summary measure on analyzing repeated measures of longitudinal data? I have an interesting question on longitudinal data and I'm looking for a proper summary measure that enables me to answer my question of interest without knowing/using anything about correlated data. 
Suppose we have two different samples - one treatment and one control. At each trial, subjects should solve a puzzle and we count number of attempts to solve the puzzle. Number of attempts could be 1, 2, 3, or if the puzzle is not solved after 3 attempts the subject is failed in this trial. We repeat the trial 10 times so that each subject gets to solve 10 puzzles. Obviously, we have correlated data since we have 10 measurements on each subject. 
My hypothesis of interest is whether there is any learning effect. Would you think of any summary measure on each subject (each subject has 10 measurements) that summarizes the measurements on that subject into a one measurement so that we can avoid (or at least attempt to avoid) getting correlated data?
Thank you,
 A: Both your suggested approaches (number of attempts in the 10th trial; and the difference between the number of attempts in the 10th and 1st trials) depend too much on the final trial.  The subject might indeed have learnt, and just has an unlucky time on the 10th trial.  You need a way to incorporate the information from the 9th, 8th, 7th... trials.
I don't think there is a way to do this well without using longitudinal data analysis techniques, specifically mixed effects modelling.
In general a mixed effects level model with "number of attempts" as the response variable and "trial number" as the explanatory variable (plus another explanatory dummy variable for treatment / control, if that is part of the experiment) will do it.  You can then have a random element for each trial-subject combination, as well as a random element for the subject.  You will have complications because 


*

*the response variable is a censored ordinal variable 

*the explanatory variable is an ordinal variable; and/or even if you were to treat it as a continuous variable, the chances are that the relationship between it and the response is non-linear


There are solutions to those challenges, ranging in sophistication.
If all that is too much, I would try as a variant on your proposed approach - average number of attempts in the last three trials minus the average number of attempts in the first three.  You still have the problem of the censoring of the data however...
