I wanted to observe the performance improvements in older people playing online cognitive games. I had 33 participants that were playing 35 online games freely and independently during 10 months. Some participants played more than others. Every time they were playing a specific game a record was created. By the end of the study, I got 28.000 observations. I clustered the data by game, so I´m presenting the number of people that played a game, the number of times each people played a game, their minimum and maximum scores and the improvement in scores.
By doing that I got 677 observations in total. In order to have independent observation (as the same people were playing the different games) I ran a regression model for each game including improvement in scores as depend variable and Number of times played; Age, Education, positive attitude towards technology and initial cognitive state as independent variables.
I have received some questions about that is not valid to have regression models having 33 participants. Even though I argued I have several observations for each subject.
An In the second place some questions about interdependence between observations, that I think is solve by analyzing the results for each game independently.
Please let me know if you know some references to support my claims and if you have any suggestion for my analysis.