Which statistical test should be used for comparing two discrete/count data? Supposing that in an experiment there are two groups: Group A and Group B, each consisting of 30 participants.
The participants are required to play a game for ten rounds. In each round, the participants may or may not exhibit a special behavior. By the end of the experiment, we count how many rounds in which a participant has exhibited this behavior out of the ten rounds. As such, the variable is discrete and can only be an integer from 0 to 10.
Now, I would like to compare if there is a difference between Group A and Group B in this variable. What statistical method should I use in this case?
I initially wanted to use ANOVA but it seems only applicable to continuous data. I tried to Google search "statistical analysis on discrete data" but many answers are ambiguous on this issue.
 A: The model you would use depends on whether you are willing to assume that the probability of a particular outcome for a group is fixed each round, and if it is not fixed each round, whether there is any auto-regression or other dependency structure in outcomes over the rounds.  Since this is a repetitive game, it is possible that players will learn and adapt their play as the rounds go on, so I would suggest starting with a simple model that allows different probabilities over rounds but does not use a complicated dependency structure (at least in the first instance).
If you want to proceed in this way (at least as a starting point), you have a regression model with a binary outcome, so you could use something like logistic regression, with the regression equation:
outcome ~ factor(group) + factor(round)

This method will require you to have a reasonable amount of data for each group in each round, to ensure reasonable estimation of the parameters.  You can then examine residual plots and auto-correlation plots for the residuals to see if there is any evidence of a more complicated dependency structure that would require a more complex model.
