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.

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.
