My data comes from an experiment in which the response is a number between 0 and 4, which will either be correct or incorrect. My problem is that the chance of guessing the correct answer due to chance follows a binomial distribution (i.e. so if an individual consistently chooses the number '2', they are likely to score quite well).

The ANOVA isn't being performed on this raw data - I need to transform it into some kind of score (i.e. how many trials the individual was correct on), so it's this transformation I'm stuck on.

Is there a simple way of converting my raw data so that it take chance into account?

Thanks!