# A binomial test with repeated measures?

I'm working on a study with a single trained animal (ie. our only participant). He is making a binary choice on a number of consecutive trials (we are essentially trying to teach him a rule -- if A, make one choice, if B make the other). We want to set a criterion for the animal reaching some significance threshold with different stimuli. We've chosen to aim for a 1-tailed p=0.05 threshold. I am trying to figure out, given this threshold, how many "correct" trials would constitute success?

If these were independent samples, I would run a simple binomial test to figure out how many successes out of some number of trials (10, 20, 30) would make for a p<0.05 effect. But given that this is a single animal doing all the trials, the binomial assumption of independent observations doesn't hold. I know about logistic regressions as a way of analyzing binary-outcome data, but the trick here is that I don't have data to analyze. Rather, I'm trying to figure out what to set as a "criterion for success".

Any help would be greatly appreciated!