Can I do a Binomial test on more than one individual/group? Can a repeated t test have different sample sizes? I've conducted an experiment on chickens, training them to associate either blue or yellow with a 30 or 1 second wait before a food reward and then giving them a preference test, 15 times in total and 8 hens, so 120 results. 
Questions:  


*

*My Supervisor told me to run a simple binomial to test their preferences. From what I see, this only gives me a P value for one chicken at a time. Is there a way to do this test to see the overall significance for all chickens to choose a certain colour? Or in my results do I present them as single chickens (i.e., 6 out of 8 preferred blue, according to individual binomial values)?

*I've also been looking at the time they take to choose each colour and want to compare the difference between the two. Because a lot of birds chose blue over yellow, the two columns will have a different numbers of values (likely 75:45). Is a repeated measures t-test thus still valid? Does this take into account the difference in sample numbers?
 A: Question 1 is if the probability of choosing blue depends on whether a chicken has been trained to associate blue with a shorter wait time. Although more sophisticated analyses might be possible, if you have complete data for all the chickens and there are only 4 chickens in each training group then little will be lost in simply pooling the 60 responses for all 4 chickens in each training group and performing the simple binomial test that your Supervisor asked for. The apparent bias toward blue, regardless of training, might pose a problem in determining a significant difference related to training and should be addressed if you continue this type of work.
For question 2, there seem to be 2 issues to deal with: is there a systematic difference in the time it takes to choose blue versus yellow, and does that difference in time depend on the prior training? That would seem to require a more complete linear model than a simple t-test. You would want to model time-to-choice as a function both of color chosen and of training regimen (and possibly their interaction); individual chickens might be included as random effects. Different numbers of blue versus yellow choices per se are OK in that type of analysis. Interpreting the results, however, will require a bit of care as you are examining the time it took to make the choice given that the choice ended up blue versus yellow, and it seems that there is already a preference for blue in your test system.
