I hope this is a simple question.

Here's the basic idea:

On each trial a child gets a choice of 12 types of candy.

She can only pick one.

After she eats it, she gets the same choice with the same 12 types of candy.

She completes 20 trials a day.

She works for 10 days.

What type(s) of candy does she prefer?

My understanding:

I would like to know for each category (type of candy) whether or not it was preferred above chance.

I am under the impression that I cannot do a normal one-sample t-test for each one because the categories are dependent on each other.

I am also under the impression that I cannot do a chi-square test because the frequency scores are not from individual subjects and thus violate the assumption of independence.

Also, I think chi-square would only tell me if the distribution of choices were evenly distributed, but would not tell me which particular category (or categories) were preferred.

I'm sure there must be a simple statistical test for such a simple food preference task, but I don't know what it is.

I hope somebody here can help me out.

Thank you very much in advance.

--Ben