I've conducted a large survey with about 600 responders. Most of the questions were multiple choice questions. I'm interested in comparing several kinds of percentages. First, I'm simply interested in determining whether the percentage of people choosing answer A is the same or different from those choosing answer B, C, D. etc. Most of the online stuff I've read suggests this is a one sample test of proportions but those seem to require a theoretical or expected value to compare the percentage to and that's not the case here. My second broad category of analyses would be to compare BETWEEN populations. So, do males and females answer the questions differently. There I would be interested in seeing whether the array of answer choices differ (e.g. males chose A 40% of the time, B 50% of the time, and C 10% of the time while females chose A 30% of the time, B 10% of the time, and C 60% of the time) and whether specific percentages differ (e.g. is the percentage of males that chose A [40%] different from the percentage of females that chose A [30%]).
I am a little unsure of exactly what you want to do but when you are dealing with integer fractions you have a binomial distribution. I would make a simple binomial test by checking to what degree their clopper pearson confidence intervals overlap. Hope this helps.
You may also find this question helpful: Simultaneous Z-test for the equality of two proportions (binomial distribution)
There are two types of comparisons you could make which I think correspond to your two queries.
Compare the responses to 2 questions (Q1, Q2):
| | A | B | C | D | | -- | --- | --- | --- | --- | | Q1 | 150 | 150 | 150 | 150 | | Q2 | 300 | 100 | 100 | 100 |
You would like compare whether question 1 and question 2 are being answered in the same way. Perform a chi-squared test.
Compare the responses to 1 question by group (G1, G2):
| | A | B | C | D | | -- | --- | --- | --- | --- | | G1 | 150 | 150 | 150 | 150 | | G2 | 300 | 100 | 100 | 100 |
You would like compare whether question 1 and question 2 are being answered in the same way. Again perform a chi-squared test!
There's an explanation of the method here