Valid to use bar graph for nominal data with "check all that apply"? I asked survey participants which people influenced their idea of what college will be like, instructing them to "check all that apply." I am trying to see if there is a difference in the type of influences between two populations, so calculating the mean does not make sense. Any advice on what kind of test I can do? Or can I just represent the responses in bar graphs, showing the differences between the two populations?
 A: A bar graph should be fine, as long as you are clear about what it is showing. In this case I would make clear that the number of survey respondents will be lower than the total number of influences reported, due to the "check all that apply" survey design. Depending on what you would like to investigate with your data, it might be worth doing additional analyses based on subpopulations sharing the total number of items checked (so, among people who marked three influences, influence X was the most common whereas among those who only marked one influence the most common was influence Y).
What tests you can do is a large question. What tests you can do that address what you would like to learn from your data is more manageable question, but one that requires more detail from you about what sorts of options your respondents had on the survey as well as what you would like to learn from the responses.
But based on what is written at present I see two straightforward types of comparison that may be of interest. First, you could compare the number of influences marked per respondent between the two populations. That would be a comparison of means, and something like a t-test would probably be appropriate. Second, you could compare the odds of a given respondent marking a particular influence for one population relative to another. The binary nature of the response (an influence is marked or left blank) suggests a logistic regression, and you could include a regressor for the number of influences a respondent marked to address the "check all that apply" setup.
