Testing whether there is a difference between two groups who were asked the same set of questions

I asked two groups of individuals (80 males and 10 females) fill out a questionnaire asking them their attitude towards a series of political variables. Every individual had to answered a set of 16 statements and tell me whether they agreed or disagreed with the statement presented to them (yes/no answers).

I would like to know whether there is an association between the two groups considering all of the variables at once.

• Could I test this by doing a single 2 x 16 $\chi^2$ test of association?
• Are there any other tests that I should be thinking of?
-
Just to be clear, the groups you would be comparing would be the group of 80 males vs. the group of 10 females? Because if so, I don't know that I would trust any tests with a group of only 10 people on one side of the test. –  Jonathan Aug 9 '12 at 23:23
@Jonathan's concern is a valid one. And if you don't have groups that are randomly sampled, or at least otherwise representative of the larger populations of interest, then doing the analysis with just 10 in one group is pretty pointless. –  rolando2 Aug 10 '12 at 6:49
Thanks for the answers. Ok, let's say i increase the female sample size to 40. Then i could do a logistic regression as Tristan suggested. But how do i get around this fact that the answers are not independent? –  user13218 Aug 11 '12 at 2:02
Assuming the sample sizes were not a concern, can you expand on what you mean by whether there is an association between the two groups considering all the variables at once? It sounds like you want to get beyond testing the difference between male/female on individual questions, but I'm not sure what sort of group-level associations you would find interesting. Are you looking for whether, overall, females or males tend to answer "yes" more? Are you try to identify groups of questions that males and females tend to answer similarly vs. differently? –  Jonathan Aug 13 '12 at 16:18
Given that if you constructed a $2 \times 16$ contingency table the sum of all the elements would exceed 90 (as each person can answer yes to more than one question) I think a $\chi^2$ test or similar would be inappropriate. The comments saying that your sample size is small are valid, but this would be my approach if there were no such concerns: