Answer to Question #6542 in Statistics and Probability for betty

Question

I have collected ordinal data on which I'd like to run non-parametric stats.
I asked a group of men and women to choose and rank as 1st most important, 2nd most important, and 3rd most important components of students' college applications from among 8 total components (GPA, essay, ethnicity, whether a student is an in or out of state applicant, etc.... ) I've summed the totals/compiled frequency counts for each component with separate tables for men and women.
Based on these frequencies, men and women both seem to agree that GPA most influences admissions. Beyond that, things get a little muddy (i.e., for men, is the 2nd most important attribute ethnicity, which received the most 2nd place votes among men, OR is it actually essay, which received the 2nd most first place rankings among men?). I'm interested in seeing which rankings are statistically significant & whether there are between-group differences in ranking patterns due to gender.
Which non-parametric statistic(s) would you use?