I have a survey asking a person's gender (M/F), geographic region (West, East, Midwest, South) and a few other demographic variables along with two dozen questions in which they can disagree / slightly disagree / slightly agree / agree. The data was given to me and whoever worked on the data has refactored the responses to a simple disagree / agree.
I am interested in whether people of different gender / region / other demographic variable have differences in responses. For example, Q1 could be something similar to 'You are stressed often' and the responses are either agree / disagree. I would want to know if gender is related to agreeing/disagreeing with Q1.
The analysis suggested to me was to build a set of contingency tables for every combination of demographic vars and questions. For example: Gender vs. Q1, Region vs. Q1, Gender vs Q2 and so on. Then I would use Fisher's exact test or the chi-squared test of independence on each of the contingency tables.
Q1: Agree Disagree Male 10 30 Female 15 32
I have two dozen questions and at least 4 demographic variables. If I were to do all combinations I would have to run at least 96 chi-squared tests. Obviously this also brings in a multiple testing issue.
As an alternative route, a colleague of mine suggested logistic regression with the following model:
Question Response ~ gender + region + other demographic vars + interactions.
This would mean fitting slightly fewer models but will still have the same issue with multiple testing. I would still need to fit a logistic regression to each question. There's also the issue of interpretability: it's a lot easier to explain the results of a chi-square test than to explain what a logistic regression is.
Which technique is preferable? Is there a better way to handle this data? In either case, how should I handle the multiple testing?