I applied a survey consisting of 12 questions to 120 people and each questions include 4 nominal categories; I want to make comparison of people's answers according to their socio-demographic characteristics such as their educational level or socioeconomic status. All of my comparison criteria consist of nominal categories and number of categories change between 3 to 6. I cannot drop or combine comparisons; categories in other words number of categories are fixed.
My question is when I compare the frequency distribution of people's answers based on their education levels (for example) through chi-squared test, I got a warning that says (for instance) 7 cells have less than count five; minimum expected count is; 43. I got this warning for almost my all questions - demographic characteristics comparisons.
Shall I underestimate this warning and use my test results or is there a different test I should use? If I should use a different test, which one?