I am going to compare means of two groups (Male, Female) from my complex stratified sample.
I have scores of 3 subjects of more then 3000 respondent for each subject.
I checked for normality and get the following picture:
i.e data for groups isn't normal in all three cases. Therefore I can not use the tests of hypothesis of homogeneity which assume normality, also randomness of sample. Nevertheless I want to compare who is better boys or girls? How can I do this correctly and without bias?
Edit: By the way there are no intersections in the three set of respondents. I visualize the three because there is the one problem for all three subjects.
May be I ask the silly question but I guess when normality and randomness conditions are violated, it is incorrect to use such methods. Am I not right?