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We characterized two social group through utilizing a 4 point likert scale and arithmetic means for 32 questions separated in 4 groups and 4 subgroups as our professor advised, we look at the difference between the two social groups, what statistical treatment would make use of the arithmetic means to find if the difference between the corresponding questions is significant.

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MANOVA do it. But what it will tell you is that there is an OVERALL difference between the two groups across ALL the questions and levels tested at the same time. If that's all you're interested in then that'll solve it in one step. But i'm guessing you'll want to test which question is different, then you go can go and do some ANOVAs i.e. test one question (4 subgroups all at once) against another.

Or, to go on an even lower scale where you test the individual sub groups; T tests can be used to compare two means.

I'm making it sound more complicated than it really is, ANOVA just is a t test if there are only two group means being compared. But be careful, your choice of test depends on your assumptions, though many of those can be relaxed if you have large sample size.

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