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I would like to analyze data on questionnaire scores on quality of life between two different groups. There are 20 quality of life questions, all with responses on a Likert scale 1-7. So I have an overall score out of 140 for each person and 20 individual scores out of 7. There are 100 individuals in group 1 and 50 in group 2.

My plan is to first perform a non-parametric Mann Whitney test to compare the overall score between the 2 groups.

I could then perform a linear regression on overall score, and/or ordinal logistic regression for each question; Y= Score(1-7) & X= control/case, but then I would have 20 models.

My question is whether I should be considering multivariate analysis in this case?

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If the quality of life questionnaire you're using is unifactorial (the validity study of it might have looked for it), then it is expected that each question behaves, roughly, as the total score and you might not get much more information from the individual questions.

Regarding the analysis of all the questions, you should also consider a correction for the $p$ value (e.g., like the Bonferroni correction) for multiple comparison.

And, in terms of selection of tests, if you are using Mann-Whitney test I deduce that your data may not be normally distributed, so doing a linear regression may not be adequate, in particular if the dependent variable is a 7 point scale. Perhaps doing an ordinal regression might be better, but I doubt that 20 ordinal regressions might help you understanding your data.

You might want to do something specific that I missed, if that is the case, please leave a comment on my answer.

So, to wrap it up, if the questionnaire is unifactorial, I suggest that you focus your analysis on the total score.

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  • $\begingroup$ There is an ongoing, and fierce, dispute if likert scale data can be treated as interval like and thus use methods like linear regression or should be considered ordinal (which formally it is). Ordered logistic regression is one option. $\endgroup$
    – user54285
    Commented Mar 19, 2019 at 1:14

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