I'm a bit puzzled how to analyse self-report questionnaires (for example psychometric studies).
For example, consider a standard Hamilton Rating Scale for Depression which comprises 21 items with numerical scores [0-4] for each item.
For example, I have a cohort of 100 subjects, who replied to this questionnaire before and after some intervention.
Question: How to assess if there is a significant difference before and after the intervention?
Conceptually, one may apply paired t-test to both groups (before and after, as they are related) and then compute p values etc.
But the problem is that the outcomes (the overall score of such questionnaires) are not ratio data, but rather ordinal.
I know, that many researchers ignore that fact and apply standard methods designed for ratio data (real numbers). I am wondering, to which extent it is justified and is safe for statistical inference?