I have a question about comparing the means of two variables that have a different meaning but a (possibly) similar ways of measuring them. To give an example:
Let's say I am conducting a study in the social sciences in which I ask my participants about their experiences of "Anger" and "Anxiety" while coping with a difficult situation. Each participant answers to both questions on a 7-point Likert-Scale.
Now my question(s):
- Can I compare the means of the two variables? (e.g., "Do my participants rather experience Anger or Anxiety in the given situation?")
- What statistical procedure is appropriate?
- Is the result actually meaningful?
The answers to the first two question might be "Yes, do a paired-sample t-test or a repeated measures ANOVA." However, the two variables are not equivalent content-wise. And in my opinion the comparison of means between two such variables is not sensible unless it can be assumed that the variable share the same scale.
So while I think that the question is possible to answer from a "strictly statistical point", I wonder if interpreting the results would actually be meaningful. From my point of view "measuring" the two variables by the same Likert-Scale is not sufficient to make the comparison meaningful but I wonder if I am discarding it too readily.