# Compare means of two (contentwise) different variables

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.

• There are paired tests that do not assume the same scale (eg rank-based); you could also re-scale/standardize the data. But - can't they experience both (could these categories be non-independent - and this might be what you are indirectly referring to)? Also, is 'situation' a factor? Commented Nov 11, 2014 at 17:14
• "Situation" is not a factor and assumed "constant". Participants can experience both, yes, maybe I should have said "Which feeling occurs more strongly/frequently?". I'll have a look into the rank-based tests, but intuitively I'd say that the problem of interpreting the results probably remains (being only vaguely familiar with non-parametric procedures). Thanks so far! Commented Nov 11, 2014 at 18:13
• rank-based approach would address "Which feeling occurs more strongly?" But is your question confounded by the fact that one is always going to be a little stronger (or easier shared in a survey;), thus the difference in scale? Yet this is something you can no longer address at the analysis stage, once the survey, responding to a known scale, has been completed. Commented Nov 11, 2014 at 18:24
• Yes, that was my initial concern. Thank you for commenting! If you summarize your point and post it as an answer, I will mark it as "accepted". Commented Nov 12, 2014 at 10:38