This is a pretest-posttest design with a control group (no treatment between measurements) and an experimental group (treatment between measurements).
All measurements consist of the same rubric and provide ordinal data (1,2,3,4).
Tests for metric data like t-tests are not appropriate. Many websites suggest using the Mann-Whitney U test as a non-parametric test for independent groups, with the difference between pretest and posttest score, i.e, gain score. My problem with these suggestions is that with ordinal data calculations like differences are not possible.
What test would be appropriate for this pre-test/post-test design?
Edit 2: Calculating differences is not possible for ordinal data
Pitouille write about "calculate the difference between post and pre-test". In my understanding, it is not possible to determine the difference with ordinal data, as it is not defined at all. If I could calculate the difference, the data would have to be at least interval scaled.
The difference corresponds to the usual gain score, which I thought of first. But because of the above reasoning, it is not possible to form the gain score.
Hence my question is: How can I determine the effects in pretest-posttest groups if I cannot calculate differences?
Edit 1: Possible examples of data.
First to be mentioned, the study is in the planning phase and I have not yet collected any data. Each group is expected to have 15 to 20 participants.
|Candidate||Control(0) or Experiment(1) group?||Pretest-Score||Posttest-Score|