We have a questionnaire measuring 9 clinical symptoms. The sum scores simply adds all these symptoms up. Symptoms are ordered (0,1,2,3), and pretty strongly skewed (lots of 0s).
1) First, we want to test whether the symptom configuration deviates from the Null-Hypothesis of all symptoms being equally severe (equally common in the population). Our hypothesis is that the data do deviate from this H0. The H0 would posit that each symptom contributes with 11.1% to the sum-score of each participant. If we average each symptom over all participants, average the sum score over all participants, and then divide the sum score by each symptom mean score, we get these values:
24.6 % 15.7 % 14.3 % 11.3 % 10.6 % 9.7 % 8.5 % 3.9 % 1.6 %
As you can see, symptoms vary drastically in severity. The pattern clearly deviates from the H0 pattern that would be
11.1 % 11.1 % 11.1 % 11.1 % 11.1 % 11.1 % 11.1 % 11.1 % 11.1 %
However, we need a statistical test for this and do not know what to use (R or SPSS).
2) As a second question, we want to investigate if the symptom configuration stays stable over time. We have a second measurement point, in which we follow the same procedure to get 9 relative severity scores, one for each symptom. The scores are very similar to the ones from the first measurement point (large symptoms stay large, small symptoms stay small. Once again we wonder how we would best measure stability statistically.