Suppose Intervention A and Intervention B are randomly allocated to 50 participants each (n = 100) to compare their efficacy in preventing a condition after a certain time period. Efficacy is ordinally categorized into six: no condition (full prevention), I – mild condition, II – moderate condition, III – severe condition, IV – critical condition, V – death. The following table is generated (see image attached). For the sake of discussion, let’s assume that this ordinal categorization is proper and evidence-based.
What statistical method/tool should I use if I wish to compare the distributions of the two groups across the ordinal categories? Because of the ordinal nature of the variable, I think that Chi-square test or the Fisher exact test (the latter I have yet to see being done outside of a 2 x 2 contingency table) cannot be used in this case. Is either Cochran-Armitage test for trend or Cochran–Mantel–Haenszel statistics viable here? Thank you!
Cochran-Armitage test is a possibility, but note, I believe this test assumes a specified spacing between the ordinal categories. Ordinal regression may be an ideal approach. But also a Mann-Whitney test that takes into account ties, will work well.
You are likely right about the chi-square test of association, depending on what you want to test.
I agree with @Salvatore. A worked example of ordinal regression can be found in the attached notes using R. Best wishes, David Booth
Looking at the data you provided, I'm wondering if you want to do separate analyses for condition vs. no-condition, and for the degree of condition for those with the condition. I don't know if this makes sense for your situation.
Thank you for your response, Salvatore S. Mangiafico and David Eugene Booth .
Salvatore S. Mangiafico, indeed, a simple 2 (intervention) x 2 (no condition and condition regardless of severity) is our first/default plan for the analysis. I agree that it makes sense given the context of our research. However, because of the multiple ordinal categories that are under the general category "condition," I think that we may be losing a lot of information detail by settling with 2 x 2. Ideally, in an attempt to reduce the likelihood of arriving at a statistically significant finding by just the mere number of analyses performed, I think that it is prudent for the group to settle with either the 2 x 2 or the 2 x 6 table analysis.
Aedrian Abrilla , my recommendation is to not limit the number of analyses you conduct. It's better to find out what you want to find out. Don't worry too much about p-values, but also, don't place too much importance on the p-value results.
Use categorical data analyses. It assumes a multinomial distribution for your table to test hypothesis.
It can test independence as well.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics