I'm examining a big dataset (n>5,000) of companies indebtness values. They are calculated as follows: total liabilities/total assets. Therefore, these are natural left-bounded data: by definition, indebtdeness cannot be less than 0%.
I've performed a number of normality tests and the data is definitely non-normal. As a matter of fact, it looks like an uniform distribution. I want to compare the median and mean values of five sectors and find out if they are different.
My questions are:
1) Can i use Kruskal-Wallis and post-hoc Dunn test with left-bounded data? If so, could you please provide some reference?
2) Would it be better if i use ANOVA provided that i have a big dataset? If so, can i use ANOVA with left-bounded and percentage data? Could you please provide some reference?
Usually Kruskal-Wallis tests for neither the mean nor the median. My advice would be to use a test that tests for what you want to know. Perhaps anova for the mean and quantile regression for the median.
With such a large sample and data that look more-or-less uniform, using these methods will probably be fine. It may be problematic if too much data is too close to 0%. You could also use a Monte Carlo or permutation approach if you have doubts.
But also, with such a large sample size, you are likely to find a low p-value for small effects. Be sure to look at the effect sizes, and assess if these effect sizes are of any practical importance.
Is the response variable a proportion, and if so why not logit?
On having a boundary, things like Tobit regression are often used. I would not advise using K-W for this, particularly with the sample size.
Daniel, what would you suggest, logit or tobit? And why?
- Badges
- Science topic
- Similar topics
- Analytical Chemistry
- Extraction