I have data on income for two groups, but the income is in deciles - how can I compare them? The income data is in interval format.
The data does not have individual income measurements. But is in {1,2...10}, that is in deciles, where 1 is the lowest income range and 10 is the highest.
What are the common ways I can compare the income distributions of two groups using this decile interval income data?
 A: It depends on what you mean by "compare". Two possibilities come to mind.


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*Your data is fully described by two histograms, where the bins are defined by income deciles. There are ways to define distances between histograms. One I personally like is the earth mover's distance or Wasserstein metric. This would allow you to say, e.g., that distributions A and B were closer together than C and D. (Which would of course depend on the specific distance measure you choose.)
You could similarly compare both distributions to a reference distribution, like the uniform one. This naturally leads to the Gini coefficient.
These are purely descriptive measures.

*If you want to do inferential statistics or similar on your data, then you can do different things. You first notice that your data is ordinal-data - we don't know the specific income of two individuals, but if they are in different deciles, then we know which individual has a higher income. So I'd recommend you read up on ways to analyze ordinal-data, e.g., by looking through our earlier questions carrying that tag. The Wikipedia page on ordinal regression may also be helpful and has a few references.
