# Sample size invariance of inequality measures

I am not an expert on inequality, so decided to drop this question. Suppose I analyze inequality of an outcome among different groups with Gini coefficient, I know that the scale of the outcome wouldn't affect the result, but what about the sample sizes of each group?

My guess, not formalized but based on intuition, is that the smaller group may have artificially different inequality due to differences in group sizes rather than the distribution per se (https://www.jstor.org/stable/3211637?seq=1 this seems to justify my worry). Is there any other inequality index that may be used that is sample invariant? (except for the suggested adjusted gini)

• I guess sample invariant means "replacing a population $P$ with a larger population formed from $n$ copies of $P$ will leave our inequality measure unchanged (for all $n \in \mathbb{N}^+$)"? Jun 7, 2022 at 17:18
• I didn't think about it in this way that is also interesting but I don't think it's the same: I have a population $P$ and I partition it in $i$ sets $S_i$ with different sample sizes $n_1,n_2,\hdots,n_i$ and then compute the Gini over these. How is the size of the partition $n_i$ going to affect my Gini? Is there a systematic bias or is it irrelevant? My goal is to regress G on a variable that tends to be negatively related to $n_i$ if the index is too then I may have a regression problem. Jun 8, 2022 at 11:49