# Test change in intersection between two sets of subsets

let's say I have a set A, and a set B, both subsets of C. To test whether A and B have statistically greater overlap, I can use the hypergeometric test. However, let's say I now have:

$$A_1, B_1 \in C_1, A_2, B_2\in C_2$$, where the sizes of $$A_1, A_2, B_1, B_2$$ are all different. I can run independent hypergeometric tests for $$A_1, B_1$$ or $$A_2, B_2$$ to examine statistically greater overlap. What I would like to understand is whether the overlap is greater in the second set of samples. How would I go about doing this?

To give a concrete example: let $$A_1$$ can be the days that it rained in NY in 2010, $$B_1$$ can be the days that I was late in 2010 (living in NY). $$A_2$$ can be the days that it rained in SF (in 2011), $$B_2$$ can be the days that I was late when living in SF (in 2011). I want to understand whether $$A_1, B_1$$ intersect more or less than $$A_2, B_2$$.

• You need to tell us how you measure "overlap." Several natural ways to do this immediately come to mind, depending on whether you just want to count the overlapping days or look at them as proportions of $A,$ $B,$ or their union.
– whuber
Oct 8, 2021 at 16:25
• @whuber I was thinking to count the number of overlapping days and compare. For examining just the days in 2010, I would use a hypergeometric, but I want to compare the differences in overlap between 2010 to 2011, accounting for the difference in size of $A$ and $B$.
– G D
Oct 10, 2021 at 21:05