Jonathan HorowitzStats / demography question: Say you have two populations with different standard deviations. Let's say you wanted to determine how much compositional differences affect the standard deviation, in contrast to the average differences of each group. The key is that it's *not* about the mean, but the dispersion, so a Kitagawa decomposition doesn't really make sense. What would I use?
Elyas Bakhtiari@jonathanhorowi1 I'm not sure if this is what you're going for, but could you simulate the data to swap compositions of the populations? In other words, simulate Population A with the composition of Population B, and see how much that changes the SD of Population A?
@elyas This sort of what I was thinking of doing because I already have those populations simulated. If I use the demographic distribution of population A and the scores of population B, I could see how much the standard deviation of population B changes as a result of the compositional effect.
@elyas That said, I'm still struggling to wrap my brain around the details. I assume the metric would be something like change in SD over SD of original population, but then comparing the two populations to each other gets confusing. It would also be neat to see if there was an interaction between composition and scores but I'm not sure how I would do that.
To get at both scores and composition, maybe you could do separate simulations using the mean and sd from each population? Simulate Pop A to have the same composition of Pop B, drawing from the Pop A score distribution. Then a second simulation where Pop A has the composition of Pop B, drawing from the Pop B score distribution.
I'm not sure how to turn that into a single decomposition metric though..