I want to estimate enlistment of African American soldiers in the Union Army (during the American Civil War) by county in order to regress this variable on county-level post-war outcomes. I ultimately want to do this for the US South as a whole, but am currently working state by state.
I know the actual number of enlistments at the state level, and I currently have the county of enlistment for ~20,000 soldiers, which is about 10% of the total. This pre-existing sample was generated by randomly selecting companies (of approximately 100 soldiers). However, these companies were formed in specific locales and thus tend to be clustered by county.
My question is: if I expand this sample using the same methodology how much larger a sample do I need to be confident that the variation in enlistment by county in my sample is a reflection of the true variation?
I'm interested in answering this question either for the South as a whole or for individual states.
The distribution of enlistment by county for the sample I've already got varies a lot by state. For some states, 75% or more recruits were enlisted in one county, for other states the county with the highest enlistment is 30%. The number of counties of course also varies a lot by state: from 3 to 132, the average being 70.