# How would I go about analyzing correlation between last name and population proportion?

I was recently admitted at a university which disseminates a list of the admitted students along with their emails in order to facilitate communication and increase camaraderie before the semester begins. I was wondering if people with last names in certain ranges (e.g. one of A, B, C... or one of Aa-Hq, Hr-Qh, Qi-Zz) are more likely to make up the graduating class.

I initially considered just taking the proportion of people with names in each range, but then I realized that I would have the same bias present in maps that measure phenomena by state--the size of the name pool would make it seem like names in those pool are more likely to be in the graduating class. For instance, if 99% of last names in general begin with A, then of course it will seem like people with A-names are more likely to be in the class.

Since the solution to this bias is usually per capita measurements, my next thought was to take per nomine measurements by dividing each number of students with some last name type by the number of names of that type in existence. So if there were 200 students with last names starting with A, and 10000 last names in existence starting with A, then the statistic for the As would be $\frac{200}{10000}$. But then again, I'm not sure if this might skew the data because of name types like J which may not have a lot of names, but include names like Johnson which capture a lot of people.

Is my thinking correct, or will my proposed "per nomine" measure do the trick? Is there a better way to do this? Maybe dividing the number of people with a certain name type by the proportion of children born in 2000 who have that name type?

I'm interested in both the most precise process from a theoretical standpoint and the most practical approach from a data-acquisition standpoint (assuming said approaches differ).