# Pearson correlation for 'lumped' populations?

I'm currently using the Pearson (product-moment) correlation coefficient (PPCC) to look at the relationship between deprivation and healthcare usage in a population, but I think I've probably got this wrong.

The problem is that the population (about a million people) is broken up into about 100 geographical groups, with group sizes of between 4,000 and 20,000 people. Each group has a single deprivation ($\mathit{x}$) value, and the healthcare usage of the people in the group is combined into a single $\mathit{y}$ value for that group.

What I'm doing is taking my 100 ($\mathit{x,y}$) points, and calculating the PPCC for those points. I think (or thought) that this makes sense, because I'm only interested in comparing the geographical groups against each other; I'm not really interested in the individual people per se.

The problem with this approach is that a group of 4,000 people is effectively given the same weight as a group 20,000 people. I'm not yet convinced that this is a problem but, if so, is there a way to handle this?

Note that I can't just calculate $\rho$ for the ungrouped population of 1,000,000 people, because a single person doesn't have a quantifiable $\mathit{y}$ value. 'Healthcare usage' only makes sense in the context of a group (a group may have 10 healthcare events per 10,000 people per month, for example).

One approach that I'm thinking about is simply to exclude outliers. This sort-of makes sense because my detection of outliers takes into account the size of the group to find out whether or not the healthcare usage of the group is within 2$\sigma$ of the entire population mean. Smaller groups are more likely to be outliers, and the $\mathit{(x,y)}$ points that are left after this process can be considered to be valid, irrespective of group size.

3) You can weight the groups by their sample size. One way to do this (probably not the best or most efficient....) would be to create individual data from your grouped data and then correlate that. You probably should add some random noise to it, but I am not sure how much (you could do this with the jitter function in R if you are using that.