Is there a statistical test that can be used to see whether health rates have changed between years and locations? I am having a difficult time deciding how to go about this. I thought a T-Test would work, but I am not 100% sure. I have two sets of data. One contains a rate for diabetes in a town in a single year. The next is a rate for diabetes (so same methods) in that same town for two years later. I have over 200 towns listed and would like to see if there is a statistically significant increase or decrease in diabetes for each year within the town (not between them). Is there a way that I can do this?
 A: Yes, you can use a t-test to check whether the observed difference indicates a difference in the underlying probabilities. Alternatively, you can use a proportion test, which is specifically devised for this situation. As your n is very large, it does not matter which test you use, and actually the results are almost identical, as shown in this hypothetical example with a realistic diabetis probability:
> p <- 5/83
> q <- p + 0.001
> n <- 5*10^5
> prop.test(x=floor(c(p,q)*n), n=c(n,n), correct=F)
    2-sample test for equality of proportions without continuity correction
X-squared = 4.3821, df = 1, p-value = 0.03632

> # t-test by hand
> sx2 <- p*(1-p)*n/(n-1)
> sy2 <- q*(1-q)*n/(n-1)
> T <- abs(q - p) / sqrt((sx2 + sy2)/n)
> k <- (n-1) * (sx2/n + sy2/n)^2 / ((sx2/n)^2 + (sy2/n)^2)
> cat(sprintf("p-value from t-test: %f\n", 2*(1-pt(T,k))))
p-value from t-test: 0.036320

I wonder, however, whether this actually is what you are interested in: do you really only want to compare two points in time? Or do you want to know whether there was a significant change with respect to the past (i.e., with taking the fluctuations in the past into account)?
In the latter case, you can fit a linear model for the town of interest and check the trend for significance. This would even allow you to check for outliers.
