I have a dataset that is composed of homicide rates (per 100,000 or per 10,000) from 1980-2014 for 11 geographical areas. I need to assess whether there are statistically differing rates between the geographical areas over those 24 years. I am not certain how to approach this analysis or what would be the best way to go about testing for difference. Chi-squared testing has been suggested to me but I'm still unsure how to apply it to this dataset. Would you be able to suggest a way to assess for statistically significant differences between these geographical areas over the time specified? If possible, could you suggest ways to approach this using R software?
So you have a time series (or multiple time series, one for each area) of yearly counts. I would start out with Poisson regression, with $\log(10 000)$ or $\log(100 000)$ as an offset, so as to modeling rates. This is called Poisson rate regression, search this site. You must have an eye out for possible overdispersion.
As for the time series aspect, look through this earlier Qs with answer. As for using R, this post Modeling multivariate Time Series Count Data in R have jags code run from R, this post have some pure R code.