How to assess differences in sets of data with yearly rates

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?

• What is the specific hypothesis you want to test? A trend of change over the 24 year period, or a difference between the average rate over all 24 years, or something else? – Don Walpola Feb 25 at 2:38
• I'm looking to establish whether a difference exists in any pairwise comparison of the areas over the 24 year span – Emily Feb 25 at 19:08
• Then you would need a full multivariate model. – kjetil b halvorsen Feb 25 at 21:22

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.