# Which correlation test to use

I'm working with datasets on economic inequality and crime rates at the county level to produce correlation matrices. My economic inequality data has several variables, which are percentage of county populations that have incomes in particular brackets (0 to 9,999, 10,000 to 14,999, 15,000 to 35,000, etc.). This is continuous, interval data. My crime rates data has several variables, which are different crime types (murder, robbery, welfare fraud, etc.). The values are the crime rate for each crime by county, calculated by dividing absolute crime counts by population. These data are also continuous, interval data.

My crime rates are all heavily skewed right (most counties have low crime rates; a few have high crime rates). My economic data is skewed right with outliers at the lowest and highest income brackets, and approaches normality toward the middle income brackets (though with long tails on both sides).

Producing some scatterplots between my economic and crime variables doesn't show clear linear/curvilinear relationships, doesn't clearly indicate monotonicity, and suggests low correlational values. My n = 1,441. I'm trying to determine whether to use Pearson's r, Kendall's t, or Spearman's rho.

Between Kendall's t and Spearman's rho, the best option seems to be Spearman's, because of my large n (Kendall's is better with small sample sizes). So the question is whether Pearson's or Spearman's is better.

Because my crime data is skewed, and because my economic data is sometimes skewed with outliers, Spearman's seems like the preferable choice over Pearson's. Note that I am assuming monotonicity (as percentage of population in a particular income bracket goes up, crime rates will go uniformly up or down), which lends support to using Spearman's.

Does my analysis appear sound? Am I missing anything? Should I use Spearman's rho or some other test?