Are you comparing the social phenomena intensity against some attribute of the crime data points (like severity)? Or are you just trying to see if crimes are more likely to happen in areas with high or low values of the social phenomena?
If it's the prior, you can join the raster values at each crime point to a new column in the crime point shapefile then run a regression (either exploratory regression, OLS, or GWR) and see if there's a correlation between the two values. If it's the latter you could do a LISA cluster analysis and map any resulting HH clusters against the IDW field to see if they tend to fall in high (or low) values of the IDW field.