On visual inspection, black crimes appear to exhibit significant clustering compared to white crimes, especially in the center of the city.  This may represent a more limited 'spatial search' by black offenders.  However, we are more interested in the relationship between the distributions of black and white crime, than looking at the distributions individually.

The comparison of G-hat and F-hat distributions looked for deviation of the G-hat distribution from the F-hat distribution. This analysis showed that there was in fact no spatial dependence between white and black crimes.  In our second analysis, we estimated L-hat using the cross-K function, and plotted this with the corresponding envelopes.  This analysis also supported the conclusion that there was no real evidence of spatial dependency between the distributions.