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Calculating the dispersion when crime increases

A long time ago in a galaxy far, far away, I wrote a paper that explored the problem of increasing crime across a city or other type of region. I called it "The spatial dependency of crime increase dispersion" because back then I used titles that actually explained what was in the paper.

Often, newspapers will scaremonger people into thinking that an increasing crime problem is citywide, when in reality it can often be caused by an increase in only a few specific places. This is not to negate any crime increases; however, the point is that one should not assume that a 5 percent increase in crime for an entire city means that every district or beat in the city increased by 5 percent. It might be that a couple of places increased dramatically, or there was a smaller increase across quite a few places. The policy response to these two scenarios would likely be quite different.

This can be demonstrated by a dispersion analysis and index first proposed and demonstrated by Marilyn Chilvers in Australia 20 years ago. In a paper for the Security Journal that I published in 2010, I showed how an Offense Dispersion Index (ODI) could be calculated relatively easily from a simple data set that contained 1) a reference for a geographic area of a city such as a beat or police sector, 2) the crime count for that location in year t1, and 3) the crime count for that location in the next year (t2).

With these three simple metrics, an index could be calculated that indicated the dispersion of a crime increase problem, on the range 0-1. Values close to zero indicated that any increase was clustered in only a few sub-regions, while values closer to 1 suggested that the increase in the entire region was a factor in a wider increase generally.

I wrote a software program years ago that calculated the ODI. It ordered the sub-regions (or areas/sectors) by the frequency of crime increasing in the area, and then removed these ordered areas one by one from the overall citywide crime total. In essence, we remove the highest increase areas until the revised citywide total shows no increase in crime. In this way, it is possible to calculate which areas contributed most to the crime increase from t1 to t2, and how many areas would need to be removed from the analysis to generate a zero increase citywide from t1 to t2. The ratio of places that had to be removed to the number of total areas dictates the ODI.


Since I migrated to a new website a year or two ago, I forgot to bring over some of the old blog posts and software programs. I've therefore remedied this here.

The paper can be found at this website at paper number 40. And if you want the software to calculate the dispersion index, there is a zip file with the program here. (Note: It will automatically start to download when you click the link) It's pretty self-explanatory. I should probably write some R code to do this as well, but that will have to wait until my to-do list is shorter than a German opera. So probably never.

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