Crime Declines in SCV: Orly?

Drawing a line between two points does not a trend make. But that’s the approach that the Sheriff’s Department and journalists tend to take when analyzing crime data in Santa Clarita. In a press release[1] published in The Signal's absurd SCV Raw Section (I guess “SCV Raw” sounds cooler than “Unedited Press Releases People Sent Us”) we are told that many crimes have undergone amazing reductions, including "a dramatic 75 percent decrease in homicides and a 50 percent decrease in arson." It's an undeniable fact: there were fewer reports of every Part I crime in 2010 except for forcible rape.

How cheering! How dramatic! But looking at year-to-year change isn't necessarily the most useful or interesting thing to do with the crime numbers. Take the touted homicide reduction. If we followed the news since 2000, we’d get whiplash from the to-ing and fro-ing of the homicide rate.

2000: Homicide rate TRIPLES! (from 1 to 3)
2001: TWO TIMES MORE Homicides! (from 3 to 6)
2002: Homicides CUT IN HALF! (from 6 to 3)
2003: 33% DECLINE in Homicides! (from 3 to 2)
2004: Homicide rate CLIMBS 50%! (from 2 to 3)...

You get the point. Rather, you get the pointlessness. Since 2000, there have been between one and six criminal homicide reports per year in the City of Santa Clarita, usually about three. If we look at a ten-year trend while controlling for population growth, there is a slight, statistically insignificant decline. Why not just note that the homicide rate is mercifully low, as usual?

The good news is that the Sheriff’s Department does a great job of making numbers related to crime available online, so you can get some perspective if you want to[2]. The far trickier task is deciding what interesting messages come out of the data. For example:

*What factors—population size? income? anti-gang initiatives? suburban vs. urban population?—predict crime rates in Santa Clarita?
*Did a new crime-fighting initiative work?
*Which crimes are highly variable—i.e., ones we would expect to swing widely from year to year?
*Are any crimes cyclical?
*Are there long-term trends in crime in Santa Clarita?

Each of these questions has a prescribed statistical approach (e.g., model selection for time-series, traditional frequentist tests…) I’m sure the Sheriff’s Department has staff or contracts to conduct these and far more sophisticated analyses. And since crime is very low in Santa Clarita relative to national averages, maybe the cursory details released every January are enough. But for those of you interested in the bigger picture, below are three visual aids. They took about 20 minutes to whip up so take from them what you will, but I think they reinforce one message: crime rates don't change as dramatically as the year-to-year comparisons might lead us to believe.

Summary Table of Crime, City of Santa Clarita
All values are taken from the reports published by the LA County Sheriff's Department[2]. These are total incidents reported.

click table to view larger image

Variability of Crime Rates, City of Santa Clarita
To control for population, here are per capita rates of crime. They are shown with standard deviation to provide an indication of how variable the numbers are[4]. If there was no directional change in crime, we’d expect to find annual crime rates within one standard deviation of the mean about 70% of the time[5]. The average rate of crime from 2000-2009 is shown as a blue bar (with standard deviation) next to the rate from 2010 alone, a black bar.

click graphs to view larger image

Annual Variation in Crimes, 2000-2010, City of Santa Clarita

This could be analyzed more rigorously—oh well, it's just a sketch. The graph shows the per capita crime rates with a best-fit line in hatched blue. None of the lines had a slope that was statistically different from zero (i.e., most crimes showed no significant, directional change) except for robbery and arson. Robbery had a significant positive slope, showing an increase in occurrence. Arson, meanwhile, had a significant negative slope so it declined in frequency as time progressed.

click graphs to view larger image

[1]SCV Raaaaaaaaaaw!
[2]Here is the preliminary 2010 report and here are the older reports
[3]I had to use the 2009 population estimate for the 2010 data; assuming the population grew in 2010, this would mean the per capita crime rates are slightly lower than presented.
[4] The most fundamental idea of statistics is that there is an average value and some random variation about that value. The annual ups and downs could indicate meaningful change, but we have to sort that out from variability or random fluctuations—background noise. I did standard deviation vs. standard error or confidence intervals because I think it's more meaningful here.
[5]Assuming normal distribution, and I know this isn't quite the technical definition of interpreting standard deviation. I’m going to stop with statistical asides now because if you don’t know them you don’t care and if you do know them you feel patronized and if you know a lot better than me you’re thinking how simplistic my approach has been. None of these are good.