Wednesday, August 8, 2012

60 Steps Revisited: Step 33 - Measure Association

Back in 2009, I did a series of posts covering the excellent book Crime Analysis For Problem Solvers. The book is published by the US DOJ's Problem Oriented Policing Center (POP Center). Because of the value I think this book has for crime analysts, and policing in general, I am going to re-post this series on here on the blog.

This post in our walk through Crime Analysis For Problem Solvers is going to cover Step 33 - Measure Association. This post is important to being able to put the previous post, Step 32 - Conduct Case Control Studies into practice.

One consequence of providing detailed crime stats to your department is that occasionally you will get that person who will look at the numbers of two different statistics and will then declare that an increase in one thing caused a decrease in something else. At my shop, I had an officer declare that an increase in the number of citations written caused a decrease in the number of accidents. At first glance that might seem logical, but unfortunately, it's not that easy.


The way to test that assumption is to use a statistical technique to calculate the coefficient of correlation between two statistical variables. 
There are many ways to calculate association. Often a correlation coefficient is used. Correlation coefficients range from -1 to 1. A negative correlation means an increase in one characteristic is associated with a decline in the other (and a decline is one associated with an increase in the other). A positive correlation means that an increase in one characteristic is associated with an increase in the other (and a decline in one is associated with a decline in the other). Big coefficients mean strong associations (positive or negative). If a correlation coefficient is near zero, there is an absence of association - a change in one characteristic is unrelated to a change in the other. Any spreadsheet or statistical analysis program can perform the calculations.
In the example I mentioned regarding traffic citations and accidents, after calculating the coefficient of correlation, his assertion was proven to be false.

But often, we're trying to determine the association of something that doesn't lend itself to the statistical technique of coefficient of correlation. In fact, the Case Control Studies we learned about in Step 32 do not lend themselves to using coefficient of correlation. The authors suggest using odds ratio to measure these associations.
Odds ratios can be any number greater than zero. When an odds ratio is equal to one, there is no association between the characteristic and the outcome. That is, the risk of the outcome is the same whether or not the characteristic is present. If the odds ratio is between 0 and 1, risk is higher when the characteristic is absent than when it is present (a negative association). An odds ratio of .1 indicates the risk of the outcome when the characteristic is present is a tenth of that when the characteristic is absent. If an odds ratio is greater than 1, the risk is higher when the characteristic is present than when it is absent (a positive association). An odds ratio of 3 means that the risk of the outcome is three times as large when the characteristic is present than when it is absent.
I would encourage you to read the entire chapter Step 33 - Measure Association to learn how to calculate odds ratio. This is a great technique for determining cause and effect and not relying on anecdotal evidence.

Next time we'll look at Step 34 - Look For Crime Facilitators.

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