Saturday, May 23, 2015

Cleveland Police Department Diversity, And Yet Another Metric

After yesterday's post on diversity indexes, I assumed I wouldn't be looking at diversity measurement in the near future.  However today's news of another acquittal in a case of white police killing a unarmed African American, I thought some people may be interested in looking at these statistics specific to Cleveland.

The case was similar to prior cases, but essentially, two unarmed African Americans were killed by Officer Michael Brelo in Cleveland after a police chase.  Here's an article that covers more details than I care to here.


Yesterday, I used the the metric of a "diversity index"  to compare police departments to their constituencies (among other things).  The diversity index is calculated as an effective number of race, a metric borrowed from other areas of study.  Please see yesterday's post for a detailed methodology.
 For the Cleveland police department, I was only able to find data broken down into three categories: black, white, other.  For consistency I aggregated general population data in this way as well.  Here's what I found:

Cleveland Population Cleveland Police
Black 0.53 0.27
White 0.33 0.67
Other 0.14 0.06
Diversity Index 2.41 1.9

So 2.41 versus 1.9 diversity index (effective races) is a fairly large difference, but isn't huge.  Compared to yesterday's look at the US Senate which is about 1.2 versus 2.2 for the rest of the US population, this is actually a mild deviation.  But this analysis suffers from the same issue as yesterday's analysis of Ferguson MO and discussion of Apartheid South Africa.    In these cases, the diversity index tends to massively understate these demographic differences.

When the majority is flip flopped between the general population and the police department as it is in these cases (see table above, African Americans make up the majority of the Cleveland Population, yet a small minority of the police force), we need another metric.


Enter the chi-squared goodness of fit test.  Which, BTW, "goodness of fit" is really what it's called.  I spent 20 minutes convincing my boss once that this was a real stats test.  No really.  This test is useful in determining if a sample (the police department in this case) matches the categorical (race) distribution of the underlying general population.  For all of you math nerds, here's how the statistic is calculated:

Where O is the observed units in a category, and E is the Expected units in a category.

So, to implement, we calculate the expected distribution for each racial group and compare it to the expectation.  Here's the calculation from the data above:

Cleveland Population Cleveland Police Chi Squared Statistic
Black 0.53 0.27 201.15
White 0.33 0.67 523.92
Other 0.14 0.06 70.86
Diversity Index 2.41 1.9 795.92

But what do these chi-square values mean?
  • The total (795.9) is a significance test against the chi-squared distribution at k-1 (2) degrees of freedom.  This is a massively significant test statistic, as the threshold for a .001 p-value is only 13.8. (NON NERDS READ: HUGE DIFFERENCE HERE)
  • Each individual statistic is a measure of the variation in each group.  This can give us an idea of where the biggest statistical anomalies exist.  In this case, of course, it's that whites make up far more of the police force than the general population.
But really, what we learn from this case, is that we don't need fancy test statistics or analytics to know how different these two groups are.  It is obvious in their simple descriptive statistics.  But using exaggerated cases like this can sometime help us develop frameworks for analysis.


Social:  From a statistical point of view, there is once again a massive demographic difference between cops and the general population.  But honestly, in this case the difference is so huge, we don't really need significance testing, or any fancy analytics to test that.

Stats:  Obviously, in this case the diversity index shows it's shortcomings. However using general "goodness of fit" testing to determine differences in all groups seems to hold up better in instances of flipped demographics.  I'm going to continue pursuing this and determine if I can use the Goodness of Fit test as good measure of overall demographic differences.

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