Police, Academy

Death and taxes are both mortal locks in this world, but the government can only spend one of them.1  Which they do.  A lot.  That's not terribly surprising, since governments have an incredible number of responsibilities that -- like many responsibilities -- require money.  And because there's a finite amount of cash to go around,2 state governments have to make some tough decisions about where to lay it, which means spending has something important to tell us about priorities.

For example, it behooves a state to have safe streets and an educated citizenry, neither of which are free.  But which one gets more fiscal attention?  Here's a breakdown of how much money states spent on their police forces and public schools in 2010.

Based on these graphs, it seems that states -- on the whole -- tend to devote more of their resources to education.  That's useful information at the national level, but what about the states individually?  One thing we could do is come up with a way to describe what a typical state spends in these two areas and then use that value as a benchmark for comparison.  It's a simple idea, but it requires a little bit of consideration.

For instance, the mean state spending in 2010 was around $10.3 billion on schools and about $1.9 billion on police; the median spending was roughly $6.6 billion and $1.1 billion, respectively.  Either set of numbers would be a reasonable way to describe a "typical" state, but they're pretty far apart.  It's not totally clear which set of values would be more useful.

If we pick just two states to look at in isolation, it helps show where some of the tension is coming from.3  California's school spending was $60 billion, and its police spending was $15 billion.  North Dakota, on the other hand, spent only $1 billion on schools and $146 million on police.  Does that mean California prioritizes public education at 60 times the level North Dakota does?  Of course not.  California has way, way more people, so it spends more money than North Dakota on just about everything.

So if we want to be able to talk about a "typical" state, we're going to have to do something about the fact that a few states are decidedly atypical in the population department.4  If we look at spending per citizen, we get a fairer picture of what's going on.

The mean per capita spending was around $1600 on schools and $260 on police; the median per capita spending was about $1700 on schools and $290 on police.  Our suspicions about population seem to be confirmed: by accounting for that factor we've drastically reduced the effect of outliers and have a better sense of what states spend.  And where their priorities lie.

Everybody still spends more on education than police, which makes intuitive sense (a relatively small police department can generally handle a largish geographic area, but the overwhelming majority of small humans require education funding), but some states tip the scale in one direction or the other.  Maine, for example, spends more than average on schools and less than average on police.  Florida, on the other hand, spends more than average on police and less than average on schools.

So what?  Well, we can also look at outcomes related to spending.  We might hope, for instance, that school spending leads to people graduating from school, or that police spending helps limit crime.  Here are two scatterplots that show those relationships:

Spending more money on schools is associated with higher graduation rates, which is at least mildly comforting.5  The police numbers are not so comforting.  It seems higher police spending isn't correlated very strongly with crime.  And, if anything, it's actually associated with more crime.6  Think for a minute why that might be; if you can get your head around it, you're well on your way to being a better statistical consumer.

So how should states spend their tax dollars?  That's not a hypothetical question.  You can answer it next time you vote.

Teachers, want to have this conversation in class?  Check out our new lesson: Police, Academy.


1.  I like to think that if the phrase "mortal lock" were available in the 18th Century, Defoe would have been all over it.  Also, though I'm  technically correct to say that the government can't spend death, it turns out death and taxes aren't entirely independent.

2.  More or less.

3.  Though lately there's been some other interesting tension between CA and ND.

4.  In particular, California, New York, and Texas are throwing things out of whack.  Defoe also would've liked "out of whack."

5.  Notice I did not say "causes higher graduation rates" or "leads to higher graduation rates."  All we're allowed to infer here is that there is a positive association.  Otherwise you go directly to statistics jail.  Which, on average, is terrible.

6.  Seriously, statistics jail.


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