Right Wing Nation

The Manhattan Institute published a study, "The Effect of Residential School Choice on Public High School Graduation Rates." It’s an interesting study, although the authors make several dubious claims, such as:

Decreasing the size of school districts could improve educational outputs, including graduation rates, because it would increase the choice that parents have in the school system that educates their child. By making it easier to relocate from one school system’s jurisdiction to the next, smaller school districts make it possible for a larger number of families to exercise choice among different school districts. The more families are able to move from district to district, the less students can be taken for granted by schools, which, for a variety of reasons, don’t want to lose enrollment. This study provides empirical evidence that increasing the choice parents have in their child’s school district contributes to higher public high school graduation rates.

There are several problems with this general assertion. First, there are people moving into an area, and people who already reside in the area. While the former may, with relative ease, be able to buy a home in the school district of their choice (and many do), it’s a significantly greater burden (economically and psychologically) for the latter to sell their home and, say, move ten miles down the road to the next district. New residents, then, get more choice than current residents. Second, from this point on in the study, the authors use school district geographical size as a proxy variable for school choice, even though the two are very different variables.

I spent several hours trying to find data on school district size and graduation rates, first at NCES, then at several state education websites (one of these days, I’m going to rant and rave about the idiotic way data are organized and made available, by both the federal government and the states). I finally went where I should have gone in the first place, to the Indiana Department of Education site, because data are comparatively easy to retrieve and search. There was no way to retrieve both graduation rates and school district sizes in the same table, so I had to put two together and use a lookup function to pull the data together (there were a number of school districts that appeared in one but not the other; these data are only school districts that reported both geographical size and graduation rates). The Indiana data also code school districts by "demographic type," that is, rural, town, suburban, and metro (1-4).

First, here is a histogram of the district sizes, mean graduation rates, and number of districts for the Indiana data (the smallest school district in Indiana is 2 square miles, the largest is 457 square miles, and the mean is 122 square miles):

The graduation rates of the largest cohort (school districts that are 250 square miles or greater) and the smallest (smaller than 50 square miles) differ by only 1.7%. This does not seem to support the authors’ assertion that there is a statistically significant negative correlation between school district size and graduation rate, but these are aggregated data. First, I ran a Spearman correlation on the school district size ranks (see above) and the graduation rate (Spearman, and not Pearson, because one of the variables is a rank).

There is a negative correlation, but only a very weak one, far smaller than the authors reported. The next step was to run a Pearson correlation on school district size in square miles and graduation rate on all the Indiana school districts, instead of the data aggregated by district size rank:

And again, although there is a negative correlation, it is negligibly small. If there is a significant correlation between school district size and graduation rates, as the authors claim, it should show up in the Indiana school districts represented here, yet it is not. One reason for this may be that the authors analyzed data over several years and looked specifically at changes in school district sizes over time, and these are data from one year (2002-2003). That’s only a partial explanation. If, as the authors claim, decreasing school district size will positively affect graduation rates, we should see higher graduation rates in smaller districts, and at least in Indiana, we do not.

The Indiana data also ranked school districts as metro, suburban, town,, and rural (1-4) based on population density (Bloomington North is ranked as metro, whereas my high school is ranked as rural). Comparing the graduation rates of these four types yields interesting results:

From these aggregated data, we see differences in graduation rates between the groups. Metro school districts have the lowest mean graduation rate, followed by town, but rural and suburban schools have the highest graduation rates. It doesn’t look like we have a significant correlation between population density and graduation rate, but to check, I ran a Spearman correlation on school district type and graduation rate:

This correlation is stronger than either of the geographical size correlations, but it’s still a weak correlation. From these data, it appears that something is going on between graduation rate and population density somehow, but from the low rs, it looks like some variable embedded in district type is affecting graduation rate. It could have something to do with culture, or crime rate, or any number of variables that factor into population density. But from these Indiana data, I cannot verify the authors’ claim.