Saturday, February 15, 2014

Operational Efficiency 2: Are bigger schools always more efficient?

The Press-Citizen had an article about ways to cut operational costs over the coming years. There must be something in the air. This post is the second part of a multi-part series on operational costs.

In my first post, I presented overall data from 2012-2013 in graphical form that (a) illustrated some of the evidence supporting the claim that school enrollment is strongly negatively correlated with lower operational costs, and (b) highlighted the fact that this relationship is not always found.

In this post, I will examine 7 elementary schools in the Iowa City Community School District. I am cherry picking them to make it abundantly clear that (b) above applies to many of our district schools. Of these seven schools, 3 of them had more than 450 general education students enrolled in 2012-2013 and 4 of them hovered around 350 students. If it were the case that a larger school always has better operational efficiency than a significantly smaller school, then we would expect to find that that the three elementary schools with more than 450 students would have significantly better operational cost than each of the 4 schools that were around 350 students.

It turns out that it is the exact opposite. That is, all 4 smaller schools have better operational efficiency than each of the 3 larger schools. Here is a graphical representation:














The trend line shows that for these 7 schools there is a strong positive correlation between school enrollment and operational efficiency. In other words, the smaller schools were significantly better in terms of operational efficiency than the larger schools. Surprising, eh?

Let's add a little more surprise! The district average operational cost per general education elementary student in 2012-2013 (when controlling for special education and at-risk funds) was $4,305. It is a little hard to tell from the graph, but 4 of these 7 schools are above that average. The three that are below the average are from the group of smaller schools, and the fourth smaller school is just barely above the average. So, 3 of these 4 smaller schools actually lower the district average, but all 3 of the larger schools increase the district average.

How about some more? The four smaller schools have about the same total enrollment (give or take a few students), and if you replaced these four smaller schools with 3 larger schools with operational efficiency akin to the three represented, you'd end up with a net loss in operational efficiency.

So what accounts for the "aberration" from the standard correlation that we find for all 19 schools? I don't know exactly. It should be noted, however, that even strong negative correlations aren't perfect. But I do have some hypotheses.

One hypothesis: it could be that some teachers and staff at some of the larger schools have significantly more seniority, which would have a significant effect on pay. I have no evidence to support or contradict that hypothesis at this point. Even if the hypothesis is correct, it seems that should be taken into account when we evaluate how operationally efficient a school is. That is, if some schools, for whatever reason, tend to have more experienced teachers for longer periods of time than some other schools, then it is simply going to cost more to operate that school.

Another hypothesis: the distribution of students may be heavily concentrated in lower grades, which tend to have smaller class sizes. Upper grades must be too small to offset the increase in operational costs. I would have to check the distribution of students at the particular schools to evaluate this hypothesis.

Some hypotheses I think we can rule out:

(1) free and reduced lunch (FRL) rates have NOT really affected the numbers. One of the smaller schools and one of the larger schools significantly exceed the district's Diversity Policy figures, but each of the other 5 schools are right about where they are supposed to be.

(2) being around 350 students doesn't seem to hit a sweet spot that's just really good for operational efficiency reasons. There are some schools around that number that do really poorly. One of which I'll discuss in a subsequent post. Still, 350 divided by 14 (2 classes per grade) is an average of 25... which gives decent class sizes if its distributed appropriately (a big if!).  Furthermore, there are some schools between 450 and 500 students that do particularly well in operational efficiency, so that isn't necessarily a particularly bad number of students in terms of operational efficiency.

So, what now? First, we need to be careful with how we employ the bigger school = better operational efficiency rhetoric. That isn't always the case, and we have a number of cases in point here. Second, we need to examine whether our schools consistently have the same relative amount of operational costs compared to other schools. In other words, how did these four smaller schools compare to the 3 larger ones over a five-year period? Third, if there is a consistent trend here, we need ask a few questions: what accounts for the lower operational costs? Are there limitations to trying to replicate the results in other similarly-sized schools? Could this method be a way to (a) cut costs while (b) keeping many of our (relatively) smaller elementary schools open as our community seems to prefer?

Thursday, February 13, 2014

Operational Cost I: Introduction

The Iowa City Community School District is really worried about operational costs right now. Operational cost is a key metric that school districts use to evaluate the success of a school. I think it is a mistake to put too much weight on this metric, but even if it is a higher priority for a district than I think it ought to be, its actual use needs to be critically evaluated.

Here is a graph I've constructed based on the 2012-2013 data about elementary school operational efficiency:



On the one hand, it provides evidence that there is a strong negative correlation between cost per student and elementary school size. This is consistent with the message from relevant studies and our local administration. On the other hand, it reveals a much more complex relationship than bigger schools have lower operational costs than smaller schools. I will be asking a number of questions about these matters over the coming weeks in order to better facilitate discussion about operational cost in general and in our district more particularly.

A couple of caveats are in order: first, the information is a one-year snapshot. There could be peculiarities to this particular year that explain the results.

Second, the graph is based on controlling for special education and at-risk funding so that we get a much better idea of the funds that we are allowed to generate as spending authority for general education students. Special education funds have their own funding category, as do At-risk funds. Thus, I thought it important to control for those factors in my analysis. Likewise, special education classrooms also mean that a school with a larger proportion of special education funds probably also have fewer general education students than a comparably sized school with a smaller proportion of special education funds.