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?

1 comment:

  1. Jeesh, Michael, can you explain everything to do with math this well? I've been trying to get at many of the things you point out here in relation to original case they made to close Hills. I'd LOVE to show you that original report someday...the data they chose was so twisted as to be unrecognizable, particularly in that they did not actually report or verify actual staffing costs. Hills was portrayed with multiple full-time grant writers for example if I remember correctly. The moment I first looked at the report it was clear it was made to come to a predetermined conclusion by any means possible (early committee meeting minutes also point this out in a number of places). One of the first things that jumped out when I saw it was, HUH? They had SO many staff listed and I just knew we did not have that many people at that I printed off the school staff list...not even I met with the principal at that time and went over the printed list from the school, updated it in my notes, and it was clear to me the district was either lying or had no idea whatsoever how many staff it had at any given school, at least, in a way they could tie numbers to names. If they can't tie numbers to names, then the numbers simply can't be verified. Nobody, not at the Gazette anyway, was willing to report on it...surprise, surprise.