Steve Fuhrmann raises the question why the smaller school divisions seem to incur relatively larger administrative costs.

To approach that issue, let’s expand on the earlier post by looking at numbers of teachers and administrative employees statewide.

To start, here is a plot by division of the 2016 number of teachers (plus guidance counselors, librarians, technology instructors, principals and assistant principals) per student, vs. the number of students (in bureaucratese, the Average Daily Membership, ADM), as of the end of the 2016 school year.

The green points are counties; the red, cities.

Excel was glad to fit a straight line to the data but the correlations were poor. A “power” function, where the ADM was raised to a negative power, gave much nicer fits. The negative exponent tells us that the number of teachers per student decreases as the number of students increases but less rapidly as the ADM grows larger.

Here are those large divisions that stretch out the graph:

It we expand the x-axis to cut off the divisions >50K, we get a clearer picture of the smaller divisions.

And a further stretch gives this.

Those very small counties (ADM < 1,000) are hiring more teachers per kid than the larger counties and, indeed, than the very small cities. Among the merely small divisions, the cities and counties are behaving similarly, with the smaller divisions hiring a few more teachers.

Turning to non-teaching staff, whom VDOE calls “Administrative, Service, and Support Personnel,” let’s start with the totals per division.

Hmmm. Those small counties are hiring a __lot__ more people while the small cities are hiring fewer, albeit the cities’ correlation is small.

Let’s expand the axis.

Those small counties are hiring quite a few more support personnel than the cities or the larger counties.

Let’s see if we can sort this out by looking at the underlying numbers. First, the flat-out bureaucrats (“Administrative” in the summary of Table 18).

Here, the excellent fit to the negative exponents confirms what our eyeballs tell us: Lots of bureaucrats in the smaller divisions, whether county or city.

I’ll bet you a #2 lead pencil that the profusion of mandatory federal and state reporting explains much if not all of this phenomenon.

But, notice that the overall non-teacher population runs around 5% while these numbers are mostly <1%, so we have a way to go.

Technical and clerical counts paint a different picture.

The correlations here are slim no matter the fitted function and the slopes tell us the small divisions are hiring about the same relative numbers of clerical and technical staff as the larger divisions. The averages run just over 1%.

Next, instructional support.

The fitted functions (logarithmic) suggest that the smaller divisions hire relatively fewer in this category (fifteen or so divisions hire none) but the scatter (and the small correlations) argue against any significant trend. And, in any case, the numbers are quite small: Instructional Support is not a major budget item.

The Other Professional data paint a similar picture (albeit only with one division at zero), with slightly larger numbers.

Trades, Labor, Operative, and Service Personnel is the largest of these non-teaching categories. Here we see contrary trends (cities increasing with ADM; counties decreasing). And the correlations are non-trivial.

As to the small cities, we might speculate that the school systems and the city governments overlap, offloading some of the work. Whatever the mechanism, reducing the number of employees needed to run those small school systems can hardly be viewed as a problem.

Looking at transportation as a percentage of the Trades *et al*. total, we see that that Transportation dominates this category in the smaller counties.

It makes sense that the counties would have buses that must travel longer routes. And the relatively larger numbers in the Trades, *et al*., category largely explain the shapes of the Totals graphs, above.

So, buses in the smaller counties; bureaucrats in all the smaller divisions.

* * *

This post already is too long so I am left with homework assignments:

- Why do those smaller divisions, both cities and counties, hire more teachers per student than the larger divisions; and
- Does the state support recognize the disproportionate paperwork and transportation burdens borne by the smaller divisions?

Stay tuned . . .