Understanding Zuni Public School Dist. No. 89 v. Dep't of Ed.

Section: 7708(b)(2)(B)(i) of the law in question disregards districts with ppe above 95 pcile or below 5pcile.

The problem remains that the formula as written into law leads to conclusions that are absolutely absurd because it weighs all districts equally instead of weighing them by the number of students.

For instance, suppose the following distribution of 100 students into ten districts as follows

# of Students PPE
46 1000
1 10
1 10
1 10
1 10
1 10
1 10
1 10
1 10
46 0.001

Now, according to the letter of the law we can discard districts “with per-pupil expenditures . . . above the 95th percentile or below the 5th percentile of such expenditures . . . in the State.”

Since the top and bottom districts are above the 95th and below the 5th percentile (by definition, if you are counting per-district and there are ten you drop exactly the top and bottom) we can discard them and are left with the conclusion that this is a system that equalizes expenditures. This is, of course, patently absurd.

What's worse, the system can fail in exactly the opposite way - labeling a system as not equal when it substantially equal. For instance, consider the same 100 students divided into districts thusly

1 10
1 9
16 8
16 8
16 8
16 8
16 8
16 8
1 6
1 5

Once again, in a ten district system, the top and bottom districts are, by definition, in the 95th and 5th percentile and are dropped. We then conclude that the difference between the greatest and least (in this smaller set) is 33%>25% and therefore this system is not equalized. But of course, it is.

It fundamentally does not make sense to evaluate the spending per pupil in the various districts without any reference to the size of those districts. It is contrary to the fundamental rules of statistical analysis which state that you must assign a sensical weight to each input instead of simply counting them all equally.

Am I wrong here?