How would you measure "racial differences in per-pupil funding" if not with difference in expenditure per-pupil?

Well how should it be measured then?

What makes it so bad, and what would be a better way?

If funding was

$6k for white pupil in NY $5k for black pupil in NY

$3k for white pupil in Ohio $2k for black pupil in Ohio

Clearly that's more money for white pupils regardless of location

Now imagine that there's 60 black students in NY and 10 in Ohio, but 10 white students in NY and 60 in Ohio

That means total funding is 320k for 70 black pupils and 240k for 70 white students

So you can spin the figures to say that black pupils get more funding, but the truth is the opposite.

I don't have a great alternative in mind, but here is why it's not a good measure: suppose I take any school, then give the teachers a pay raise or a pay cut of X%. Nothing has fundamentally changed about the school, but per student expenditure has gone up or down, respectively, depending on which direction the salary adjustment was.

If you increase or decrease the pay of the teachers, I would expect to see an outcome on student educations over the long term.

For example, if District X pays better than neighboring district Z, District X will most likely have greater chance of hiring teachers in both districts, letting them choose the most qualified. Resulting in the school with higher salaries naturally getting more teacher candidates to choose from.

While some expenditures might not have a direct impact on student educations, they still have some effect. Another one would be - a school investing in a new Air conditioning and filtration system, students are probably going to have an easier time learning when they don't have to worry about being too hot or too cold in their classrooms.

I mean hypothetically all the money given to a school could be used to build a giant statue but does that actually happen? In your example, are we sure giving teachers a pay rise does not make them more motivated and hence leading to better outcomes?

Okay, that's a fair point. Give the lunch room staff a pay raise instead, or build that statue lol :)

Or allow that school to recruit better teachers over time or have fewer students per teacher.