Follow the money

To absolutely nobody’s surprise, towns in Massachusetts with higher median household income do significantly better than towns with lower median household income. You can see a nice little scatter plot here for HH income and percent proficiency (average of math, English and science for a school district).

Other than the hard cap at 100 (no matter how well funded a school is, it’s not going to have more than 100 percent of its students passing); its a really damn good correlation.

Proficient Scatterplot


Here’s the same data but with advanced:


Advanced Scatterplot

It’s even more clear (also, the hard cap doesn’t really come into effect). A full 65% of the variance in advanced test scores can be explained by median household income.

So whats going on here? Well, the obvious idea is that these schools have more funding than poor school districts; this leads to better schools. Is that true?

In Massachusetts, the school system with the least per pupil expenditures is East Bridgewater. Yet they are above average in the MCAS (the state testing regime) for proficiency in English, Math and Science. The highest is Cambridge, yet they are below average in English and Science. Well, those are just anecdotes; so lets talk data:

I ran regressions for percent of students who are proficient in English, Math and Science and who are advanced in English Math and Science, all against per pupil expenditures.

The result, of the six regressions, none of the test scores were positively and significantly correlated with expenditures. Two, (percent of students who are advanced at English and percent of students advanced at math), were negatively correlated at p < 1%. Percent of Students advanced in Science was negatively correlated with expenditures at p <10%. The other three were not significant, but all the signs were negative.

Here’s the scatterplot for  for the percent of students advanced at English (with a trend line):

Eng Adv Scatterplot

The answer is no, it is not explained by (only) funding. If anything, funding is negatively correlated with test scores (ok, this is a cheat, I’m doing two single-linear regression at the same time and comparing them which is kind of a statistical bad thing. I did run a some multiple linear regressions, which don’t change much, although the the sign on funding flips to positive but not significant for advanced; the sign for advanced is still negative but also not significant).

This is weird at first glance it appears that rich towns have better schools, but that this has nothing to do with funding.

One theory is reverse causation; that is some school systems are randomly good, which attracts well off people. After all, school systems are probably the number one concern for for families in choosing which town to live in. There’s a ton of truth in this, I imagine. But i highly doubt its the whole story.

The most likely theory is that, for whatever reason, children of well off families are more likely to do well then children of less well off families. Whether that thing is due to culture, genetics, or other economic reasons (better access to healthcare as an example), I don’t know, but I think this is very important.
So here’s the aside where I’ll talk about how I wanted to finish this. I wanted to make points about culture, about moral reasoning, about economic aid and welfare. And I’m realizing that I’m just not able to do those topics justice, at least right here. So I’ll close with one thought.

The above analysis should scare you. Because, basically, the rich are getting richer. And its not because we just poor resources in to the rich districts and starve resources from poor districts. If it was we’d almost have reason to celebrate. All we’d have to do to fix schools is just pass a bill and move money around; but its just not that simple.


(all stats regarding education from

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