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[May 2012 note: Needle, the database system I used to collect, analyze and show this information, was acquired and shut down by Google. Thus many of the links below go to non-functional snapshots of Needle pages I took before the shutdown. The points should survive.]  

Boston Magazine recently published their annual Best Schools ranking. They've been doing this for years, and are known for various other Boston rankings as well (places to live, places to eat...), so by now you'd expect them to be pretty good at it.  

Here's what "pretty good at it" amounts to, in 2011: two lists of 135 school districts, one with some configuration information (enrollment, student/teacher ratio, per-pupil spending, graduation rate, number of sports teams, what kind of pre-k they offer, how many AP classes), the second with test scores, and exactly this much methodological transparency: "we crunched the data and came up with this".  

Some obvious things that you can't do with this information:  

- sort it by any criteria other than the magazine's rank
- see the stuff in the first table alongside the stuff in the second
- understand which figures are actually part of the ranking, in what weights
- fact-check it
- compare it in bulk to any other information about these schools
- compare it to any other information about the towns served by these districts
- figure out why certain towns were included or excluded
- find out what towns are even meant by non-town district names if you don't already happen to know
- evaluate the significance of any individual factor, or the correlations of any set of them  

This is not a proud state of the art. And the quality of secondary journalism around it emphasizes the point further: this article about Salem's low ranking basically just turns a table-row into prose sentences, with no context or analysis, and fails to even realize that the 135 districts in the ranking represent just the immediate vicinity of Boston, not the whole state. This Melrose article claims Melrose "climbed" from 97th last year to 94th, but then has to add a note that last year's ranking was of high schools, not whole districts, and thus not even the same thing. Swampscott exults in making the top 50. Malden fights back at being ranked 119th. But nobody actually knows what the rankings mean or signify, because Boston Magazine doesn't say.  

In an attempt to improve this situation a little, I imported these two tables of information into Needle:  


This in itself was sufficient to unify the two tables and render them malleable, which seems to me like the most basic start. Now at least you can re-sort them yourself, and choose what to look at next to what.  

And a little sorting, in fact, quickly reveals some statistical oddities. North Attleborough was listed with an SAT Reading score of 823, which since SAT scores only go up to 800, is very obviously wrong. Some trivial research verifies that this was a typo for 523, and while typos happen in journalism all the time, a typo in data journalism is a dangerous indication that some human has been retyping things by hand, which is never good. (This datum has now been fixed in the magazine's table.)  

More interestingly, when you start scrutinizing each district's 5th/8th/10th-grade MCAS scores, you find some surprising skews. Here are the MCAS and SAT scores for Georgetown:  

MCAS 5 English: 74
MCAS 5 Science: 54
MCAS 5 Math: 42  

MCAS 8 English: 81
MCAS 8 Science: 36
MCAS 8 Math: 51  

MCAS 10 English: 92
MCAS 10 Science: 90
MCAS 10 Math: 88  

SAT Reading: 570
SAT Writing: 566
SAT Math: 584  

Boston Magazine says they "looked within those districts to determine how schools were improving (or not) over time". But that's not what these scores are measuring. These aren't time-slices for a single cohort, these are different tests being given to different kids. If you're interested in history, the Department of Education profile of Georgetown includes annual MCAS results for 2006-2009, and all you have to do is scan down the page to spot the weird anomaly that is 8th grade Science. Every other test has healthy dark-blue bars for "Advanced" scores; but in 8th grade Science virtually no kids managed Advanced scores in any year. This pattern repeats in Wellesley in an even more dramatic fashion. An article from Wellesley Patch explains that their 8th grade science curriculum doesn't cover "space", while the MCAS does. It's an interesting ideological question whether curricula should be matched to the standardized tests, but whatever your opinion on that, it seems clearly misleading to interpret this policy issue as a quality issue.  

A little more sorting repeatedly raised another question: why is Cambridge ranked 25th? In virtually every test-score-based sort it falls close to the bottom of the table. In the magazine's ranking, Cambridge comes in ahead of Westford, at #26. But observe these scores for the two:  

MCAS 5 English: 59 - 88
MCAS 5 Math: 53 - 86
MCAS 5 Science: 45 - 85
MCAS 8 English: 75 - 95
MCAS 8 Math: 45 - 86
MCAS 8 Science: 34 - 78
MCAS 10 English: 70 - 97
MCAS 10 Math: 77 - 95
MCAS 10 Science: 59 - 94
SAT Reading: 498 - 587
SAT Writing: 493 - 582
SAT Math: 503 - 602
Graduation Rate: 85.2 - 94.6  

This doesn't even look close. But then notice these:  

Students per Teacher: 10.5 - 14.6
Per-Pupil Spending: $25,737 - $10,697  

Cambridge's spending per student is remarkable. It's almost 50% higher than the next highest, which is Waltham at $18,960. The 10.5 students per teacher is also the best ratio of the 135 schools listed, with 115th-ranked Salem in second place with 11. These factors seem like they should matter, and clearly they must be part of the magazine's ranking calculation, but if they're so uniformly not translating to better test scores or graduation rates in Cambridge, does this really make any sense?  

At least we ought to be able to say that these, along with the other non-test characteristics in the magazine like the number of sports teams and the number of AP classes, are different sorts of statistics than test scores. This seems increasingly true as you start looking at them in detail. Plymouth is listed as having 94 sports teams, for example. Can you name 94 different sports? I can't, and the Plymouth High School web site only claims they participate in 19. Newton is listed as having 39 AP classes, and Boston as having 155. But there are only 34 AP subjects, so it seems like a pretty safe guess that in these two multi-high-school districts the magazine is adding the totals for each school. It's hard for me to see what that accomplishes.  

So for my own interest, at least, I created my own Quant Score, which is calculated like this:  

- take all 9 of the listed MCAS scores, drop the lowest one, and sum the other 8
- divide each of the three SAT scores by 3, to put them into a range where they're each worth around twice as much as an individual MCAS score, and add those in
- multiply the graduation rate by 2, to put it into a similar range to the SAT scores, and add that in, as well  

These factors are admittedly arbitrary, so you're welcome to try your own variations, but at least I'm telling you exactly what goes into mine, so you know what you're varying against. I deliberately left out all the other descriptive metrics from this calculation, including student/teacher ratio and spending. I then reranked the schools according to these Quant Scores. See the comparison of the magazine's ranking and mine here.  

The differences are pretty dramatic. Three schools from outside the magazine's top 20 move into my top 10 (and 2 more from outside the magazine's top 10). The magazine's #s 6 and 8 drop to 28 and 30 in my list. Watertown and Waltham drop from 53 and 54 in the magazine to 100 and 114 in my list. Swampscott will be displeased to see that my re-ranking them sends then back out of the top 50. Malden will probably not be much appeased that I've bumped them up from 119 to 118. Acton and Winchester will be thinking about staging parades for me. And Cambridge (where I live, and where my pre-K daughter will go to school unless we take some drastic action) plunges from 25th to 107th.  

But these are not answers, these are more questions. Most obviously: Why? I'm not claiming my Quant Score is definitive in any way, but it measures something, and I'm willing to claim that what it measures is something more coherent than what the magazine's rank measures. So this sets me off on the quest for better explanations, for which we obviously need more data.  

Needle is good at integrating data, so I have integrated a bunch of it: per-capita incomes, town populations, unemployment rates, district demographic breakdowns, lunch subsidy percentages and 2010 election results. Some of these apply to towns, not districts, and several districts serve multiple towns, but Needle loves one-to-one and one-to-many relationships the same, so I've done properly weighted multi-town averages. (Don't try that in a spreadsheet.)  

And then I started comparing things. Per-pupil spending seems like it ought to matter, but it shows very little statistical correlation to quant scores. Student/teacher ratios, sports-team counts and AP classes also seem like they ought to matter, but the numbers don't support this.  

Per-capita income, on the other hand, matters. The percentage of students receiving lunch subsidies matters even more. In fact, this last factor (the precise calculation I used was adding the percentage of students receiving free lunch and half of the percentage of students receiving partially subsidized lunch) is the single best predictor of quant score that I've found so far. This is depressingly unsurprising: poverty at home is hard to overcome: hard enough for individuals, and even harder in aggregate.  

With this in mind, then, I ran a quick linear regression of quant score as a strict function of lunch-subsidy percentage, and used that to calculate predicted quant scores for each district. The depressing headline is how small those variations are. In a quant-score range from 1531 to 727, only 10 districts did more than 100 quant points better than predicted, and only 10 districts did more than 100 points worse. If I use the square roots of the lunch-subsidy percentages, instead, only 6 districts beat their predictions by 100, and only 8 miss by 100.  

If I toss in town unemployment rates, Democratic vote percentages in the 2010 Senate election, and town per-capita income, I can get my predictions so close that only 1 school did more than 100 points better than expected, and only two did more than 100 points worse. This is daunting precision.  

But OK, even if the variations are small, they're there. So surely this is where those aspirational metrics like spending must come into play. Throwing money at students in school may not be able to counteract poverty at home, but doesn't it at least help?  


Students per Teacher? No.
AP classes? No.
Percentage of minority students? No.  

I'm by no means saying that there isn't an explanation, or more of an explanation, or other factors. But if there are, I haven't found them yet.  

But at least I'm trying. And I give you the data so you can try, too. I submit that this is what data journalism should be trying to do. We are trying to find knowledge in data. Secrecy and opaqueness and non-interactivity are counter-productive. It's more than hard enough to find truth even with all the data arrayed in front of us. If there's an equivalent of the Hippocratic Oath for data journalists, it should be that we will endeavor to never make the truth more obscure.  

[Space for discussion here.]  

[Postscript, 10 September: The more I thought about that 823/523 error, the more I worried that there might be other errors that weren't as obvious, so I used Needle to cross-check all the test-scores against the official DOE figures. Two more were wrong. Manchester Essex's SAT Reading score was 559, not 599, which I'm guessing would lower their #6 magazine rank, perhaps considerably. In my rankings it dropped them from 28 to 31. Ashland's SAT Reading score was also wrong, 531 not 537, but this didn't change their rank in my method. Both corrections moved those schools' scores closer to my predictions.]  

[Postscript, 12 September: But charter schools do better relative to expectations, right? Nope.]
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