The “One of Many” Fallacy

September 30, 2016 1 comment

I’ve been on book tour for nearly a month now, and I’ve come across a bunch of arguments pushing against my book’s theses. I welcome them, because I want to be informed. So far, though, I haven’t been convinced I made any egregious errors.

Here’s an example of an argument I’ve seen consistently when it comes to the defense of the teacher value-added model (VAM) scores, and sometimes the recidivism risk scores as well. Namely, that the teacher’s VAM scores were “one of many considerations” taken to establish an overall teacher’s score. The use of something that is unfair is less unfair, in other words, if you also use other things which balance it out and are fair.

If you don’t know what a VAM is, or what my critique about it is, take a look at this post, or read my book. The very short version is that it’s little better than a random number generator.

The obvious irony of the “one of many” argument is, besides the mathematical one I will make below, that the VAM was supposed to actually have a real effect on teachers assessments, and that effect was meant to be valuable and objective. So any argument about it which basically implies that it’s okay to use it because it has very little power seems odd and self-defeating.

Sometimes it’s true that a single inconsistent or badly conceived ingredient in an overall score is diluted by the other stronger and fairer assessment constituents. But I’d argue that this is not the case for how teachers’ VAM scores work in their overall teacher evaluations.

Here’s what I learned by researching and talking to people who build teacher scores. That most of the other things they use – primarily scores derived from categorical evaluations by principals, teachers, and outsider observers – have very little variance. Almost all teachers are considered “acceptable” or “excellent” by those measurements, so they all turn into the same number or numbers when scored. That’s not a lot to work with, if the bottom 60% of teachers have essentially the same score, and you’re trying to locate the worst 2% of teachers.

The VAM was brought in precisely to introduce variance to the overall mix. You introduce numeric VAM scores so that there’s more “spread” between teachers, so you can rank them and you’ll be sure to get teachers at the bottom.

But if those VAM scores are actually meaningless, or at least extremely noisy, then what you have is “spread” without accuracy. And it doesn’t help to mix in the other scores.

In a statistical sense, even if you allow 50% or more of a given teacher’s score to consist of non-VAM information, the VAM score will still dominate the variance of a teacher’s score. Which is to say, the VAM score will comprise much more than 50% of the information that goes into the score.

An extreme version of this is to think about making the non-VAM 50% of a teacher’s score always exactly the same. Denote it by 50. When we take the population of teacher VAM scores and average them with 50, the population of teacher VAM scores are now between 25 and 75, instead of 0 and 100, but besides being squished into a smaller range, they haven’t changed with respect to each other. Their relative rankings, in particular, do not change. So whoever was unlucky enough to get a bad VAM score will still be on the bottom.

Screen Shot 2016-09-30 at 6.30.44 AM.png

y=(x+50)/2

This holds true for other choices of “50” as well.

A word about recidivism risk scores. It’s true that judges use all sorts of information in determining a defendant’s sentencing, or bail, or parole. But if one of the most trusted and most statistically variant ones is flawed – and in this case racist – then a similar argument to the above could be made, and the conclusion would be as follows: the overall effect of using flawed recidivism risk scores is stronger, rather than weaker, than one might expect given its weighting. We have to be more worried about it, not less.

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Stuff I’ve been reading this week

September 24, 2016 4 comments
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In London next week

September 23, 2016 3 comments

I’m flying to London Sunday night to conduct my UK book tour. Here’s the schedule so far:

Cambridge University

Date: Tuesday, September 27th

Time: 12:30pm

Place: Faculty of Education, 184 Hills Road, Cambridge

More info: here

London’s How To Academy

Date: Tuesday, September 27th

Time: 6:45pm

Place: CNCFD- Condé Nast College of Fashion & Design, 16-17 Greek Street, Soho, London

More info: here

King’s College London

Date: Wednesday, September 28th

Time: 3pm

Place:  S-2.08, King’s College London, Strand, London

More info: here

In addition to the above, I’ll also be on BBC’s Today Programme on Tuesday morning, and I’ll be interviewed by Significance, the Royal Statistical Society & American Statistical Association magazine, the Guardian Science podcast, and Business Daily for BBC’s The World Service.

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WMD articles and interviews

September 22, 2016 6 comments

I haven’t been posting too often, in part because I’ve been traveling a lot on book tour, and also because I’ve been writing for other things and interviewing quite a bit. Today I wanted to share some of that stuff.

  1. I wrote a Q&A for Jacobin called Welcome to the Black Box.
  2. I wrote a piece for Slate called How Big Data Transformed Applying to College.
  3. Times Higher Education chose my book as their reviewed Book of the Week and had a nice spread about it.

There may be more, and I’ll post them when I remember them.

Also, great news! My book is a best-seller in Canada! Those Canadians are just the smartest.

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When statisticians ignore statistics

September 21, 2016 6 comments

This article about recidivism risk algorithms in use in Philadelphia really bothers me (hat tip Meredith Broussard). Here’s the excerpt that gets my goat:

“As a Black male,” Cobb asked Penn statistician and resident expert Richard Berk, “should I be afraid of risk assessment tools?”

“No,” Berk said, without skipping a beat. “You gotta tell me a lot more about yourself. … At what age were you first arrested? What is the date of your most recent crime? What are you charged with?”

Let me translate that for you. Cobb is speaking as a black man, then Berk, who is a criminologist and statistician, responds to Cobb as an individual.

In other words, Cobb is asking whether black men are systematically discriminated against by this recidivism risk model. Berk answers that he, individually, might not be.

This is not a reasonable answer. It’s obviously true that any process, even discriminatory processes that have disparate impact on people of color, might have exceptions. They might not always discriminate. But when someone who is not a statistician asks whether black men should be worried, then the expert needs to interpret that appropriately – as a statistical question.

And maybe I’m overreacting – maybe that was an incomplete quote, and maybe Berk, who has been charged with building a risk tool for $100,000 for the city of Philadelphia, went on to say that risk tools in general are absolutely capable of systematically discriminating against black men.

Even so, it bothers me that he said “no” so quickly. The concern that Cobb brought up is absolutely warranted, and the correct answer would have been “yes, in general, that’s a valid concern.”

I’m glad that later on he admits that there’s a trade-off between fairness and accuracy, and that he shouldn’t be the one deciding how to make that trade-off. That’s true.

However, I’d hope a legal expert could have piped in at that moment to mention that we are constitutionally guaranteed fairness, so the trade-off between accuracy and fairness should not really up for discussion at all.

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Let’s hear it for Penn Station bathrooms!

September 20, 2016 1 comment

I don’t know about you, but every time I go into the bathroom at Penn Station I cry a little bit.

That’s because I remember the 1980’s version of them, and believe you me, they’re so much better now. I grew up in the Boston area but I visited a bunch in high school, which means I spent way too much time in the very few available public toilet facilities. So I can appreciate me some improved amenities.

They are relatively clean! They have toilet paper, consistently! There’s soap available next to working sinks! And, probably most importantly, it’s not a threatening experience with dirty needles all over the floor.

For that matter, while I’m on the theme, have you noticed how much nicer JFK is now compared to 1988? Maybe it’s because I’ve been flying JetBlue a lot, but that terminal is nothing like the broken-down middle school experience I remember not so fondly.

That’s all I have today, just gratitude and anti-nostalgia. And I’m sure there are lots of things we miss as well from those days of New York City, but right now I can’t think of any besides cheaper rent.

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National Book Awards Longlist Finalist!

September 16, 2016 10 comments

It’s been an amazing two weeks – or actually, holy crap, only 10 days – since my book launched.

I found out two days ago that my book made it onto the Longlist for the National Book Award in Nonfiction, along with 9 other books. I haven’t had time to read the other books, but I did want to mention that last year’s NBA Nonfiction winner was Ta-Nehisi Coates’s excellent Between The World And Me, which I highly recommend.

What’s exciting about being on this list is that it means the ideas in the book will get exposure. So many really excellent books never get read by many people, because of bad timing, or small marketing and publicity budgets, or just bad luck. I’m so lucky to have a book that’s been given an extremely generous amount of all of that.

This week I’ve been busy on the West Coast going to book events and giving talks. My last one is today at noon in Berkeley (820 Barrows Hall). I’ve gotten almost no sleep what with jetlag, weird traveling requirements, and pure adrenaline, but it’s been absolutely incredible.

It’s been especially fantastic to meet the people who come to these events, which so far have taken place in Seattle, the San Francisco area, and a couple in New York last week. It seems like almost every person has something to tell me, a story of algorithms they encounter at work, or that their friends do, or questions about how to get a job that they can feel proud of in data science. Some of them are lawyers offering to talk to me about FOIA law or the Privacy Act. Incredible.

Some people who have read the book already will tell me it really changed their perspective, and others will tell me they’ve been waiting years for this book to be written, because it echoes their experience and long-held skepticism.

What?! Do you guys know what that means? It means the book is working!

In any case I’m overwhelmed and grateful to be able to talk to all of them and to start and continue the conversation. It’s never been more timely, and although I had hoped to get the book out sooner, I actually ended up thinking the timing couldn’t be better.

There’s only one thing. I wish I could send a message back to myself four years ago, when I decided to write the book, or even better, to Christmas 2014, when I was convinced it was an unwritable book. I’d just want to send some encouragement, a signal that it would eventually cohere. Those were some dark days, as my family can attest to.

Luckily for me, I had good friends who kept me from losing all hope. Thank you, blog readers, and thank you friends, and thank you Jordan and Laura especially, you guys are the best!

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