Causal inference is hard

From Slate we have this interesting debate about what ended China's famines:

Scholars continue to argue over how much of China’s agricultural turnaround was due to the capitalist incentive structure, how much resulted from earlier investments, and how much was a trick of the weather. Some say the end of collective farming accounted for nearly three-quarters of the improvements in productivity, while others say it was responsible for no more than one-third.

It’s fine to treat China’s food revolution as a fairy tale. The changes were so dramatic that it’s hard not to. But let’s make sure we get the moral of this story correct. Changing the incentives isn’t a magic trick that can turn any lagging economy into a global juggernaut. Investment in infrastructure, research and development, and putting money into the pockets of workers work wonders as well. And a little sunshine doesn’t hurt, either.

So we basically have five possible explanations, all of which could explain some or all of this change:

 

1. Ending collective farming (capitalist reform)
2. Infrastructure development
3. Government subsidies to farmers (i.e. financial support to poor people)
4. Research on improved crops
5. Unexpected good weather

What makes this tough is that many of these explanations suggest different policy conclusions when you try and apply these lessons to other contexts.  For example, if the dominant cause was improved infrastructure then maybe we should tax more in order invest in infrastructure projects.  If it was giving more money to poor people then maybe the minimum wage is where we should put our focus.  If it was the weather (luck) then maybe these results can't be generalized. 

Since complex phenomenon, like improved food supply, like have many causes, it can be hard to decide which ones to focus on.  After all, some of these factors could have been counter-productive, but the next causal effect could be positive. 

But it seems pretty obvious why experiments are not sensible here.  These sorts of questions are, and I think always will be, very hard to answer. 

There are valid reasons to be concerned about the SAT, starting with its history

Given the dust and confusion being kicked up by the SAT, there's a point that I want to get on the record. Though the standard critiques of the SAT, most notably from the New York Times are flawed in almost every particular (except about the essay section, which pretty much everyone now agrees was a train wreck), there are valid critiques of the test, both in its current state and in where it came from.

From Wikipedia:

After the war in 1920, Brigham joined Princeton as a faculty member, and he collaborated with Robert Yerkes' from the Army Mental Tests and published their results in the influential 1923 book, A Study of American Intelligence authored by Brigham with the forward by Yerkes. Analyzing the data from the Army tests, Brigham came to the conclusion that native born Americans had the highest intelligence out of the groups tested. He proclaimed the intellectual superiority of the "Nordic Race" and the inferiority of the "Alpine" (Eastern European) and "Mediterranean Races" and argued that immigration should be carefully controlled to safeguard the "American Intelligence." Nothing troubled Brigham so much however, as miscegenation between blacks and whites, as Brigham believed "Negroes" were by far the most intellectually inferior race.

Though he later in 1930 denounced his expressed views on the intellectual superiority of the "Nordic Race" and specifically disowned the book, it had already been instrumental in fueling anti-immigrant sentiment in America and the eugenics debate. It was used most effectively by Harry Laughlin in the 1924 congressional debates leading to anti-immigrant legislation. 

Brigham chaired the College Board commission from 1923 to 1926, leading to the creation of the Scholastic Aptitude Test, now simply called the SAT Reasoning Test.

One of the hidden costs of bad arguments dominating one side of a debate is that they tend to crowd out the valid arguments on that side. I haven't seen convincing evidence that the SAT is being over-emphasized in the college selection process or that, other than the essay section, the test was urgently in need of radical changes, but there serious and precedented concerns with the way the test can be misused.

Being a management consultant who does not suffer fools is like being an EMT who faints at the sight of blood

An April 1st post on foolishness.

When [David] Coleman attended Stuyvesant High in Manhattan, he was a member of the championship debate team, and the urge to overpower with evidence — and his unwillingness to suffer fools — is right there on the surface when you talk with him.

Todd Balf writing in the New York Times Magazine

Andrew Gelman has already commented on the way Balf builds his narrative around Coleman ( "In Balf’s article, College Board president David Coleman is the hero and so everything about him has to be good and everything he’s changed has to have been bad.") and the not suffering fools quote certainly illustrates Gelman's point, but it also illustrates a more important concern: the disconnect between the culture of the education reform movement and the way it's perceived in most of the media.

(Though not directly relevant to the main point of this post, it is worth noting that the implied example that follows the line about not suffering fools is a description of Coleman rudely dismissing those who disagree with his rather controversial belief that improvement in writing skills acquired through composing essays doesn't transfer to improvements in writing in a professional context.)

There are other powerful players (particularly when it comes to funding), but when it comes to its intellectual framework, the education reform movement is very much a product of the world of management consultants with its reliance on Taylorism, MBA thinking and CEO worship. This is never more true than with David Coleman. Coleman is arguably the most powerful figure in American education despite having no significant background in either teaching or statistics. His only relevant experience is as a consultant for McKinsey & Company.

Companies like McKinsey spend a great deal off their time trying to convince C-level executive to gamble on trendy and expensive "business solutions" that are usually unsupported by solid evidence and are often the butt of running jokes in recent Dilbert cartoons.  While it may be going too far to call fools the target market of these pitches, they certainly constitute an incredibly valuable segment.

Fools tend to be easily impressed by invocations of data (even in the form of meaningless phrases like 'data-driven'), they are less likely to ask hard questions (nothing takes the air out of a proposal faster than having to explain the subtle difference between your current proposal and the advice you gave SwissAir or AOL Time Warner), and fools are always open to the idea of a simple solution to all their problems which everyone else in the industry had somehow missed. Not suffering fools gladly would have made for a very short career for Coleman at McKinsey.

Perhaps we should add "opaque" to the list of journalists' vocabulary questions

Last week, Andrew Gelman criticized Todd Balf for picking words and phrases for their emotional connotation rather than for their actual meaning in his New York Times Magazine article on the changes in the SAT. 'Jeffersonian' was the specific term that Gelman choked on. I'd add 'opaque' to the list though the blame here mainly goes to David Coleman, president of the College Board and quite possibly the most powerful figure in the education reform movement:

For the College Board to be a great institution, [Coleman] thought at the time, it had to own up to its vulnerabilities. ... “It is a problem that it’s opaque to students what’s on the exam."

There's a double irony here. First because Coleman has been a long-standing champion of some very opaque processes, notably including those involving standardized tests, and second because test makers who routinely publish their old tests and who try to keep those tests as consistent as possible from year to year are, by definition, being transparent.

This leads to yet another irony: though the contents of the tests are readily available, almost none of the countless articles on the SAT specifically mention anything on the test. The one exception I can think of is the recent piece by Jennifer Finney Boylan, and it's worth noting that the specific topic she mentioned isn't actually on the test.

Being just a lowly blogger, I am allowed a little leeway with journalistic standards, so I'm going to break with tradition and talk about what's actually on the math section of the SAT.

Before we get to the questions, I want to make a quick point about geometry on the SAT. I've heard people argue that high school geometry is a prerequisite for the SAT. I don't buy that. Taking the course certainly doesn't hurt, but the kind of questions you'll see on the exam are based on very basic geometry concepts which students should have encountered before they got to high school. With one or two extremely intuitive exceptions, all the formulas you need for the test are given in a small box at the top of the first page.

As you are going through these questions, keep in mind that you don't have to score all that high. 75% is a good score. 90% is a great one.

You'll hear a lot about trick questions on the SAT. Most of this comes from the test's deliberate avoidance of straightforward algorithm questions. Algorithm mastery is always merely an intermediary step -- we care about it only because it's often a necessary step in problem solving (and as George Pólya observed, if you understand the problem you can always find someone to do the math) -- but when students are used to being told to factor this and simplify that, being instead asked to solve a problem, even when the algorithms involved are very simple, can seem tricky and even unfair.

There are some other aspects of the test that contribute to the reputation for trickiness:

Questions are written to be read in their entirety. One common form breaks the question into two parts where the first part uses a variable in an equation and the second asks the value of a term based on that variable. It's a simple change but it does a good job distinguishing those who understand the problem from those who are merely doing Pavlovian mathematics where the stimulus is a word or symbol and the response is the corresponding algorithm;

Word problems are also extensively used. Sometimes the two-part form mentioned above is stated as a word problem;

One technique that very probably would strike most people as 'tricky' actually serves to increase the fairness of the test, the use of newly-minted notation. In the example below, use of standard function notation would give an unfair advantage to students who had taken more advanced math courses.

One thing that jumps out when us math types is how simple the algebraic concepts used are. The only polynomial factoring you are ever likely to see on the SAT is the difference between two squares.

A basic understanding of the properties of real numbers is required to answer many of the problems.

A good grasp of exponents will also be required for a perfect score.

There will be a few problems in basic statistics and probability:

I've thrown in a few more to make it a more representative sample.

We can and should have lots of discussions about the particulars here -- I'm definitely planning a post on Pavlovian mathematics (simple stimulus/algorithmic response) -- but for now I just want to squeeze in one quick point:

Whatever the SAT's faults may be, opaqueness is not among them. Unlike most of the instruments used in our metric-crazed education system, both this test and the process that generates it are highly transparent. That's a standard that we ought to start extending to other tests as well.

Weekend blogging -- due to cuts in arts programs, school orchestras have been forced to adopt extreme cost-cutting measures

When you get past the novelty, the musicianship is even more impressive.



The novelty is, of course, what initially drives the clicks but it ages quickly when played badly. (From Spike Jones to the Austin Lounge Lizards, successful comic music acts tend to require solid musicians.)

I'd go further in this case. For me, they move entirely past the joke. Their AC/DC covers are so driving and percussive you soon stop wondering why these cellos are playing heavy metal and start wondering why don't all heavy metal acts use cellos.




A musician friend, who had only seen "Every Teardrop," asked if they always played just one cello. I told him no, someone would lose a finger.







These guys aren't the first classical musicians to display a talent for popular music. Yo-Yo Ma comes to mind and, believe it or not, Liberace started out as both a very promising concert pianist and a first rate Boogie-woogie piano player, but I can't recall any performers who moved so smoothly back and forth.

Fiscal prudence (a never ending saga)

This is an important point about financial planning from Megan McArdle:

When people end up in financial trouble, you often hear tsk-tsking about premium cable and fancy vacations. But if you talk to bankruptcy lawyers and financial counselors, that isn't the normal story you hear. You're more likely to hear about car loans, mortgages, alimony. In other words, it's not the luxury splurges that do you in -- it's the fixed expenses. That's because discretionary luxury expenses can be cut in an emergency, while the fixed payments go on and on until they empty your bank account.

She might be a libertarian in her politics, but she is a lot like a Canadian in terms of fiscal prudence.  Now I agree that there may be larger social issues that are making it harder for people to meet fixed expenses (e.g. wage stagnation) but at an individual level this is a calculation well worth making. 

On SAT changes, The New York Times gets the effect right but the direction wrong

That was quick.

Almost immediately after posting this piece on the elimination of the SAT's correction for guessing (The SAT and the penalty for NOT guessing), I came across this from Todd Balf in the New York Times Magazine.

Students were docked one-quarter point for every multiple-choice question they got wrong, requiring a time-consuming risk analysis to determine which questions to answer and which to leave blank. 

I went through this in some detail in the previous post but for a second opinion (and a more concise one), here's Wikipedia:

The questions are weighted equally. For each correct answer, one raw point is added. For each incorrect answer one-fourth of a point is deducted. No points are deducted for incorrect math grid-in questions. This ensures that a student's mathematically expected gain from guessing is zero. The final score is derived from the raw score; the precise conversion chart varies between test administrations.

The SAT therefore recommends only making educated guesses, that is, when the test taker can eliminate at least one answer he or she thinks is wrong. Without eliminating any answers one's probability of answering correctly is 20%. Eliminating one wrong answer increases this probability to 25% (and the expected gain to 1/16 of a point); two, a 33.3% probability (1/6 of a point); and three, a 50% probability (3/8 of a point). 

You could go even further. You don't actually have to eliminate a wrong answer to make guessing a good strategy. If you have any information about the relative likelihood of the options, guessing will have positive expected value.

The result is that, while time management for a test like the SAT can be complicated, the rule for guessing is embarrassingly simple: give your best guess for questions you read; don't waste time guessing on questions that you didn't have time to read.

The risk analysis actually becomes much more complicated when you take away the penalty for guessing. On the ACT (or the new SAT), there is a positive expected value associated with blind guessing and that value is large enough to cause trouble. Under severe time constraints (a fairly common occurrence with these tests), the minute it would take you to attempt a problem, even if you get it right, would be better spent filling in bubbles for questions you haven't read.

Putting aside what this does to the validity of the test, trying to decide when to start guessing is a real and needless distraction for test takers. In other words, just to put far too fine a point on it, the claim about the effects of the correction for guessing aren't just wrong; they are the opposite of right. The old system didn't  require time-consuming risk analysis but the new one does.

As I said in the previous post, this represents a fairly small aspect of the changes in the SAT (loss of orthogonality being a much bigger concern). Furthermore, the SAT represents a fairly small and perhaps even relatively benign part of the story of David Coleman's education reform initiatives. Nonetheless, this one shouldn't be that difficult to get right, particularly for a publication with the reputation of the New York Times.

Of course, given that this is the second recent high-profile piece from the paper to take an anti-SAT slant, it's possible certain claims weren't vetted as well as others.

The SAT and the penalty for NOT guessing

Last week we had a post on why David Coleman's announcement that the SAT would now feature more "real world" problems was bad news, probably leading to worse questions and almost certainly hurting the test's orthogonality with respect to GPA and other transcript-based variables. Now let's take a at the elimination of the so-called penalty for guessing.

The SAT never had a penalty for guessing, not in the sense that guessing lowed your expected score. What the SAT did have was a correction for guessing. On a multiple-choice test without the correction (which is to say, pretty much all tests except the SAT), blindly guessing on the questions you didn't get a chance to look at will tend to raise your score. Let's say, for example, two students took a five-option test where they knew the answers to the first fifty questions and had no clue what the second fifty were asking (assume they were in Sanskrit). If Student 1 left the Sanskrit questions blank, he or she would get fifty point on the test. If Student 2 answered 'B' to all the Sanskrit questions, he or she would probably get around sixty points.

From an analytic standpoint, that's a big concern. We want to rank the students based on their knowledge of the material but here we have two students with the same mastery of the material but with a ten-point difference in scores. Worse yet, let's say we have a third student who knows a bit of Sanskrit and manages to answer five of those questions, leaving the rest blank thus making fifty-five points. Student 3 knows the material better than Student 2 but Student 2 makes a higher score. That's pretty much the worst possible case scenario for a test.

Now let's say that we subtracted a fraction of a point for each wrong answer -- 1/4 in this case, 1/(number of options - 1) in general -- but not for a blank. Now Student 1 and Student 2 both have fifty points while Student 3 still has fifty-five. The lark's on the wing, the snail's on the thorn, the statistician has rank/ordered the population and all's right with the world.

[Note that these scales are set to balance out for blind guessing. Students making informed guesses ("I know it can't be 'E'") will still come out ahead of those leaving a question blank. This too is as it should be.]

You can't really say that Student 2 has been penalized for guessing since the outcome for guessing is, on average, the same as the outcome for not guessing. It would be more accurate to say that 1 and 3 were originally penalized for NOT guessing.

Compared to some of the other issues we've discussed regarding the SAT, this one is fairly small, but it does illustrate a couple of important points about the test. First, the SAT is a carefully designed tests and second, some of the recent changes aren't nearly so well thought out.

Why I am optimistic about 538

As people may or may not know, Nate Silver has launched an independent website.  Some of the people whom I respect the most on the internet (Noah Smith, Paul Krugman, Andrew Gelman) have pointed out some of the teething problems, where the inclusion of either more data or more model information in the article would have been helpful. 

In essence, I think that the website is trying to balance a number of things at the same time:

1. Use of predictive statistical models
2. Accessible journalism
3. Thought provoking/contrarian views
4. A diverse body of topics

All of these elements can be important, but there can be a steep learning curve as to where the value is to the news consumer.  For example, Andrew Gelman points out in the sports column (as I best understand it -- I know nothing about sports and I am going entirely on the model comments) that he is having trouble figuring out the underlying model which makes interpretation more complicated.   In the comments, there was a request for the correlation matrix, which is deadly reasonable in the statistics field but might not appeal to the median reader.

So why am I optimistic?  Because Nate Silver has tended to be very data driven in his endeavours.  I have a strong prior expectation that the initial offerings are, at least partially, a test to see where he can add value relative to other media services (both on and off of the web).  Under these conditions, a good empirical tester would deliberating try out approaches and opinions that will likely fail.  Because that is the only way to get actual data on what works and to find unexploited niches. 

If people constantly want more statistics and articles with well described models (or links to well described models) do well then I bet we will see a lot more of them.  Or at least I hope so. 

So I am going to wait for about 90 days and then see what the site looks like.  I could be wrong about this approach -- but I am willing to put my opinion out there and see if the data support it going forward. 

A tentative foray into e-publishing

Regulars may have noticed that the blog went a bit fallow in late April and early March, though Joseph (who is disgustingly hardworking) picked up a great deal of the slack. My time was being diverted into putting together a couple of small books of puzzles from the Thirties and Forties and, sometimes more dauntingly, learning the subtleties of Kindle publishing.

The titles are "Classic Puzzles for the Classroom" and "Classic Word Puzzles for the Classroom." Other than some pagination and layout issues (more on that later in the post), the results were fairly close to what I had in mind. I believe they meet Abraham Lincoln's famous standard of literary acceptability: people who like this sort of thing will find in this the sort of thing they like.

Both books are collections of puzzles and games from Golden Age comics, selected from books now in the public domain and arranged in teacher-friendly sections. The target audience is small but the material was a good fit with the ongoing math ed and mathematical recreation threads here and at You Do the Math (which is about to go active again). I'll come back to the actual puzzles in future posts. For now though, here are a few notes on my (very limited) experience with e-books.

I like old comic books to look like old comic books, but not too much. Since I was using publicly available scans of very old magazines, some retouching was necessary but I tried to make it as unobtrusive as possible. I used GIMP for individual touch-ups and ImageMagick for things like rescaling large numbers of pictures. I'm no expert on graphics (more of a video guy) but the learning curve wasn't bad at all.

I had initially planned on doing the books as PDFs but Amazon's instructions said that would cause formatting problems and suggested submitting Word documents instead so that's what I did. I'm not sure it helped. Based on my experience and what I've read since, Kindle e-books are not a graphics-friendly format and, unfortunately, I was doing a couple of picture book. Formatting and pagination changed from device to device and, in the case of the Kindle preview function, changed while viewing the document on the same device -- as I flipped back and forth through the preview, a picture that started out on page nine might be on page ten when I flipped back. I tried playing with formatting and inserting a break for every new page but I eventually accepted defeat and simply left the page numbers out of the index with an explanatory note.

Recently, I came across a tool called Kindle Comic Creator, which I will try if I do another graphics-heavy e-book.

The rest of the publishing process was remarkably easy. The online form is fairly short and if I hadn't had to keep uploading reformatted drafts the process would probably have taken an hour or two.

I'll open the floor for suggestions now. Does anyone out there have relevant e-publishing experience to share?

This is also true in Epidemiology

Frances Woolley is back with a great post on how junior people focus on the statistical models and not the data set itself.  This is unfortunate as domain-specific knowledge of the data and the expected relations in the data is often the most important contributions.  When I worry about "field-jumping", it is this sort of problem that jumps up:

But all else is not equal. Using probit will not save a regression that combines men and women together into one sample when estimating the impact of having young children on the probability of being employed, and fails to include a gender*children interaction term. (The problem here is that children are associated with a higher probability of being employed for men, and a lower probability of being employed for women. These two effects cancel out in a sample that includes both men and women.)

Here we have a well understood and theoretically clear interaction that could easily be missed if one was not aware the body of work under-pinning it. 

It's also why I am suspicious of simplistic explanations for why entire fields have missed the obvious confounder/true exposure.  It is possible that this is true, but a command of the literature is needed to really understand why such a blind spot developed.  Which is not to say outsiders never bring in value (the Emperor has no clothes effect really exists).  But that I am much happier when I see a very detailed command of the data being used, the questions that were asked, the population that was included, ways in which the data collection may have influenced the results, and so forth.

Definitely go and read.

SAT winners and losers

One thing I've noticed about the recent calls to end the SAT is that the test is framed entirely as an obstacle. At no point is there any suggestion that some students might have more educational opportunity because of the test. Obviously that can't be true. There is clearly a zero sum aspect to this. When someone bombs their SAT, Harvard does not reduce its admissions by one.

This pool of those likely to gain is quite large. Having gone to a perfectly good but not outstanding public high school in the middle of the country, I can tell you that the best and often the only feasible way for most students to catch the eye of an elite college recruiter (with the possible exception of athletic accomplishment) is through high SAT scores. It is possible for a valedictorian from a no-name high school to get in to an Ivy League school without killer test scores, but they won't be pursued the way students who have broken 700 across the board on the SAT will. For a a lot of middle-class students, the SAT and ACT represent their best chances at a really prestigious school, not to mention the scholarships most Americans need to attend those schools.

This suggest an interesting framework for looking at the likely winners and losers under the current SAT system. Let's define winners as those for whom the potential benefits of a very high score are larger than the potential downside from an average or below score and losers as the opposite.

What would these two groups tend to look like? We have already partially answered this question for the winners. They would come from no name public high schools. They would tend not live near a major academic center such as the Northeast or Central or Southern California (since proximity increases the chance of networking). They would be middle or lower income (or at least low enough for twenty or thirty thousand of annual tuition to be a significant hardship).

How about the losers by the standard? Remember these are people who would gain relatively little from a very high score. That rules out anyone not fairly well to do (most of the rest of us can really use a full ride scholarship). They would probably attend the kind of elite and very pricey prep schools that are expert at getting their students into top universities. They would have the support network of connections and role models that make the application process go much smoother.

We previously discussed the op-ed by Jennifer Finney Boylan. Boylan clearly saw herself as someone who was more likely to be hurt than helped by the SAT so it would be interesting to see how well her background matches the group above. A quick stop at Wikipedia reveals that, though Boylan has overcome many challenges in her life, academic hardship does not appear to have been one of them. At the time her anecdote took place, she was about to graduate from the Haverford School. Haverford is almost a living cliche of an elite prep school, one of those places where the rich and powerful graduate from and send their children to.

It's true that there are ways that people with money can gain an advantage on the SAT. There are, however, considerably more and more effective ways that people with money and position can gain an advantage in all of the other factors used to rank potential college applicants: grades; school standing; extracurricular activities; recommendations; connections; the daunting application process. Students in Boylan's position have massive advantages. You could make the case that, as a high school student competing for a spot in an prestigious university, the only time Boylan had to compete on a roughly even playing field was when she took the SAT and it is worth noting that she resents it to this day.

That said, I don't want to single Boylan out. My concern here is with the insularity of the elites in our society and with the way that certain media outlets, particularly the New York Times, have come to view the world from their vantage point.

Weekend blogging -- What kind of urban culture attracts the creative class? (answered in comic strip form)

About a month ago, we had an interesting discussion here and on Andrew Gelman's blog regarding Richard Florida's theories about the creative class and urban culture (see here, here and here). It got me thinking about one of Florida's favorite examples, Austin, Texas. These days when people think of the culture of that town, the first name that generally comes to mind is South by Southwest, but it's important to note that SxSW came after Dell.

If you were to have asked people in 1980 (shortly before the town started becoming a tech center) about Austin's culture, I suspect the answers would have focused on two main topics: the first would be the outlaw country scene (contrary to the song, Waylon and Willie actually hung out in Austin. Nobody hung out in Luckenbach); the second would be the then dominant effect of the massive UT campus on the town.

You can get a pretty good idea what people thought of that UT/frat dominated culture, from the Academia Waltz, Berkeley Breathed's first cartoon and something of a proto-Bloom County.

Question of the day

Roger Farmer:

Why is this a big deal? Because 90% of the macro seminars I attend, at conferences and universities around the world,  still assume that the labor market is an auction where anyone can work as many hours as they want at the going wage.  Why do we let our students keep doing this?

A model is a tool for better understanding the world.  While there may be problems where this particular simplification allows complex estimation, when labor markets (e.g. unemployment) is a major target of inference this simplification seems to remove the most interesting variation (e.g. employment friction and how it makes fast job changes undesirable all around). 

Clearly, if this is the state of the art, these models could be improved (heck, even an employment change penalty function would do wonders). 

Sometimes, the SAT you read about in the news doesn't look much like the actual SAT

[Unless otherwise noted, 'SAT' refers to the SAT Reasoning Test]

There are real concerns about the SAT. The emphasis on vocabulary can and sometimes does create a problem with cultural bias and the test has a history of being misused, as do most psychometrics. Though it is possible to make too much of these abuses, we should remember that, like the IQ test, people have and in a more subtle fashion, continue to use tests like the SAT to make racist arguments.

But while there are valid arguments for changing, deemphasizing, or even eliminating the SAT, these are not the arguments you will see in the anti-SAT editorials in Esquire or the New York Times. Instead, we get attacks on an SAT test that doesn't actually exist (Though it quite possibly may after David Coleman is finished with his reforms).

Though it has long tried to live down the fact for various reasons, the SAT was designed to be what its original name suggests, a scholastic aptitude test. It was also designed to be largely orthogonal to GPA and other information found in high school transcripts. (you can find a more detailed discussion of this point here and here)

In order to achieve that orthogonality the SAT test to be written in such a way that students have taken more advanced classes do not have an unfair advantage. Partly for that reason, the SAT is perhaps unique among major measures of academic accomplishment in that it has almost no rote memory component other than vocabulary.* (From here on out, I am going to focus primarily on the mathematics section though most of the general comments will apply to the entire test.)

An old professor of mine, Bill Condon, once described the analytic SAT as the toughest ninth grade math test you will ever take. That's an extremely apt way of putting it. All of the mathematical concepts are either common sense or things which a ninth grader should have covered. Almost all of the rules and formulas needed for the test are printed in the front of the booklet.

The trouble with coverage of the SAT and to a slightly lesser extent the ACT is that virtually everyone whom you will find discussing it in the pages of a major newspaper or magazine has intense but old and usually highly unreliable memories of the test. Add to that the generally poor quality of the emotionally-charged education reform debate and the result is an incredibly unproductive discussion.

For a  representative example, check out this opinion piece written by Jennifer Finney Boylan for the New York Times, which puts the trauma front and center starting with the first sentence:

I WAS in trouble. The first few analogies were pretty straightforward — along the lines of “leopard is to spotted as zebra is to striped” — but now I was in the tall weeds of nuance. Kangaroo is to marsupial as the giant squid is to — I don’t know, maybe D) cephalopod? I looked up for a second at the back of the head of the girl in front of me. She had done this amazing thing with her hair, sort of like a French braid. I wondered if I could do that with my hair.

I daydreamed for a while, thinking about the architecture of braids. When I remembered that I was wasting precious time deep in the heart of the SAT, I swore quietly to myself. French braids weren’t going to get me into Wesleyan. Although, in the years since I took the test in the mid-’70s, I’ve sometimes wondered if knowing how to braid hair was actually of more practical use to me as an English major than the quadratic equation. But enough of that. Back to the analogies. Loquacious is to mordant as lachrymose is to ... uh ...

This was the moment I saw the terrible thing I had done, the SAT equivalent of the Hindenburg disaster. I’d accidentally skipped a line on my answer sheet, early in that section of the test. Every answer I’d chosen, each of those lines of graphite-filled bubbles, was off by one. I looked at the clock. Time was running out. I could see the Wesleyan campus fading before my eyes.

High school is a trauma-filled time and its humiliations and disappointments can stay fresh for decades as they obviously have here. They do not, however, often lead to objective or accurate analyses. It may well have seemed unfair at the time to be judged on knowledge of relatively obscure words, but given that vocabulary tracks fairly well with reading ability, it doesn't seem unreasonable to ask a future English major to display an understanding of words like 'loquacious,' 'mordant' or even 'cephalopod.' As for the math section, I assume from the definite article that "the quadratic equation" refers to the quadratic formula. If so, that's an interesting choice because that formula does not appear on the SAT.

The math that does appear on the SAT relies on the following:

properties of numbers;

basic algebraic manipulation;

very basic (junior high level) geometry (with relevant formulas printed on the first page);

simple probability;

reading graphs and tables;

logic and problem-solving.

All of these fall into the good-to-know category for the general population and I'd argue the last is especially valuable for English majors (bad logic makes for bad literary criticism and often bad literature).

Boylan then goes on to complain that the SAT relies too much on memorization and to argue for the superiority of high school GPA as an academic metric. As mentioned before, the rote learning component of the SAT is extraordinarily small, far smaller than the corresponding component for almost every test-based grade a student will receive in junior high and high school.

This oddly self-defeating argument "We should drop the SAT because it's too ____; instead, we should rely more on grades/other tests/whatever (which happen to be more _____ than the SAT)" also features prominently in a less personal but much less coherent piece by Esquire.com news editor Ben Collins. Collins' argument consists of a series of largely arbitrary but highly emotional associations (it's not entirely clear why he makes these connections but he certainly feels strongly about them).

The first and possibly strangest of these associations involves Google.

Google, a company that evolved from a search engine into the world’s de facto incubator for great ideas that define our future, does not look at standardized tests when they hire applicants. They don't look at whether or not an applicant went to a Holy Grail of the standardized test lottery -- an Ivy League school -- either.

The wording here is somewhat unclear (this almost sounds like the company redacts the education sections from applicants' resumes), but I know that the big players like Google are very interested in students coming of top computer science programs like the UC schools and particularly Stanford. Take a look at this SAT breakdown for the school that produced Google:

Score	Percent of Applicants	Admit Rate	Percent of Admitted Class
800	15%	10%	25%
700–799	45%	7%	54%
600–699	28%	4%	19%
Below 600	12%	1%	2%

Keep in mind that these numbers include humanities majors.  The graduates that a company like Google are interested would almost all be in the first two bins. Google doesn't talk much about SATs at least in part because they've largely maxed out the metric.

Collins' piece actually gets worse from there.

All of that is antithetical to the dog-eat-dog, score-high-at-all-costs test-taking culture that America has distilled in its young people. And all of that is exactly why Google is the most futuristic corporation on this planet.

They know that this kind of ingenuity and collaboration — not just knowledge — is what makes a smarter world. It is also what makes better people.

We have ritually and ceaselessly sucked the fun and wonder out of learning in a country that is pushing kids into adulthood aimless, goalless, robotic and depressed as a way to feed a system that we now know does not work.

Then we blame the adults for questioning the intent of that system, even when there is none.

Do not mistake a less-tested America for an Everybody Wins America — an academic extension of those soccer games where nobody keeps score. We need to keep score to stay competitive, to remark on ingenuity and encourage drive, to understand where help is needed and where greatness needs to be challenged further.

But we don’t need to do it in this increasingly antiquated, old-world way, a holdover from when we knew much less about our kids’ biology, how they learn, and how to compel them to be better.

Currently, we have our kids fill in bubbles, and if those kids fill in the bubbles wrong on a forgotten Saturday morning when they are 17, they’re cast to a lower lot for the rest of their lives.

This cannot be the American ideal.

Make no mistake: The next revolution is not another industrial one or another technological one but it will be our first educational one. America can lead the pack if it gets over its hubris, identifies and changes its faults, and unshackles itself from the tyranny of rules and routine that exist only for the sake of themselves.

Why try to play catch up with the old world when the greatest companies in the new economy are already here, in this country, creating new ways to make the world better? These companies are disregarding the rest of the world’s urge to retrofit an exponential stream of new information into a few hundred bubbles on a thin, white sheet of paper.

Only those kinds of companies are forging our future. Why don’t our kids deserve to be taught the same way?

China has better test scores across the board than the U.S. They do not have Apple or Facebook or Microsoft or Google. They do not have our ingenuity. Let’s start appreciating it, rewarding it, fighting for it. Let's start drilling a love of learning into the brains of our kids, in the place where fear and anxiety currently reside.

Where to start...

In some parts of this passage, Collins seems to be talking about some tests other than the SAT such as the PISA exams when addressing China** or VAM-based tests when discussing the effects on learning.  If this had led up to a condemnation of tests in general the conflation might be at least internally consistent, but with the paragraph about the importance of keeping score that possibility goes out the window. We have to limit his criticisms, however odd, to the SAT.

The only real specific Collins offers about why the SAT should be singled out for elimination is that the test is old. That's partially true. The test has constantly evolved, driven by some of the best and most sophisticated analytic techniques in the field, but in terms of the test's format and its role in the education system, we've had the current set-up since 1930.

I'd argue that the country has had a pretty good run of innovation since 1930 and while I wouldn't claim that the SAT was a major driver, it would be difficult to argue that it held us back. Collins seems to agree on the first part but he takes a strange turn from there. As best I can make it out, he's arguing that America is the most innovative country in the world so it's essential that we drop a major, longstanding component of our education system or we'll become like China.

All snark aside, we probably should have a good debate about the way college admissions work and about the (I think misplaced) emphasis we have come to put on getting into the 'right' schools. Unfortunately, writers like Boylan and Collins aren't contributing to that debate; they're just supplying misplaced anger and emotional baggage.

*There's a big question (too big to address here) about the role of vocabulary in the SAT. Ideally there should be no rote learning element here at all. The vocabulary component is supposed to measure things like how reading volume and comprehension. Memorizing lists of words is, in a sense, cheating; it's also of questionable effectiveness compared to good, active reading habits.

** From China Daily:

The first annual report on the SAT performance of Chinese students found the average score was 1,213 points out of the total of 2,400, some 296 points lower than US students and 337 points lower than the benchmark set by College Board, the organizer of the test.

The gap is mainly derived from the reading and writing parts of the test. Chinese students scored 170 points less than US students in the reading part, which reveals Chinese students lack training in critical thinking, according to the report.

Chinese students, known to excel in mathematics, earned 547 points out of the total of 800, only 30 points higher than US students. The report attributed the lower-than-expected performance to Chinese students' poor knowledge of English mathematical terms and the test is aimed at a junior level which is easier for US students.