Jaime Escalante and the full factorial

Just so there isn't any confusion following my previous post, having followed education from lots of angles for a long time (including stints teaching in Watts and the Delta), I have no doubt that Jaime Escalante was the real thing, a genuinely great teacher with exceptional technique and a profound understanding of both the cognitive and emotional aspects of learning.

I brought up the fact that Escalante wasn't able to duplicate his results, not because he was overrated (I honestly don't believe he was), but because the results of even the best teachers are affected by a number of factors and interactions. Escalante was a great teacher in the right school and community with the right administrator at the right time. That was part of why he accomplished so much at a school that most teachers would have struggled with.

The idea that one teacher might do better in school A than in school B while another teacher might do better in B may not seem like that radical a notion but it has big and potentially troubling implications.

Consider three of the factors that might interact with the teacher effect:

Level (remedial, average, advanced);

Class size (small, medium and large);

Administrator (for the sake of the discussion, we'll limit this to two -- A, who keeps a high profile and is liked and respected by the kids and B, who doesn't and isn't).

Both common sense and anecdotal data should alert us to the potential for first, second, even third order interaction here.

As a personal example, my preferred approach to teaching secondary math classes (particularly when students came in below grade level) was to reserve some time at the end for kids to work individually on worksheets and homework while I went from desk to desk to make sure that each student understood the lesson and was doing the problems correctly. Every student got some personal attention and none got left behind.  (By comparison, my college teaching style was mostly lecture/Q&A-based and worked about as well for two hundred students as it did for twenty.)

For a teacher with a style that relied ono one-to-one interaction to help struggling students, you might not see a first order interaction with level and teacher effect (as long as you kept the size small), or with size and effect (as long as you kept the level advanced), but the combination of large and remedial would severely limit the effectiveness of this approach. The administrator and school culture also play a role here -- it's easier to spend time with the kids who are falling behind if the rest of the class is quietly doing its work.

These interactions seem reasonable enough, certainly not the sort of thing you can rule out, but in a real sense, proposals for test based teacher evaluation routinely do just that. Most evaluation periods, by necessity, cover a tiny range of data: one school; one administrator; one subject; one level; one class size. The result is a ridiculously narrow picture of a teacher's performance. If there's a serious potential for interaction, their conclusions can't possibly be valid.

Even if we ignore the potential for interaction, three or four years of confounded, nested data is an awfully thin basis for decisions about bonuses, promotions and dismissals. If we allow for the obvious possibility that some teachers work better with certain students and under certain administrators and in certain environments (as Escalante did), we will either need a fractional (perhaps even full) factorial approach which will require huge samples or we will have to have a sophisticated understanding of just how teaching styles, learning styles and management styles interact not only with each other but with subject matter, school and class structures, adolescent psychology, group dynamics, cultural differences and government policy.

Good luck

One more argument for the list

I think that this argument is the weakest valid one for preserving Social Security that I am aware of:

One thing it made me realize is that I was (I think) wrong to support full social security privatization. Of course, that's a cheap concession for me to make, since nothing like that is on the horizon. But this has relevance to other potential issues, so it's worth thinking through.

 

When social security privatization was being debated, I looked at successful schemes like the ones in Chile and, er, Sweden. And of course, sovereign wealth funds like Norway's. But I didn't think about the vast gulf between us and them. The US has the largest, deepest, most liquid capital markets in the world, by a fair margin. Small countries can safely invest in our markets (and others) without moving prices or outcomes much.

 

The unfunded liability of social security, by contrast, is in the tens of trillions (net present value). Where would we put enough investment to cover that kind of liability? Our investments would swamp markets, including our own, in a way that Sweden's just don't. And if they were directed by a single government entity, that swamping effect would hand a disastrous amount of power to the investment committee.
 

But it does point out the huge issues that setting such a project up would involve.  Notice, as well, that the safest investments (like government bonds) are just as subject to political risk as social security.  Governments renegotiate bonds all of the time.  Not usually the United States, I agree, but then they haven't been defaulting on social security payments either.

That said, I am much more interested in the implicit insurance that being able to tax the US population gives the payments.  Even if the return is lower than in the private market (qustionable at today's yields), being protected against fraud or large losses is very, very valuable.  

What is the new interest in complexity?

One thing that I have been wondering a lot about lately is the move towards more and more complex ways of doing things that should be relatively simple.  Consider a few examples:

1. School choice and voucher systems.  This requires an informed parent to research options, see through marketing hype and balance factors like location versus performance.  How is this necessarily better than a system designed to just improve schools?
2. Medicare advantage programs.  This requires older adults to balance complex features of different plans and try to ensure that their provider is going to treat them well at a point of great personal stress.  How is having the government or the courts acting as a post-hoc check better than just have a simple system of insurance to begin with?
3. 401(k) and other defined contribution accounts.  Individual investors have enormous information deficits relative to instituitional investors.  Individual investors bear far higher levels of market risk and making the funds able to be withdrawn (even at a penalty) forces complex balancing decisions.  How is this better than an automatic pension plan like Social Security?

I totally understand that high information individuals may be able to optimize more clearly in a complex environment.  But the increase in transaction costs (needing to advertise, sorting through options) seems to suggest the median user will be worse off. 

Now this might be different if there was an open market in any of these examples.  But medicine is tightly regulated, we have laws saying that children must go to school, and anybody who was worked for an employer with a badly selected 401(k) knows that there is no free market alternative to shop your account to another employer.  It is not like a restaurant or a clothing store where the conditions for free markets will end up making it easy to find what you want.  But you can't switch health care providers or schools based on the sale of the week. 

So why do we want to make these things harder and harder to understand or engage with? 

Even Jaime Escalante wasn't a Jaime Escalante

A quick follow-up to Joseph's last post, particularly his use of the late Jaime Escalante as an example.

Perhaps the central assumption of the reform movement is the belief that the best way to fix education is by identifying and and retaining great teachers (generally defined as those who can dramatically raise students' test scores). Quite rightly, Escalante is the first name that comes to most people's mind when they hear about this, but his career suggests that being a great teacher is a necessary but not sufficient condition for getting great results.

Following Mark's link on education

As a follow-up to Mark I wanted to specically call out some of the pieces of Felix Salmon's piece on test scores and education. 

Instead, reformers are rushing to use this data as a quantitative performance-review tool, something which can get you a raise or which can even get you fired. And by so doing, they’re turning it from something potentially extremely useful, into a bone of contention between teachers and managers, and a metric to be gamed and maximized.
 

When all decisions on based on a single score, you incent behavior which maximizes the score and minimize additional focus.  Felix makes an interesting point that if you used this data to provide coaching and feedback then it could actually be really useful.  Teachers would still want students to do well on the test (it is much, much nicer to talk to your principal about how generally well your students are doing than to get coaching on how to try and shore up a weak point). 

I also think that this point was really sharp:

School reformers in general, it seems to me, tend to be obsessed with the idea of Good Teachers and Bad Teachers, as though the quality of the education a kid gets in any given classroom is somehow both predictable and innate to the teacher. And yes, at the extremes, there are a few great inspirational teachers who we all remember decades later, and a few dreadful ones who had no idea what they were talking about and who had no control of their classes. But frankly, you don’t need student surveys to identify those outliers. And the fact is that schools are much more than just the sum of their parts: that’s one of the reasons that reformers love to talk about excellent principals who can turn schools around.

He is very cleverly and accurately pointing out a form of equivocation that is being used here.  There are extreme examples, but they were never the problem in terms of identification.  There are some odd employment rules in some places that made acting on this knowledge awkward, but very few people saw these as being good policy.  The real use of these tests to to try and break apart the middle of the distribution.  But, by definition, the gain in the middle of the distribution is much less than the difference between exceptional and abysmal.  You are not taking Jaime Escalante versus an incompetent as your contrast.  You are taking pretty good versus very good as your contrast, and thus setting things up for a life event to move people back and forth in the distribution.  Your child gets ill, you are more tired and work so you lsoe your job because you slip below the median.  No wonder teachers are suspicious of such metrics. 

Data is good but one of the lessons of the MBA approach to management is that not everything can be broken down into numbers on a spreadsheet to be maximized.  I fear we'll figure that out, sooner or later. 

Essential Felix

It's a busy week so I don't have the time to give this the build-up it deserves, but if you've been following the education reform debate, you need to read this.

The main reason epidemiology is hard... urgency

There's a point I should have emphasized in my previous post about this news story

Researchers have long documented that the most educated Americans were making the biggest gains in life expectancy, but now they say mortality data show that life spans for some of the least educated Americans are actually contracting. Four studies in recent years identified modest declines, but a new one that looks separately at Americans lacking a high school diploma found disturbingly sharp drops in life expectancy for whites in this group. Experts not involved in the new research said its findings were persuasive.

I commented that cohort effects could complicate things in a study like this. What I should have made clear was that, even with these complications:

1.  These numbers are horrifying;

2. Even if the effects are less dramatic than what the most recent study indicated, there is considerable evidence that life expectancies are getting worse for the most disadvantaged people in our country.

I'm primarily a marketing statistician. I hardly ever make life and death decisions. Epidemiologists play for higher stakes. I believe it's healthy for outside statisticians like me to point out concerns with epidemiological research, but we need to remember that researchers inside the field don't have the option of waiting for a perfect data set. Their findings have a huge impact on the health of millions of people and those millions can't wait for perfect.

More on the whole "Epidemiology is Hard" thing

There's a new study that's been getting a lot of press:

For generations of Americans, it was a given that children would live longer than their parents. But there is now mounting evidence that this enduring trend has reversed itself for the country’s least-educated whites, an increasingly troubled group whose life expectancy has fallen by four years since 1990.
Researchers have long documented that the most educated Americans were making the biggest gains in life expectancy, but now they say mortality data show that life spans for some of the least educated Americans are actually contracting. Four studies in recent years identified modest declines, but a new one that looks separately at Americans lacking a high school diploma found disturbingly sharp drops in life expectancy for whites in this group. Experts not involved in the new research said its findings were persuasive.

The reasons for the decline remain unclear, but researchers offered possible explanations, including a spike in prescription drug overdoses among young whites, higher rates of smoking among less educated white women, rising obesity, and a steady increase in the number of the least educated Americans who lack health insurance.

The steepest declines were for white women without a high school diploma, who lost five years of life between 1990 and 2008, said S. Jay Olshansky, a public health professor at the University of Illinois at Chicago and the lead investigator on the study, published last month in Health Affairs. By 2008, life expectancy for black women without a high school diploma had surpassed that of white women of the same education level, the study found.

White men lacking a high school diploma lost three years of life. Life expectancy for both blacks and Hispanics of the same education level rose, the data showed. But blacks over all do not live as long as whites, while Hispanics live longer than both whites and blacks. The decline among the least educated non-Hispanic whites, who make up a shrinking share of the population, widened an already troubling gap. The latest estimate shows life expectancy for white women without a high school diploma was 73.5 years, compared with 83.9 years for white women with a college degree or more. For white men, the gap was even bigger: 67.5 years for the least educated white men compared with 80.4 for those with a college degree or better.
...
The decline among the least educated non-Hispanic whites, who make up a shrinking share of the population, widened an already troubling gap. The latest estimate shows life expectancy for white women without a high school diploma was 73.5 years, compared with 83.9 years for white women with a college degree or more. For white men, the gap was even bigger: 67.5 years for the least educated white men compared with 80.4 for those with a college degree or better.

This is, unquestionably, a troubling finding and I have every reason to believe that the researchers did a responsible job. None the less, this part still troubles me:

Researchers said they were baffled by the magnitude of the drop. Some cautioned that the results could be overstated because Americans without a high school diploma — about 12 percent of the population, down from about 22 percent in 1990, according to the Census Bureau — were a shrinking group that was now more likely to be disadvantaged in ways besides education, compared with past generations.

Professor Olshansky agreed that the group was now smaller, but said the magnitude of the drop in life expectancy was still a measure of deterioration. “The good news is that there are fewer people in this group,” he said. “The bad news is that those who are in it are dying more quickly.”

Dying at the age of seventy in 1990 would mean you were born in 1920. Dying at the age of sixty-seven in 2008 would mean you were born in 1941. If you were to build a model to predict whether someone born in in 1920 would finish high school, it would certainly look different than a model predicting the same thing for someone born in 1941. We know this, for one reason, because the target variable was much less frequent for the second group.

Of course, we're talking about averages and distributions and that can complicate things in a number of ways (most of which don't make it into a newspaper account of a research paper), but no matter how you slice it, what it meant to have a high school diploma changed greatly from the early to the middle part of the Twentieth Century, and that change is very difficult to control for.

I think it's generally a good, conservative rule to assume that when the relative size of a segment of the population drops dramatically, the composition of the segment is likely to shift. Thus a sharp increase in a behavior in these groups' behavior may simply be a result of the people who didn't show the behavior not being in the group any longer.

I'm not saying that this is the case here. I'm just saying that this sort of analysis makes me  nervous.

(I have the same problem with dropping poll responses, but more on that later

This does not seem to be a hoax

From Marketplace:

But the course of true investing never did run smooth, and there are some traders who look to the stars to tell them what to do. Financial astrologers like Karen Starich say traders know they're up against a lot of rich, smart people.

"They want to have that edge," she says. "They want to know what the future is."

Starich chargest $237 annually for her newsletter, which 300 traders subscribe to for news of what will happen to the stock prices of companies, or even bigger, to the Federal Reserve. She sees dark times ahead in the Fed's horoscope.

"They now have Saturn squared to Neptune, which is really bankruptcy," Starich explains.

Neptune represents money. But when Saturn shows up in a chart, it indicates restriction. So for the Fed, that means the "fiscal cliff is here, and there’s no place to go except to print more money or unravel these financial institutions," Starich says.

Of course, a lot of Wall Street traders, and others, don't want it to be known that they're relying on anything other than their own talent. Arch Crawford, a financial astrologer who actually got his start on Wall Street as a stock analyst at Merrill Lynch, recalls one subscriber asking for his newsletter in "brown paper wrappers."

Crawford warns his 2,000 subscribers particularly against the dangers of Mercury in retrograde, a time when the planet appears to be going in reverse across the sky. The phenomenon, which happens three times or more a year, indicates a month when communications will be screwed up. He warns his subscribers never to start anything new during that time. He points to the fact that Knight Capital launched a new software program in August, when Mercury was in retrograde, and the brokerage firm nearly went out of business. He also notes that most major market glitches have happened while Mercury was in retrograde.

LA billboards -- another n = 1 hypothesis

I have absolutely nothing more than vague impressions to back this up but it seems that a disproportionate share of the billboards of in this town, particularly around Burbank and Hollywood, are dedicated to TV shows. Of course, LA is a trend setter and a lot of media writers are based here, but billboards seem an inefficient way of targeting a relatively few influential players.

I suspect that (if I'm right about the over-representation) there's a bigger factor that has nothing to do with maximizing corporate profits. Instead the objective is to maximize the profile and reputation of the executives running the networks. The target audience is colleagues and acquaintances and the purpose is to create the impression that the executives are successful and influential.

William Goldman once observed that studio executives would rather make big budget films even when low budget alternatives made more business sense because, even if the big films lost money, they still gave you something to talk about at parties. ("I just greenlit the new Hanks/Roberts project. How about you?") After reading that, a number of why-did-they-make-that pictures were suddenly more explicable.

Lots of business decisions make more sense when you apply this cocktail-party standard (including the majority of sports sponsorships), but I wonder if anyone has seriously tried to study and quantify the extent to which home industries of a region are over-represented in local advertising. If not and if anyone's interested, I might have some design and metric ideas.

Back on the down ticket question

As mentioned before, one of the most interesting aspects of this election is the way the different races interact.

Thomas Ferraro has a good report on the topic:

It is axiomatic that a strong presidential nominee can boost the chances for other party candidates, particularly those in close U.S. Senate races.

But the presidential candidate can also hurt those farther down the ticket.

While a single comment might not alter particular races, a lagging campaign could. Republican Representative Steven LaTourette of Ohio, who is retiring from Congress, defended Romney's remarks, but said they "don't help in swing districts like mine." "People were ready to throw Obama over, like dumping a boyfriend, and were ready to be courted by a new boyfriend," he said. "But now they're having second thoughts," LaTourette said.

Republican Representative Tom Cole of Oklahoma called Romney's remarks "an unfortunate choice of words," but predicted the comments would be "a one- or two-day story."

"The election is going to turn on the economy," Cole said. University of Virginia political scientist Larry Sabato, whose "Crystal Ball" blog closely tracks congressional races, said Romney's performance would be particularly influential in Senate races in Virginia, Connecticut, Montana, North Dakota and Florida.

"Scott Brown can't survive much more undertow in Massachusetts," he said. George Allen, the Republican Senate contender in Virginia, "depends on a Romney win," Sabato added.

"As I go through the states, I'd say Romney's performance will help to determine most of the close Senate contests," he said in an email interview.

"It's going to be very difficult for Republicans to take over the Senate if Romney doesn't capture the White House. That's a different evaluation than a year ago when the GOP looked to be a good bet to grab the Senate."

Why is investment in human capital out of favor?

David Brooks:

The final thing the comment suggests is that Romney knows nothing about ambition and motivation. The formula he sketches is this: People who are forced to make it on their own have drive. People who receive benefits have dependency.

But, of course, no middle-class parent acts as if this is true. Middle-class parents don’t deprive their children of benefits so they can learn to struggle on their own. They shower benefits on their children to give them more opportunities — so they can play travel sports, go on foreign trips and develop more skills.

People are motivated when they feel competent. They are motivated when they have more opportunities. Ambition is fired by possibility, not by deprivation, as a tour through the world’s poorest regions makes clear.

 

I got this quote via Aaron Carroll.  One thing that seems to have really changed in the public mind over the past 5 years is the simple relationship between investment in human capital and improved outcomes.  Putting aside the Randian fantasy of super-men who can do it all on their own, all of us are dependent on others to a greater or lesser extent.  Hard work may well make opportunity into success but all of the hard work in the world doesn't help in the absence of opportunity.  Just ask any coal miner or subsistence farmer . . . 

Another recommend (this time not blind)

Dana Goldstein has some smart observations on Chicago and the teacher testing debate.

Another reason observational epidemiology is hard

John D Cook:

And yet behind every complex set of rules is a paper showing that it outperforms simple rules, under conditions of its author’s choosing. That is, the person proposing the complex model picks the scenarios for comparison. Unfortunately, the world throws at us scenarios not of our choosing. Simpler methods may perform better when model assumptions are violated. And model assumptions are always violated, at least to some extent.
 

 One of the hardest things with simulation studies is that we get to develop our own set of assumptions.  So we actually know how to correctly model the phenomenon of interest. 

The problem is that we usually do not know how much error is introduced when the complex (and often non-linear) model fails.  On the other hand, it is amazing how far one can get with a clear set of rules of the thumb. 

I wonder if it would be better if we had a different person test the model than the one who proposed it? 

Important if true

In the Nineteenth Century, news stories sometimes carried the disclaimer "Important if true." It was used for news that couldn't be confirmed but was too big to leave unreported. That line always struck me as a perfect representation of one of the three fundamental tensions of journalism, the one between getting it right and getting it first (the other two are between these goals and making the story interesting).

In a follow-up to a discussion about the way the press corp handled the 2000 election, I claimed that the culture of journalism was placing increasingly less value on accuracy. To support the accusation, I listed some examples from recent discussions, but there is a more direct and damning way to make the point.

Viewed in absolute terms the level of accuracy in current journalism is certainly not what it could be and is arguably in decline, but what about relative to cost? One hundred years ago, the time required to check a story was substantial. Sources were difficult to contact, reference materials had to be accessed in person and were often unindexed, and there was simply less recorded information. This time requirement translated to both labor and opportunity costs.

Over the years (particularly the last twenty), these costs have dropped sharply. The time required to get a story right has decreased by at least a couple of orders of magnitude. If we hold the value of accuracy constant, we would expect to see factual errors all but disappear. Instead we're seeing something between "as bad as ever" and "even worse." That means the value journalism as an industry puts on accuracy must have dropped as or more sharply than the costs of fact-checking did.

Think of it as Moore's law of diminishing journalistic quality.