Superman and Statistics

In the 1978 movie “Superman,” Lois Lane, star journalist, crash-lands in a helicopter on top of a 50-story skyscraper.   The helicopter is hanging by a strut to the edge of the roof, and Lois is hanging on to a microphone cord.  Finally, the cord breaks, and Lois falls 45 floors before (of course) she is swooped up by Superman, who flies her back to the roof and sets her down gently. Then he says to her:

“I hope this doesn’t put you off of flying. Statistically speaking, it is the safest form of travel.”

She faints.

Don’t let the superhero thing fool you: The “S” is for “statistics.”

I’ve often had the very same problem whenever I do public speaking.  As soon as I mention statistics, some of the audience faints dead away. Or perhaps they are falling asleep. But either way, saying the word “statistics” is not usually a good way to make friends and influence people.

 

The fact is, most people don’t like statistics.  Or more accurately, people don’t like statistics except when the statistical findings agree with their prejudices.  At an IES meeting several years ago, a well-respected superintendent was invited to speak to what is perhaps the nerdiest, most statistically-minded group in all of education, except for an SREE conference.  He actually said, without the slightest indication of humor or irony, that “GOOD research is that which confirms what I have always believed.  BAD research is that which disagrees with what I have always believed.”  I’d guess that the great majority of superintendents and other educational leaders would agree, even if few would say so out loud to an IES meeting.

If educational leaders only attend to statistics that confirm their prior beliefs, one might argue that, well, at least they do attend to SOME research.  But research in an applied field like education is of value only if it leads to positive changes in practice.  If influential educators only respect research that confirms their previous beliefs, then they never change their practices or policies because of research, and policies and practices stay the same forever, or change only due to politics, marketing, and fads. Which is exactly how most change does in fact happen in education.  If you wonder why educational outcomes change so slowly, if at all, you need look no further than this.

Why is it that educators pay so little attention to research, whatever its outcomes, much in contrast to the situation in many other fields?  Some people argue that, unlike medicine, where doctors are well trained in research, educators lack such training.  Yet agriculture makes far more practical use of evidence than education does, and most farmers, while outstanding in their fields, are not known for their research savvy.

Farmers are, however, very savvy business owners, and they can clearly see that their financial success depends on using seeds, stock, methods, fertilizers, and insecticides proven to be effective, cost-effective, and sustainable.  Similarly, research plays a crucial role in technology, engineering, materials science, and every applied field in which better methods, with proven outcomes, lead to increased profits.

So one major reason for limited use of research in education is that adopting proven methods in education rarely leads to enhanced profit.  Even in parts of the educational enterprise where profit is involved, economic success still depends far more on politics, marketing, and fads, than on evidence. Outcomes of adopting proven programs or practices may not have an obvious impact on overall school outcomes because achievement is invariably tangled up with factors such as social class of children and schools’ abilities to attract skilled teachers and principals.  Ask parents whether they would rather have their child to go to a school in which all students have educated, upper-middle class parents, or to a school that uses proven instructional strategies in every subject and grade level.  The problem is that there are only so many educated, upper-middle class parents to go around, so schools and parents often focus on getting the best possible demographics in their school rather than on adopting proven teaching methods.

How can education begin to make the rapid, irreversible improvements characteristic of agriculture, technology, and medicine?  The answer has to take into account the fundamental fact that education is a government monopoly.  I’m not arguing whether or not this is a good thing, but it is certain to be true for many years, perhaps forever.  The parts of education that are not part of government are private schools, and these are very few in number (charter schools are funded by government, of course).

Because government funds nearly all schools, it has both the responsibility and the financial capacity to do whatever is feasible to make schools as effective as it possibly can.  This is true of all levels of government, federal, state, and local.  Because it is in charge of all federal research funding, the federal government is the most logical organization to lead any efforts to increase use of proven programs and practices in education, but forward-looking state and local government could also play a major role if they chose to do so.

Government can and must take on the role that profit plays in other research-focused fields, such as agriculture, medicine, and engineering.   As I’ve argued many times, government should use national funding to incentivize schools to adopt proven programs.  For example, the federal government could provide funding to schools to enable them to pay the costs of adopting programs found to be effective in rigorous research.  Under ESSA, it is already doing this, but right now the main focus is only on Title I school improvement grants.   These go to schools that are among the lowest performers in their states.  School improvement is a good place to start, but it affects a modest number of extremely disadvantaged schools.  Such schools do need substantial funding and expertise to make the substantial gains they are asked to make, but they are so unlike the majority of Title I schools that they are not sufficient examples of what evidence-based reform could achieve.  Making all Title I schools eligible for incentive funding to implement proven programs, or at least working toward this goal over time, would arouse the interest and enthusiasm of a much greater set of schools, virtually all of which need major changes in practices to reach national standards.

To make this policy work, the federal government would need to add considerably to the funding it provides for educational research and development, and it would need to rigorously evaluate programs that show the greatest promise to make large, pragmatically important differences in schools’ outcomes in key areas, such as reading, mathematics, science, and English for English learners.  One way to do this cost-effectively would be to allow districts (or consortia of districts) to put forward pairs of matched schools for potential funding.   Districts or consortia awarded grants might then be evaluated by federal contractors, who would randomly assign one school in each pair to receive the program, while the pair members not selected would serve as a control group.  In this way, programs that had been found effective in initial research might have their evaluations replicated many times, at a very low evaluation cost.  This pair evaluation design could greatly increase the number of schools using proven programs, and could add substantially to the set of programs known to be effective.  This design could also give many more districts experience with top-quality experimental research, building support for the idea that research is of value to educators and students.

Getting back to Superman and Lois Lane, it is only natural to expect that Lois might be reluctant to get on another helicopter anytime soon, no matter what the evidence says.  However, when we are making decisions on behalf of children, it’s not enough to just pay attention to our own personal experience.  Listen to Superman.  The evidence matters.

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

Cost-Effectiveness of Small Solutions

Imagine that you were shopping for a reliable new car, one that is proven to last an average of at least 100,000 miles with routine maintenance and repairs. You are looking at a number of options that fit your needs for around $24,000.

You happen to be talking to your neighbor, an economist, about your plans. “$24,000?” she says. “That’s crazy. You can get a motorcycle that would go at least 100,000 miles for only $12,000, and save a lot on gas as well!”

You point out to your neighbor that motorcycles might be nice for some purposes, but you need a car to go to the grocery store, transport the kids, and commute to work, even in rain or snow. “Sure,” says your neighbor, “but you posed a question of cost-effectiveness, and on that basis a motorcycle is the right choice. Or maybe a bicycle.”

In education, school leaders and policy makers are often faced with choices like this. They want to improve their students’ achievement, and they have limited resources. But the available solutions vary in cost, effectiveness, and many other factors.

To help leaders make good choices, economists have devised measures of cost-effectiveness, which means (when educational achievement is the goal) the amount of achievement gain you might expect from purchasing a given product or service divided by all costs of making that choice. Cost-effectiveness can be very useful in educational policy and practice in helping decision makers weigh the potential benefits of each of a set of choice available to them. The widespread availability of effect sizes indicating the outcomes and costs of various programs and practices, easily located in sources such as the What Works Clearinghouse and Evidence for ESSA, make it a lot easier to compare outcomes and costs of available programs. For example, a district might seek to improve high school math performance by adopting software and professional development for a proven technology program, or by adopting a proven professional development approach. All costs need to be considered as well as all benefits, and the school leaders might make the choice that produces the largest gains at the most affordable cost. Cost-effectiveness might not entirely determine which choice is made, but, one might argue, it should always be a key part of the decision-making process. Quantitative researchers in education and economics would agree. So far, so good.

But here is where things get a little dodgy. In recent years, there has arisen a lot of interest in super-cheap interventions that have super-small impacts, but the ratio between the benefits and the costs makes the super-cheap interventions look cost-effective. Such interventions are sometimes called “nudge strategies,” meaning that simple reminders or minimal actions activate a set of psychological process that can lead to important impacts. A very popular example right now is Carol Dweck’s Growth Mindset strategy, in which students are asked to write a brief essay stating a belief that intelligence is not a fixed attribute of people, but that learning comes from effort. Her work has found small impacts of this essentially cost-free treatment in several studies, although others have failed to find this effect.

Other examples include sending messages to students or parents on cell phones, or sending postcards to parents on the importance of regular attendance. These strategies can cost next to nothing, yet large-scale experiments often show positive effects in the range of +0.03 to +0.05, averaging across multiple studies.

Approaches of this kind, including Growth Mindset, are notoriously difficult to replicate by others. However, assume for the sake of argument that at least some of them do have reliably positive effects that are very small, but because of their extremely small cost, they appear very cost-effective. Should schools use them?

One might take a view that interventions like Growth Mindset are so inexpensive and so sensible that what the heck, go ahead. However, others take some time and effort on the part of staff.

Schools are charged with a very important responsibility, ensuring the academic success, psychological adjustment, and pro-social character of young people. Their financial resources are always limited, but even more limited is their schoolwide capacity to focus on a small number of essential goals and stick with those goals until they are achieved. The problem is that spending a lot of time on small solutions with small impacts may exhaust a school’s capacity to focus on what truly matters. If a school could achieve an effect size of +0.30 on important achievement measures with one comprehensive program, or (for half the price) could adopt ten small interventions with effect sizes averaging +0.03, which should it do? Any thoughtful educator would say, “Invest in the one program with the big effect.” The little programs are not likely to add up to a big effect, and any collection of unrelated, uncoordinated mini-reforms is likely to deplete the staff’s energy and enthusiasm over a period of time.

This is where the car-motorcycle analogy comes in. A motorcycle may appear more cost-effective than a car, but it just does not do what a car does. Motorcycles are fine for touring in nice weather, but for most people they do not solve essential problems. In school reform, large programs with large effects may be composed of smaller effective components, but because these components are an integrated part of a well-thought-out plan, they add up to something more likely to work and to keep working over time.

Cost-effectiveness is a useful concept for schools seeking to make big differences in achievement, using serious resources. For small interventions with small impacts, don’t bother to calculate cost-effectiveness, or if you do, don’t compare the results to those of big interventions with big impacts. To do so is like bragging about the gas mileage you get on your motorcycle driving Aunt Sally and the triplets to the grocery store. It just doesn’t make sense.

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

Achieving Breakthroughs in Education By Transforming Effective But Expensive Approaches to be Affordable at Scale

It’s summer in Baltimore. The temperatures are beastly, the humidity worse. I grew up in Washington, DC, which has the same weather. We had no air conditioning, so summers could be torture. No one could sleep, so we all walked around like zombies, yearning for fall.

Today, however, summers in Baltimore are completely bearable. The reason, of course, is air conditioning. Air conditioning existed when I was a kid, but hardly anyone could afford it.  I think the technology has gradually improved, but there was no scientific or technical breakthrough, as far as I know.  Yet somehow, all but the poorest families can afford air conditioning, so summer in Baltimore can be survived. Families that cannot afford air conditioning need assistance, especially for health reasons, but this number is small.

The story of air conditioning resembles that of much other technology. What happens is that a solution is devised for a very important problem.  The solution is too expensive for ordinary people to use, so initially, it is used in circumstances that justify the cost.  For example, early automobiles were far too expensive for the general public, but they were used for important applications in which the benefits were particularly obvious, such as delivery trucks and cars for doctors and veterinarians.  Also, wealthy individuals and race car drivers could afford the early autos.  These applications provided experience with the manufacture, use, and repair of automobiles and encouraged investments in infrastructure, paving the way (so to speak) for mass production of cars (such as the Model T) that could be afforded by a much larger portion of the population and economy.  Modest improvements are constantly being made, but the focus is on making the technology less expensive, so it can be more widely used.  In medicine, penicillin was invented in the 1920s, but not until the advent of World War II was it made inexpensive enough for practical use.  It saved millions of lives not because it had been invented, but because the Merck Company was commissioned to find a way to make it practicable (the solution involved growing penicillin on rotting squash).

Innovations in education can work in a similar way.  One obvious example is instructional technology, which existed before the 1970s but is only now becoming universally available, mostly because it is falling in price.  However, what education has rarely done is to create expensive but hugely effective interventions and then figure out how to do them cheaply, without reducing their impact.

Until now.

If you are a regular reader of my blog, you can guess where I am going: Tutoring.  As everyone knows, one-to one tutoring by certified teachers is extremely effective.  No surprise there. As you regulars will also know, rigorous research over the past 20 years has established that tutoring by well-trained, well-supervised teaching assistants using proven methods routinely produces outcomes just as good as tutoring by certified teachers, at half the cost.  Further, one-to-small group tutoring, up to one to four, can be almost as effective as one-to-one tutoring in reading, and equally effective in mathematics (see www.bestevidence.org).

One-to-four tutoring by teaching assistants requires about one-eighth of the cost of one-to-one tutoring by teachers.  The mean outcomes for both types of tutoring are about an effect size of +0.30, but several programs are able to produce effect sizes in excess of +0.50, the national mean difference on NAEP between disadvantaged and middle-class students.  (As a point of comparison, average effects of technology applications with elementary struggling readers average +0.05 in reading, and in math, they average +0.07 for all elementary students.  Urban charter schools average +0.04 in reading, +0.05 in math).

Reducing the cost of tutoring should not be seen as a way for schools to save money.  Instead, it should be seen as a way to provide the benefits of tutoring to much larger numbers of students.  Because of its cost, tutoring has been largely restricted to the primary grades (especially first), to perhaps a semester of service, and to reading, but not math.  If tutoring is much less expensive but equally effective, then tutoring can be extended to older students and to math.  Students who need more than a semester of tutoring, or need “booster shots” to maintain their gains into later grades, should be able to receive the tutoring they need, for as long as they need it.

Tutoring has been how rich and powerful people educated their children since the beginning of time.  Ancient Romans, Greeks, and Egyptians had their children tutored if they could afford it.  The great Russian educational theorist, Lev Vygotsky, never saw the inside of a classroom as a child, because his parents could afford to have him tutored.  As a slave, Frederick Douglass received one-to-one tutoring (secretly and illegally) from his owner’s wife, right here in Baltimore.  When his master found out and forbade his wife to continue, Douglass sought further tutoring from immigrant boys on the docks where he worked, in exchange for his master’s wife’s fresh-cooked bread.  Helen Keller received tutoring from Anne Sullivan.  Tutoring has long been known to be effective.  The only question is, or should be, how do we maximize tutoring’s effectiveness while minimizing its cost, so that all students who need it can receive it?

If air conditioning had been like education, we might have celebrated its invention, but sadly concluded that it would never be affordable by ordinary people.  If penicillin had been like education, it would have remained a scientific curiosity until today, and millions would have died due to the lack of it.  If cars had been like education, only the rich would have them.

Air conditioning for all?  What a cool idea.  Cost-effective tutoring for all who need it?  Wouldn’t that be smart?

Photo credit: U.S. Navy photo by Pat Halton [Public domain]

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

Hummingbirds and Horses: On Research Reviews

Once upon a time, there was a very famous restaurant, called The Hummingbird.   It was known the world over for its unique specialty: Hummingbird Stew.  It was expensive, but customers were amazed that it wasn’t more expensive. How much meat could be on a tiny hummingbird?  You’d have to catch dozens of them just for one bowl of stew.

One day, an experienced restauranteur came to The Hummingbird, and asked to speak to the owner.  When they were alone, the visitor said, “You have quite an operation here!  But I have been in the restaurant business for many years, and I have always wondered how you do it.  No one can make money selling Hummingbird Stew!  Tell me how you make it work, and I promise on my honor to keep your secret to my grave.  Do you…mix just a little bit?”

The Hummingbird’s owner looked around to be sure no one was listening.   “You look honest,” he said. “I will trust you with my secret.  We do mix in a bit of horsemeat.”

“I knew it!,” said the visitor.  “So tell me, what is the ratio?”

“One to one.”

“Really!,” said the visitor.  “Even that seems amazingly generous!”

“I think you misunderstand,” said the owner.  “I meant one hummingbird to one horse!”

In education, we write a lot of reviews of research.  These are often very widely cited, and can be very influential.  Because of the work my colleagues and I do, we have occasion to read a lot of reviews.  Some of them go to great pains to use rigorous, consistent methods, to minimize bias, to establish clear inclusion guidelines, and to follow them systematically.  Well- done reviews can reveal patterns of findings that can be of great value to both researchers and educators.  They can serve as a form of scientific inquiry in themselves, and can make it easy for readers to understand and verify the review’s findings.

However, all too many reviews are deeply flawed.  Frequently, reviews of research make it impossible to check the validity of the findings of the original studies.  As was going on at The Hummingbird, it is all too easy to mix unequal ingredients in an appealing-looking stew.   Today, most reviews use quantitative syntheses, such as meta-analyses, which apply mathematical procedures to synthesize findings of many studies.  If the individual studies are of good quality, this is wonderfully useful.  But if they are not, readers often have no easy way to tell, without looking up and carefully reading many of the key articles.  Few readers are willing to do this.

Recently, I have been looking at a lot of recent reviews, all of them published, often in top journals.  One published review only used pre-post gains.  Presumably, if the reviewers found a study with a control group, they would have ignored the control group data!  Not surprisingly, pre-post gains produce effect sizes far larger than experimental-control, because pre-post analyses ascribe to the programs being evaluated all of the gains that students would have made without any particular treatment.

I have also recently seen reviews that include studies with and without control groups (i.e., pre-post gains), and those with and without pretests.  Without pretests, experimental and control groups may have started at very different points, and these differences just carry over to the posttests.  Accepting this jumble of experimental designs, a review makes no sense.  Treatments evaluated using pre-post designs will almost always look far more effective than those that use experimental-control comparisons.

Many published reviews include results from measures that were made up by program developers.  We have documented that analyses using such measures produce outcomes that are two, three, or sometimes four times those involving independent measures, even within the very same studies (see Cheung & Slavin, 2016). We have also found far larger effect sizes from small studies than from large studies, from very brief studies rather than longer ones, and from published studies rather than, for example, technical reports.

The biggest problem is that in many reviews, the designs of the individual studies are never described sufficiently to know how much of the (purported) stew is hummingbirds and how much is horsemeat, so to speak. As noted earlier, readers often have to obtain and analyze each cited study to find out whether the review’s conclusions are based on rigorous research and how many are not. Many years ago, I looked into a widely cited review of research on achievement effects of class size.  Study details were lacking, so I had to find and read the original studies.   It turned out that the entire substantial effect of reducing class size was due to studies of one-to-one or very small group tutoring, and even more to a single study of tennis!   The studies that reduced class size within the usual range (e.g., comparing reductions from 24 to 12) had very small achievement  impacts, but averaging in studies of tennis and one-to-one tutoring made the class size effect appear to be huge. Funny how averaging in a horse or two can make a lot of hummingbirds look impressive.

It would be great if all reviews excluded studies that used procedures known to inflate effect sizes, but at bare minimum, reviewers should be routinely required to include tables showing critical details, and then analyzed to see if the reported outcomes might be due to studies that used procedures suspected to inflate effects. Then readers could easily find out how much of that lovely-looking hummingbird stew is really made from hummingbirds, and how much it owes to a horse or two.

References

Cheung, A., & Slavin, R. (2016). How methodological features affect effect sizes in education. Educational Researcher, 45 (5), 283-292.

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

The Farmer and the Moon Rocks: What Did the Moon Landing Do For Him?

Many, many years ago, during the summer after my freshman year in college, I hitchhiked from London to Iran.  This was the summer of 1969, so Apollo 11 was also traveling.   I saw television footage of the moon landing in Heraklion, Crete, where a television store switched on all of its sets and turned them toward the sidewalk.  A large crowd watched the whole thing.  This was one of the few times I recall when it was really cool to be an American abroad.

After leaving Greece, I went on to Turkey, and then Iran.  In Teheran, I got hold of an English-language newspaper.  It told an interesting story.  In rural Iran, many people believed that the moon was a goddess.  Obviously, a spaceship cannot land on a goddess, so many people concluded that the moon landing must be a hoax.

A reporter from the newspaper interviewed a number of people about the moon landing.  Some were adamant that the landing could not have happened.  However, one farmer was more pragmatic.  He asked the reporter, “I hear the astronauts brought back moon rocks.  Is that right?”

“That’s what they say!” replied the reporter.

“I am fixing my roof, and I could sure use a few of those moon rocks.  Do you think they might give me some?”

The moon rock story illustrates a daunting problem in the dissemination of educational research. Researchers do high-quality research on topics of great importance to the practice of education. They publish this research in top journals, and get promotions and awards for it, but in most cases, their research does not arouse even the slightest bit of interest among the educators for whom it was intended.

The problem relates to the farmer repairing his roof.  He had a real problem to solve, and he needed help with it.  A reporter comes and tells him about the moon landing. The farmer does not think, “How wonderful!  What a great day for science and discovery and the future of mankind!”  Instead, he thinks, “What does this have to do with me?”  Thinking back on the event, I sometimes wonder if he really expected any moon rocks, or if he was just sarcastically saying, “I don’t care.”

Educators care deeply about their students, and they will do anything they can to help them succeed.  But if they hear about research that does not relate to their children, or at least to children like theirs, they are unlikely to care very much.  Even if the research is directly applicable to their students, they are likely to reason, perhaps from long experience, that they will never get access to this research, because it costs money or takes time or upsets established routines or is opposed by powerful groups or whatever.  The result is status quo as far as the eye can see, or implementation of small changes that are currently popular but unsupported by evidence of effectiveness.  Ultimately, the result is cynicism about all research.

Part of the problem is that education is effectively a government monopoly, so entrepreneurship or responsible innovation are difficult to start or maintain.  However, the fact that education is a government monopoly can also be made into a positive, if government leaders are willing to encourage and support evidence-based reform.

Imagine that government decided to provide incentive funding to schools to help them adopt programs that meet a high standard of evidence.  This has actually happened under the ESSA law, but only in a very narrow slice of schools, those very low achieving schools that qualify for school improvement.  Imagine that the government provided a lot more support to schools to help them learn about, adopt, and effectively implement proven programs, and then gradually expanded the categories of schools that could qualify for this funding.

Going back to the farmer and the moon rocks, such a policy would forge a link between exciting research on promising innovations and the real world of practice.  It could cause educators to pay much closer attention to research on practical programs of relevance to them, and to learn how to tell the difference between valid and biased research.  It could help educators become sophisticated and knowledgeable consumers of evidence and of programs themselves.

One of the best examples of the transformation such policies could bring about is agriculture.  Research has a long history in agriculture, and from colonial times, government has encouraged and incentivized farmers to pay attention to evidence about new practices, new seeds, new breeds of animals, and so on.  By the late 19th century, the U.S. Department of Agriculture was sponsoring research, distributing information designed to help farmers be more productive, and much more.  Today, research in agriculture is a huge enterprise, constantly making important discoveries that improve productivity and reduce costs.  As a result, world agriculture, especially American agriculture, is able to support far larger populations at far lower costs than anyone ever thought possible.  The Iranian farmer talking about the moon rocks could not see how advances in science could possibly benefit him personally.  Today, however, in every developed economy, farmers have a clear understanding of the connection between advances in science and their own success.  Everyone knows that agriculture can have bad as well as good effects, as when new practices lead to pollution, but when governments decide to solve those problems, they turn to science. Science is not inherently good or bad, but if it is powerful, then democracies can direct it to do what is best for people.

Agriculture has made dramatic advances over the past hundred years, and continues to make rapid progress by linking science to practice.  In education, we are just starting to make the link between evidence and practice.  Isn’t it time to learn from the experiences of medicine, technology, and agriculture, among many other evidence based fields, to achieve more rapid progress in educational practice and outcomes?

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.