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Thanks for posting this. Salient point for me was the following bit I'd never considered before, but explains quite well the feeling I've had about testing for

Thanks for posting this. Salient point for me was the following bit I'd never considered before, but explains quite well the feeling I've had about testing for a long time. There’s a great observation called Goodhart’s Law that basically says any metric becomes useless once you start using it for control purposes. So the SAT, for example, is a good general test of academic aptitude. But since it’s used so much for admission to college, kids are trained and coached. They spend lots of time and effort, specifically to improve their SAT score at the expense of a well-rounded education, to the point where [the SAT] may not be such a good guide to general academic excellence, even though it used to be before students started optimizing

kiba 12y ago
Certain things cannot be gamed, or even if they're gamed, they're still good, like your IQ score.
- S4M 12y ago
  You can improve your IQ score by taking lots of IQ tests (your "IQ" will slowly improve), and I don't consider IQ to be a good thing by itself.
  - sz4kerto 12y ago
    Not really -- the IQ tests used by MENSA for example are quite reliable/stable. You can improve your result by 6-10 points with a lot of training, but that's usually the most that people can achieve.
    - S4M 12y ago
      Maybe the reason MENSA's tests are reliable is that not many people are interested in joining MENSA - I am not denying that MENSA can be of interest, but its admittance would not be worth preparing IQ tests like crazy. On the other hand, if IQ tests were used for admissions in prestigious universities, you can bet some students will train specifically for IQ tests.
      - skj 12y ago
        Maybe they'd all get a bit smarter as a result?
    - bradleyjg 12y ago
      A standard deviation on IQ tests is 15 points. A 6-10 point improvement from the median represents a jump of 15.5 - 24.75 percentile rank. Even at the level MENSA is looking at, someone with a 10 point improvement could have a "true IQ" at just above the 95th percentile and qualify for their 98th percentile cutoff.
mathattack 12y ago
This is true in most of social science. Metrics work when people don't know they're being measured. Once people learn they're being measured on something, they optimize to it. On another note... If a metric is being used properly, it might not seem like it's working. For example... Harvard saw that GMATs didn't correlate with their MBA's success, so they dropped it as admission criteria. Years later they checked the GMAT scores for the classes where they weren't required. What happened? GMATs correlated to performance. What's the cause? Earlier on they were properly weighting in. (Higher GPA? GMAT doesn't matter much. Lower GPA? It matter mores. Grad degree in stats? Lower undergrad GPA and GMAT don't matter as much, etc.) If you're weighting it properly, the importance won't show. (In essence, a 780 is the right marginal score to let one person in, a 680 on another) All that said, in a way, the perfect measure is an unfair one, because you don't know what you're being measured on so you can't change it.
- ken47 12y ago
  That is partially true. A metric should continue to "work" when people know they are being measured on it. A good metric is one which makes the measured person more effective when they explicitly try to optimize it. So for example, pro basketball player knows they are measured by their accuracy. However, when a player optimizes his accuracy, that does not compromise the effectiveness of that metric.
  - bzbarsky 12y ago
    The important thing here is that a metric that is a _correlate_ of the thing you care about but can't measure directly might start to work less well once people know you're measuring it. And the reason is that the correlation with the thing you really care about might decrease. To use your basketball example, say you have a player that takes a shot every time they get close enough to the basket, scoring 60% of them. You decide to measure accuracy. They get more conservative with when they take shots, so now half the time they run out of shot clock (resulting in a turnover) and the other half of the time they take a shot and score with 100% accuracy. Their accuracy went from 60% to 100%, but the fraction of time possession results in scoring went from 60% to 50%. The issue there is that you don't _really_ care about accuracy per se. What you care about is contribution to the score differential vs the opposing team. But that's hard to quantify, so people come up with various metrics that correlate to such contribution (shooting accuracy, rebound percentage, etc, etc), along with relative weights for these metrics. In fact, the weights depend on the exact team you're playing, who your current teammates are, etc. In any case, it's actually fairly rare to be able to directly measure the thing you care about, especially in the social sciences, not least because a lot of the things we care about ("success in life", "college preparedness", "job satisfaction", "knowledge and understanding of the material covered by this class") are fairly difficult to quantify. So instead one ends up measuring various correlates and hoping that either people don't adjust their behavior too much to degrade the correlation before you're done measuring or that your measurement process attempts to account for such adjustments.
yummyfajitas 12y ago
I'm truly impressed by the cognitive dissonance here. On the one hand, this is a wildly popular platitude for intellectuals to endorse, and Terry Tao would certainly suffer some social penalties if he strongly opposed it. On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory. It's also strange that proponents of this view rarely apply it uniformly. There are many metrics that are quite popular among proponents of Goodhart's law - for instance, CO2 emissions, capital reserve requirements, etc. (Also SAT prep barely works http://online.wsj.com/news/articles/SB124278685697537839?mg=reno64-wsj&url=http%3A%2F%2Fonline.wsj.com%2Farticle%2FSB124278685697537839.html http://online.wsj.com/news/articles/SB124278685697537839?mg=... - it's the "well rounded" portion of college applications that people spend the most time gaming.)
- VLM 12y ago
  "On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory." I might be able to help by pointing out that a technology that depends on random sampling of small components of "intelligence" or whatever is going to be totally screwed up if the sampling is no longer random and now the outcome of the test depends mostly on the amount of money spent on prep classes. From manufacturing I can predict a lot about the quality of something in general off just one graph of the distribution of length of one part compared to other manufacturers graphs of the same single measurement on the same part, but if the mfgr "cooks the books" by optimizing one measurment of that part to perfection while taking away labor from other areas of part quality, then my comparisons will be useless, especially when comparing optimizers vs non-optimizers.
- mrow84 12y ago
  I'm not sure your strong criticism of Goodhart's Law is quite fair. It is stated so as to be pithy, but I think it is fairly obviously meant to be applied only to those situations where the thing being measured in some sense "judges itself" by that score, and adjusts its performance to try and improve that score. This is quite likely the case with school children, but often not the case with, say, industrial processes. If, however, you make someone's job dependent on meeting some particular target for that process, then a feedback loop is created that can lead to the kinds of problems being discussed. If the feedback loop isn't there, then the metric will remain as useful as it ever was. So the point is, be wary of unintentional feedbacks in your system, not some grandiose rejection of the possibility of optimisation.
shamney 12y ago
Test preparation does not do much to increase SAT scores: "For students that have taken the test before and would like to boost their scores, coaching seems to help, but by a rather small amount. After controlling for group differences, the average coaching boost on the math section of the SAT is 14 to 15 points. The boost is smaller on the verbal section of the test, just 6 to 8 points. The combined effect of coaching on the SAT for the NELS sample is about 20 points." http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionstestpreparation.pdf http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionst...
- watwut 12y ago
  They did not measured whether it is possible to prepare for SAT. They measured whether commercial courses boost your score. The comparison is not between student who does no additional work for SAT and the one who study a lot. The comparison is between student enrolled paying coach and the one who is not paying special SAT coach. The latter one can still work a lot with help of books and websites. It does not mean you can not prepare for SAT, it just means that money spent on commercial coach are probably wasted. It says nowhere that if you skip all preparation altogether, you will get good result. Quote: "Most studies have focused on estimating the effect of one specific type of test preparation, known as “coaching.” In this analysis, students Students have been coached if they have enrolled in a commercial preparation course not offered by their school but designed specifically for the SAT or ACT. The distinction made here is whether a test-taker has received systematic instruction over a short period of time. Preparation with books, videos and computers is excluded from the coaching definition because while the instruction may be systematic, it has no time constraint. Preparation with a tutor is excluded because while it may have a time constraint, it is difficult to tell if the instruction has been systematic." Article conclusion focus on coached students only. Note the time constraint in the above quote. People who take those tests seriously not only take the short course, but probably focused on the test long before the course started. At least, that is how well performing students I knew years ago behaved. The course itself might have boost their score only a little, but their preparation consisted of much more then just one course. After all, they are adults about to enter college - they are expected to be able to learn alone.
- kenjackson 12y ago
BrandonMarc 12y ago
Sounds like Google's toolbar pagerank, which was a neat way of seeing the very generic "relevance" score Google assigned to a page. Then Search Engine Optimization really started catching ground, and some SEO's would obsess about that number, going through all kinds of work to manage that number, and basing business decisions (such as: should we link to this site? should we request a link from that site?) far too heavily on that number, as opposed to the actual business relevance of what they were doing, and as opposed to whether it would be a useful result for their own visitors (or those of the other site).
tokenadult 12y ago
It is of course important to look at whether or not what you are measuring validly predicts what you are trying to predict. Despite much worry about SAT coaching courses, I get the very strong impression that the young people who score highest on the SAT are still, after all these decades, the young people who read widely for fun and who think about math problems for fun, just as they were in the 1970s when young people in my region of the United States were not coached for the SAT at all. The standardized conditions for administering the SAT have always included (in my lifetime) giving students registered for the test access to a complete previously administered test to serve as practice material. According to a psychometrician I know, precisely because the SAT allows everyone to practice in advance, it is an especially valid estimate of the test-taker's general ability to learn and to reason. You can look up research about SAT correlations with general intelligence[1] and IQ test scores[2] and college grades[3] (what SAT scores are intended to predict) on Google Scholar and see for yourself what the empirical research says. No one-factor means of predicting college success is perfect (and if college admission officers were forced to use ONE factor to admit applicants to college, the factor they would be wise to choose to predict college grades is UNWEIGHTED high school grade average), but SAT scores (or ACT scores) are still used in the admission process of most colleges that are at all selective because they provide helpful information for comparing applicants who attended different high schools. If you would like to put names of particular researchers into a Google Scholar search to find out what they have discovered about current use of SAT tests, I would suggest Nathan Kuncel or Paul Sackett, both of whom have studied quite a few detailed data sets about SAT-takers and what their scores predict. AFTER EDIT: Terence Tao, in the interview kindly posted to open this thread, makes the important point that sometimes teachers entertain more than they actually teach. (I think a lot of commercial test-prep courses have this defect.) He said, "Sometimes making a class more enjoyable or entertaining is not the same as making it more educational. I remember once when I taught calculus, one of the sections was quadric surfaces, like ellipsoids, paraboloids and so forth. So there’s this thing called a hyperbolic paraboloid, and I wanted to demonstrate this. It turns out that a Pringle has the shape of a hyperbolic paraboloid. So I brought in a pack of Pringles to class and said, 'this is a hyperbolic paraboloid, this is what it looks like.' I ate the Pringle as I was writing equations on the board. Well many years later, I ran into someone on the street who said, 'Oh, I know you. I took one of your classes. I forget what it was, but there was a Pringle.' So I thought, 'you didn’t remember any of the math, but you remember the Pringle.' So it didn’t really work." Following up on that in the context of this subthread, I think a lot of students know who Joe Bloggs[4] is without being able to reason successfully to find the right answer choice on the harder SAT questions. [1] http://scholar.google.com/scholar?hl=en&q=SAT+general+intelligence http://scholar.google.com/scholar?hl=en&q=SAT+general+intell... [2] http://scholar.google.com/scholar?q=SAT+IQ+test http://scholar.google.com/scholar?q=SAT+IQ+test [3] http://scholar.google.com/scholar?q=SAT+college+grades http://scholar.google.com/scholar?q=SAT+college+grades [4] http://books.google.com/books?id=K4SteOicBAQC&pg=PA23&lpg=PA23&dq=joe+bloggs+principle http://books.google.com/books?id=K4SteOicBAQC&pg=PA23&lpg=PA...
graycat 12y ago
> control purposes Here you have an implicit assumption that the system being controlled can react, that is, in the sense of control theory, change its plant dynamics, due to the effort of the control. Well, for a lot of work in control, say, in most aerospace applications, that assumption is false or essentially so. Then getting a good metric and using it is fine. E.g., get the power spectrum of ocean wave noise and use that in a control system to keep a submarine at essentially a constant depth. We don't expect that the metric of the ocean wave power spectrum and the control system in the submarine will change the ocean very much! E.g., GPS is a terrific metric, but we don't expect that using it will change the shape of the earth. Etc.

kiba 12y ago

Certain things cannot be gamed, or even if they're gamed, they're still good, like your IQ score.

S4M 12y ago
You can improve your IQ score by taking lots of IQ tests (your "IQ" will slowly improve), and I don't consider IQ to be a good thing by itself.
- sz4kerto 12y ago
  Not really -- the IQ tests used by MENSA for example are quite reliable/stable. You can improve your result by 6-10 points with a lot of training, but that's usually the most that people can achieve.
  - S4M 12y ago
    Maybe the reason MENSA's tests are reliable is that not many people are interested in joining MENSA - I am not denying that MENSA can be of interest, but its admittance would not be worth preparing IQ tests like crazy. On the other hand, if IQ tests were used for admissions in prestigious universities, you can bet some students will train specifically for IQ tests.
    - skj 12y ago
      Maybe they'd all get a bit smarter as a result?
  - bradleyjg 12y ago
    A standard deviation on IQ tests is 15 points. A 6-10 point improvement from the median represents a jump of 15.5 - 24.75 percentile rank. Even at the level MENSA is looking at, someone with a 10 point improvement could have a "true IQ" at just above the 95th percentile and qualify for their 98th percentile cutoff.

mathattack 12y ago

This is true in most of social science. Metrics work when people don't know they're being measured. Once people learn they're being measured on something, they optimize to it. On another note... If a metric is being used properly, it might not seem like it's working. For example... Harvard saw that GMATs didn't correlate with their MBA's success, so they dropped it as admission criteria. Years later they checked the GMAT scores for the classes where they weren't required. What happened? GMATs correlated to performance. What's the cause? Earlier on they were properly weighting in. (Higher GPA? GMAT doesn't matter much. Lower GPA? It matter mores. Grad degree in stats? Lower undergrad GPA and GMAT don't matter as much, etc.) If you're weighting it properly, the importance won't show. (In essence, a 780 is the right marginal score to let one person in, a 680 on another) All that said, in a way, the perfect measure is an unfair one, because you don't know what you're being measured on so you can't change it.

ken47 12y ago
That is partially true. A metric should continue to "work" when people know they are being measured on it. A good metric is one which makes the measured person more effective when they explicitly try to optimize it. So for example, pro basketball player knows they are measured by their accuracy. However, when a player optimizes his accuracy, that does not compromise the effectiveness of that metric.
- bzbarsky 12y ago
  The important thing here is that a metric that is a _correlate_ of the thing you care about but can't measure directly might start to work less well once people know you're measuring it. And the reason is that the correlation with the thing you really care about might decrease. To use your basketball example, say you have a player that takes a shot every time they get close enough to the basket, scoring 60% of them. You decide to measure accuracy. They get more conservative with when they take shots, so now half the time they run out of shot clock (resulting in a turnover) and the other half of the time they take a shot and score with 100% accuracy. Their accuracy went from 60% to 100%, but the fraction of time possession results in scoring went from 60% to 50%. The issue there is that you don't _really_ care about accuracy per se. What you care about is contribution to the score differential vs the opposing team. But that's hard to quantify, so people come up with various metrics that correlate to such contribution (shooting accuracy, rebound percentage, etc, etc), along with relative weights for these metrics. In fact, the weights depend on the exact team you're playing, who your current teammates are, etc. In any case, it's actually fairly rare to be able to directly measure the thing you care about, especially in the social sciences, not least because a lot of the things we care about ("success in life", "college preparedness", "job satisfaction", "knowledge and understanding of the material covered by this class") are fairly difficult to quantify. So instead one ends up measuring various correlates and hoping that either people don't adjust their behavior too much to degrade the correlation before you're done measuring or that your measurement process attempts to account for such adjustments.

yummyfajitas 12y ago

I'm truly impressed by the cognitive dissonance here. On the one hand, this is a wildly popular platitude for intellectuals to endorse, and Terry Tao would certainly suffer some social penalties if he strongly opposed it. On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory. It's also strange that proponents of this view rarely apply it uniformly. There are many metrics that are quite popular among proponents of Goodhart's law - for instance, CO2 emissions, capital reserve requirements, etc. (Also SAT prep barely works http://online.wsj.com/news/articles/SB124278685697537839?mg=reno64-wsj&url=http%3A%2F%2Fonline.wsj.com%2Farticle%2FSB124278685697537839.html http://online.wsj.com/news/articles/SB124278685697537839?mg=... - it's the "well rounded" portion of college applications that people spend the most time gaming.)

VLM 12y ago
"On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory." I might be able to help by pointing out that a technology that depends on random sampling of small components of "intelligence" or whatever is going to be totally screwed up if the sampling is no longer random and now the outcome of the test depends mostly on the amount of money spent on prep classes. From manufacturing I can predict a lot about the quality of something in general off just one graph of the distribution of length of one part compared to other manufacturers graphs of the same single measurement on the same part, but if the mfgr "cooks the books" by optimizing one measurment of that part to perfection while taking away labor from other areas of part quality, then my comparisons will be useless, especially when comparing optimizers vs non-optimizers.
mrow84 12y ago
I'm not sure your strong criticism of Goodhart's Law is quite fair. It is stated so as to be pithy, but I think it is fairly obviously meant to be applied only to those situations where the thing being measured in some sense "judges itself" by that score, and adjusts its performance to try and improve that score. This is quite likely the case with school children, but often not the case with, say, industrial processes. If, however, you make someone's job dependent on meeting some particular target for that process, then a feedback loop is created that can lead to the kinds of problems being discussed. If the feedback loop isn't there, then the metric will remain as useful as it ever was. So the point is, be wary of unintentional feedbacks in your system, not some grandiose rejection of the possibility of optimisation.

shamney 12y ago

Test preparation does not do much to increase SAT scores: "For students that have taken the test before and would like to boost their scores, coaching seems to help, but by a rather small amount. After controlling for group differences, the average coaching boost on the math section of the SAT is 14 to 15 points. The boost is smaller on the verbal section of the test, just 6 to 8 points. The combined effect of coaching on the SAT for the NELS sample is about 20 points." http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionstestpreparation.pdf http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionst...

watwut 12y ago
They did not measured whether it is possible to prepare for SAT. They measured whether commercial courses boost your score. The comparison is not between student who does no additional work for SAT and the one who study a lot. The comparison is between student enrolled paying coach and the one who is not paying special SAT coach. The latter one can still work a lot with help of books and websites. It does not mean you can not prepare for SAT, it just means that money spent on commercial coach are probably wasted. It says nowhere that if you skip all preparation altogether, you will get good result. Quote: "Most studies have focused on estimating the effect of one specific type of test preparation, known as “coaching.” In this analysis, students Students have been coached if they have enrolled in a commercial preparation course not offered by their school but designed specifically for the SAT or ACT. The distinction made here is whether a test-taker has received systematic instruction over a short period of time. Preparation with books, videos and computers is excluded from the coaching definition because while the instruction may be systematic, it has no time constraint. Preparation with a tutor is excluded because while it may have a time constraint, it is difficult to tell if the instruction has been systematic." Article conclusion focus on coached students only. Note the time constraint in the above quote. People who take those tests seriously not only take the short course, but probably focused on the test long before the course started. At least, that is how well performing students I knew years ago behaved. The course itself might have boost their score only a little, but their preparation consisted of much more then just one course. After all, they are adults about to enter college - they are expected to be able to learn alone.
kenjackson 12y ago

BrandonMarc 12y ago

Sounds like Google's toolbar pagerank, which was a neat way of seeing the very generic "relevance" score Google assigned to a page. Then Search Engine Optimization really started catching ground, and some SEO's would obsess about that number, going through all kinds of work to manage that number, and basing business decisions (such as: should we link to this site? should we request a link from that site?) far too heavily on that number, as opposed to the actual business relevance of what they were doing, and as opposed to whether it would be a useful result for their own visitors (or those of the other site).

tokenadult 12y ago

It is of course important to look at whether or not what you are measuring validly predicts what you are trying to predict. Despite much worry about SAT coaching courses, I get the very strong impression that the young people who score highest on the SAT are still, after all these decades, the young people who read widely for fun and who think about math problems for fun, just as they were in the 1970s when young people in my region of the United States were not coached for the SAT at all. The standardized conditions for administering the SAT have always included (in my lifetime) giving students registered for the test access to a complete previously administered test to serve as practice material. According to a psychometrician I know, precisely because the SAT allows everyone to practice in advance, it is an especially valid estimate of the test-taker's general ability to learn and to reason. You can look up research about SAT correlations with general intelligence[1] and IQ test scores[2] and college grades[3] (what SAT scores are intended to predict) on Google Scholar and see for yourself what the empirical research says. No one-factor means of predicting college success is perfect (and if college admission officers were forced to use ONE factor to admit applicants to college, the factor they would be wise to choose to predict college grades is UNWEIGHTED high school grade average), but SAT scores (or ACT scores) are still used in the admission process of most colleges that are at all selective because they provide helpful information for comparing applicants who attended different high schools. If you would like to put names of particular researchers into a Google Scholar search to find out what they have discovered about current use of SAT tests, I would suggest Nathan Kuncel or Paul Sackett, both of whom have studied quite a few detailed data sets about SAT-takers and what their scores predict. AFTER EDIT: Terence Tao, in the interview kindly posted to open this thread, makes the important point that sometimes teachers entertain more than they actually teach. (I think a lot of commercial test-prep courses have this defect.) He said, "Sometimes making a class more enjoyable or entertaining is not the same as making it more educational. I remember once when I taught calculus, one of the sections was quadric surfaces, like ellipsoids, paraboloids and so forth. So there’s this thing called a hyperbolic paraboloid, and I wanted to demonstrate this. It turns out that a Pringle has the shape of a hyperbolic paraboloid. So I brought in a pack of Pringles to class and said, 'this is a hyperbolic paraboloid, this is what it looks like.' I ate the Pringle as I was writing equations on the board. Well many years later, I ran into someone on the street who said, 'Oh, I know you. I took one of your classes. I forget what it was, but there was a Pringle.' So I thought, 'you didn’t remember any of the math, but you remember the Pringle.' So it didn’t really work." Following up on that in the context of this subthread, I think a lot of students know who Joe Bloggs[4] is without being able to reason successfully to find the right answer choice on the harder SAT questions. [1] http://scholar.google.com/scholar?hl=en&q=SAT+general+intelligence http://scholar.google.com/scholar?hl=en&q=SAT+general+intell... [2] http://scholar.google.com/scholar?q=SAT+IQ+test http://scholar.google.com/scholar?q=SAT+IQ+test [3] http://scholar.google.com/scholar?q=SAT+college+grades http://scholar.google.com/scholar?q=SAT+college+grades [4] http://books.google.com/books?id=K4SteOicBAQC&pg=PA23&lpg=PA23&dq=joe+bloggs+principle http://books.google.com/books?id=K4SteOicBAQC&pg=PA23&lpg=PA...

graycat 12y ago

> control purposes Here you have an implicit assumption that the system being controlled can react, that is, in the sense of control theory, change its plant dynamics, due to the effort of the control. Well, for a lot of work in control, say, in most aerospace applications, that assumption is false or essentially so. Then getting a good metric and using it is fine. E.g., get the power spectrum of ocean wave noise and use that in a control system to keep a submarine at essentially a constant depth. We don't expect that the metric of the ocean wave power spectrum and the control system in the submarine will change the ocean very much! E.g., GPS is a terrific metric, but we don't expect that using it will change the shape of the earth. Etc.