William M. Briggs, Statistician

I have no idea, but two gentlemen from the Johnson School of Management at Cornell and one from the Economics department at Purdue seem to think so. They have written a paper, which has found interest at Slate, which they boast as an “exclusive.”

Waldman’s (and others) paper, which is a couple of years old, is a prime example of how to get carried away with an idea, so it is worthwhile to review it. It’s best to download the paper so you can follow along (the paper is freely available).

The genesis of the idea was noticing that autism rates at birth in the state of California started to increase in the early 1970s, picking up pace until 2000, when their data stops (see their Figure 1). It is true to say that something caused this increase. But what?

There is no way to know, but we can posit causes and then test them. The best way to do that is by direct measurement: Propose a cause, design an experiment or collect data in which the cause was controlled and the effect happened. That is difficult to do in the case of autism, of course, since you won’t know a child is inflicted for some time after his birth. But, of course, it would not be ethical to let a cause stay in place if you suspected it would lead to autism. It is also not clear when the cause, or causes, whatever they might be, have to manifest themselves. That is, the same cause might be in place for two children, but miss its timing, so to speak, in the first case and get it right in the second. A plausible biological mechanism for the cause that fits in with other known medical science must also be in place. In short, this kind of investigation is not impossible, but it is difficult and must proceed by, if I can use the pun, baby steps.

Another way to assign a cause is by guessing. This is the easiest method by far. It starts with some guys sitting around a table and saying something like, “How about watching TV? That can’t be good. Especially if kids watched old Three Stooges reruns.” Something like that happened here. Waldman said “I asked around and found that medical researchers were not working on this [possible connection], so accepted that I should research it myself.”

To demonstrate that watching TV is a possible cause involves nothing more than showing that watching TV is correlated (a word I use here in it’s non-technical, plain English sense) with autism. If watching TV had something to do with autism, then the two pieces of data would be correlated, it is true. But if TV had nothing to do with autism, the two pieces of data might still be correlated. The kick is, there is no way to know, by just looking at the TV/autism data, whether this correlation was real or spurious. Of course, autism might be correlated with lots of things, none of which were its cause. This fact means we are on thin ice, and the slightest misstep will cause us to fall through.

Since autism rates have increased since the 1970s anything that also increased, even at different rates, during that same period will be correlated with autism. As the Slate article cautions “petroleum use also rose during the period but is unrelated to autism.” I agree that oil and autism are not related, but you must understand that this is not something which could learn by examining the data. Oil use and autism are correlated. It is only an extra-statistical judgment that tells us the relationship is silly.

In medicine, there is something called dose response, a fancy way of saying that more of the drug leads to stronger effects (or increases side effects). What might this dose response be with TV and autism? Well, watching more TV is an obvious culprit: the more hours spent in front of the tube, the greater the chance of developing autism—so speculated the researchers.

But how can you tell how much TV all these kids watched? You can’t. There is no way to go back to 1970 and count how many hours each baby watched TV. This is a dilemma, because we would really like to test the dose response. Perhaps there is a proxy? A proxy is a stand-in variable that is so strongly associated with hours of TV watched that it’s almost as good as the real thing. Can you think of any?

How about precipitation? Sure, rain and snow. After all, when it rains, what else is there to do but watch TV? Actually, lots, and when it snows, there’s even more. But, this is the proxy chosen by the researchers (their Figure 6 will hold some interest for those interested in global warming).

They plotted up maps by county for California, Oregon, and Washington, and colored in counties that had more than median precipitation (from 1990-2001) and then colored those with higher than median autism rates. These colored squares tended to be in the same spot, and is what led them to the conclusion that watching TV causes autism. Case closed.

But can we think of alternate explanations? Take a look at their Figures 3-5 and you’ll see that the high precipitation counties are all coastal, which are the same places that people choose to live. That is, there is, in these three states, a vastly greater population density on the coasts then in the interior and it is in these regions where the autism rates are higher. Populations in these high-density areas are also more heterogeneous, with greater disparities in behavior, income, health care access, and on and on. Wouldn’t it be more likely that one or more of these disparities were the cause or causes of autism rather than the county precipitation rate?

That’s my bet, but again this in a extra-data judgment. The authors of the paper do go on and calculate “linear regression models”, which ties all these and some other variables together. These models have the assumption that everything is related by a straight line, which is probably not true or even a good approximation. But even if they were straight-line related, the models cannot fix the problem that any other variable that increases since the 1970s—like oil use—would have also given significant results. These models only quantify the idea of correlation, after all.

What happens, then, is that these great, complicated tables, built with sophisticated software have given the authors the illusion of certainty. A reporter picks up the story, and then “activists” get involved, and, well, you know the rest.

(Here’s a cute article on other scares, most brought about in the same way as the TV/autism research was done.)

UPDATE: All seems well again. Thanks to everybody for their help!

I have been having a hell of a time trying to upgrade.

Everything now seems OK, except that I can’t see my other pages (Resume, Services, etc.). I can see them in the database and on the wp-admin Manage -> Pages. But they don’t show up on screen.

I tried creating a new page called “Test” and that doesn’t show either.

If you go directly to http://wmbriggs.com/blog/resume/ then you can see the resume page, but it doesn’t show on the top row of tags.

I have double-checked the database privileges and all seems well there.

Anybody have any ideas?

I had a hell of a scare when I tried the WPAU plugin. It is the Word Press Automatic Update software, maintained here. This blog runs on Wordpress, served by Yahoo, a great host, but the version of WP I have is old (2.0.2).

The WPAU software is supposed to first create a Wordpress and database backup, then install the newest version of WP (it actually tried to install one version back). It looked like all was well until I tried looking at the site. All my categories were gone, as were my Resume and other pages. Clicking on any link set up an infinite loop, mainly because of the “new and improved” database.

That is, the backup files were corrupted and the database was hosed: certain tables were deleted, others modified. For example, all my comments were gone! Thousands of them. I wept.

But I checked with Yahoo and it turns out that they provide snapshots every four hours (I pay 20 bucks a month for this privilege) and I was able to restore my entire database as of a few hours ago.

All seems well now, and I have a current backup.

So this is a tale of caution. Be careful what you are doing and always—simply always—regularly backup.

Today’s headlines mostly got it wrong:

• The New York Sun said “Study Shatters Myth That Boys Are Better At Math.”
• The New York Post said “Girls = boys in math skills.”
• The New York Daily News said “Math gender differences erased.”
• The New York Times said “Math Scores Show No Gap for Girls, Study Finds.”

Only Keith Winstein at the Wall Street Journal got it right:

• “Boys’ Math Score Hit Highs and Lows.”

This is, of course, a political topic. This is evidenced by the Times beginning their take on the story by recalling the fate of Larry Summers, ex-president of Harvard, who dared to publicly wonder whether males and females have similar mathematical ability. In case you don’t recall, he surmised that they did not, and he was crucified for uttering such politically-incorrect heresy.

Janet Hyde, who is a professor at the University of Wisconsin, Madison, and who led the study, said the idea that boys might be better at math is a “stereotype.” Well, let’s see.

Hyde’s study, which is wholly statistical, is typical. And none of the headlines, save the WSJ, correctly describe what Hyde actually did. To explain it, I have to get a bit technical, but stay with me because this is very important.

Hyde fit a probability model to her data and then made an indirect statement about the value of that models’ parameters. What does this mean? She first assumed that the approximate uncertainty in math scores could be modeled by a normal distributions. Normal distributions have two parameters which must be specified. The first is usually (and mistakenly) called the “mean” and it describes where the peak or center of the normal distribution lies. The second is usually (and mistakenly) called the “variance” and it describes the spread of the distribution: larger variances mean that the data is more uncertain.

A statistical test is then run, asking “Are the mean parameters for boys and girls equal or unequal?” If the mean for the boys is larger than the mean for the girls, the implication is that boys are better at math than are girls. If the means are roughly equal, then people conclude—sometimes incorrectly—that the performance of boys and girls are “the same.”

It is important to emphasize that the study as reported in most newspapers only said something about the mean parameters for the boys and girls. These parameters were roughly equal, and this implied, all other things being equal, that boys’ and girls’ ability is equal.

But all things are not equal.

What all the news reports, except the WSJ, forgot was the variance. The following picture will help explain what I mean.

The top picture shows the normal distributions of what might be normalized math test scores for girls and boys: scores greater than 0 are better than average, scores less than 0 are worse than average (these data are just an illustration; I don’t have Hyde’s study data, but the point is the same). The girls are the solid line, the boys are the dashed. You can see that both have a peak in exactly the same place. This implies that the mean performance for both boys and girls is the same, that is, on average, their performance is the same.

But notice that the boy’s line is a little—only just a tiny—bit more spread out than the girls’. This is because the variance for the boys is larger than for the girls, but just a little larger. Can this make any difference to the performance on math tests? Yes, a huge difference.

The lower-left picture is just like the larger picture, but it blows up the area of high test scores (those greater than 3.5). The dashed line (the boys) is everywhere on top of the solid line (the girls), which means it is more likely for boys to outscore the girls at the highest levels of the test.

The picture on the lower-right shows how much more likely. For example, for test scores of 5 or higher, boys are over 9 times more likely to do better than the girls! This is not to say that there will not be any girls at the very top: there will be.

What this all means is that you will see many more boys than girls at the very top of the test scores. But it also means that you will see many more boys than girls at the very bottom of the test scores! We could draw a similar picture to the lower-right which shows those who do very badly at the math tests: boys outnumber girls here, too.

As the WSJ said “Girls and boys have roughly the same average scores on state math tests, but boys more often excelled or failed”. This is all because, for every grade and in every state, the mean of the boys and the girls is the same, but the boys are always more variable.

Now, if this difference—for it is a difference—persists at the college and post-graduate level, and if math professors are chosen by their ability, than males will outnumber females. Which is exactly what is found at actual colleges and universities.

Why the difference in variance exists is unknown, but it is again a political question. We could surmise, with Mr Summers, that the difference is due to innate tendencies, but to admit that is to admit that, at the top, men are better than women. But this also admits that, at the bottom, men are worse than women. The difference might be due to education: teachers could be singling out the best—and worst—boys and then treat them differently than the best and worst girls. But this is unlikely at the college level, and does not account for post-graduate performance either (number and quality of papers published, etc.).

It is more plausible that males and females are different in their abilities. Just don’t say this very loudly, or you will get yourself into some serious trouble, like Mr Summers, who, as the philosopher David Stove often said, “quickly rediscovered the definition of the word sacred“.

UPDATE: some statistics on this from Investor’s Business Daily.

What would you think if you were reading a new research result, written by people who all had advanced academic degrees in the relevant fields, that claimed that smoking cigarettes had no correlation with cancer?

You would almost certainly discount that report, given all the other information you have acquired about smoking’s effects.

Now what if you also learned that the new report was written by a group funded by R J Reynolds, the large tobacco company? Further, it comes out that nearly all of the people who contributed to the report smoked. Now what would you think?

Obviously, you would not only discount whatever you heard from the group, but you would be suspicious that whatever they told you was the exact opposite of the truth. Right?

UPDATE: Something happened to the original, which is still linked below (the second one). But somebody else has posted the same video, at another link. Thanks to John for the heads up..

“Too embarrassed to stand up“? Good grief!

A tip of the hat to Dennis Dutton’s Arts and Letters Daily where this article from the Chronicle of Higher Education appeared. Incidentally, since the Chronicle bought out A&LD, there have been a lot more links to Chronicle stories, which inevitably means some weaker stories get linked.

Like this one by Russell Jacoby entitled “Gone, and Being Forgotten: Why are some of the greatest thinkers being expelled from their disciplines?” He starts

How is it that Freud is not taught in psychology departments, Marx is not taught in economics, and Hegel is hardly taught in philosophy? Instead these masters of Western thought are taught in fields far from their own. Nowadays Freud is found in literature departments, Marx in film studies, and Hegel in German.

Jacoby seems to think that these three were “leading historical thinkers” and he laments their absence from college syllabi. He sneers, “Psychology without Freud, economics without Marx, philosophy without Hegel: For disciplinary cheerleaders, this confirms intellectual progress. The cloudy old thinkers have made way for new scientific researchers.”

Well, yes.

No psychologist, after reading Frederick Crews’s devastating critiques can take Freud seriously, no economist who has at least a passing knowledge of history can but laugh at Marx, and no philosopher familiar with David Stove’s quip that Hegel was a philosopher “of the kind who would quickly starve to death if [his] food supply depended on [his] ability to argue” would spend much time with our German friend.

The reason, then, that these gentlemen are not taught in their respective fields is because of the simple fact that their theories have been discredited and so should not be taught—except as they are historically interesting. For example, it is a fascinating sociological question to ask why people were so eager to believe in Freud’s manufactured experimental “evidence”, or why so many who thought that communal “ownership” of property were so willing to slaughter their fellows in the name of utopia. These three “thinkers” were “leaders” in the sense that they won many converts based upon faulty, “cloudy” reasoning, but not because their ideas were any good.

In, for example, the field of physics, Newton is still taught in mechanics, even though his ideas have been superseded by quantum mechanics, because Newtonian mechanics are more than reasonable approximations to everyday phenomena. Too, physics texts do not spend much time with failed, obvious false theories because the purpose of these books is to teach what is true and useful. Physics books are not meant to be works of history. There is no analogy for Jacoby’s crew. Freud’s etc. theories are not approximately true or even useful, but just plain false or intentionally misleading. Their names can, of course, show up in the relevant psychology, economic, and philosophy courses, but as examples of “what not to do”, but that’s about it.

Jacoby’s question, then, is rhetorical. They are not taught because they should not be taught.

That this is recognized means that there is some hope in academia. But it is significant that Jacoby found Freud being taught in literature courses, Mark in “film studies” programs, and Hegel in German language classes. Obviously, the people who teach these subjects will, on average, know less about psychology, economics, and philosophy than their peers in those fields. Meaning, naturally, that they will be less well equipped to know which ideas are bad and which good. They will more likely act on what they hope or wish to be true. They will have a better chance of being seduced by easy theories.

Bad ideas never die. They just shift departments.

The New Museum is hosting an exhibition entitled “After Nature” whose tagline is “THE earth will pass away with a great noise and there will be no place for it.”

It is not clear what they will do with the earth, as it’s rather large. But it doesn’t matter, because this is art.

A key “piece” is Maurizio Cattelan’s “Untitled”, pictured below.

It’s a little difficult to see, but the thing that mom and dad are pushing is a stroller (see the cover of today’s New York Sun for a glorious half-page picture of the horse). Dad is cradling baby, hiding the exhibit from baby’s eyes. He is thus depriving baby of bringing to mind “apocalyptic thoughts.” Shame on him.

When I gaze upon the backside of the horse, I don’t know about you, but I see it as “a story of abandonment, regression, and rapture?an epic of humanity coming apart under the pressure of obscure forces and not-so-distant environmental disasters.”

Such a work of art is priceless, as will be obvious to all but the lowest Philistine, so I have been unable to find how much it costs. It might help to know that recently Damien Hirst’s similar work “Away From the Flock, Divided” (1995) went for just over $3 million. This daring art featured a “sheep, sliced in two and preserved in aqua-colored formaldehyde.”

I don’t know who it was that said that modern artists and the rich who buy their works are horse’s asses, but it’s obvious that this was a person of low education.

If you doubt any claim made about man-made global warming, Jennifer Jacquet thinks you are a “miscreant” and on par with those who deny that “smoking causes cancer.” She also draws the conclusion that since one “denialist” sports the same upper-lip fuzz as Snidely P. Whiplash, the rest of them are somewhere twirling their moustaches and up to now good.

Well, these kinds of childish insults are common by now. Sticks and stones, etc. What makes Jacquet’s edge-of-sanity ramblings interesting is her involvement in work called “Shifting Baselines.” Jacquet, and others at her web site, call “Shifting Baselines” a syndrome.

In case you weren’t paying attention, I said s-y-n-d-r-o-m-e. These are scary things and ordinarily require medical treatment, or even psychological counseling, so we are talking of serious things here. What are the signs of this dread malady? From Jacquet’s link to Wikipedia:

Shifting baseline (also known as sliding baseline) is a term used to describe the way significant changes to a system are measured against past baselines, which themselves may represent significant changes from the original state of the system.

For example (also on Wikipedia)

A cup of coffee may have only cost a $0.05 in the 1950’s, but in the 1980’s the cost shifted to $1.00 (ignoring inflation). The current (21st century) coffee prices are based on the 1980s model, rather than the 1950s model. The point of reference moved.

In other words, the term “shifting baselines” is based on the trivial observation that statements you make about the state of system will change depending on what you reference them to. Originally applied to fish stocks, an example might be that you could have said “Since 1950, fish species A stocks (in area B etc.) have decreased by 32%” or you could have said “Since 1930, fish stocks have decreased by 36%.” Both statements are true (we are supposing), because both have different baselines.

This wouldn’t be in the least interesting, except that people like Jacquet and her advisor Daniel Pauly at the University of British Columbia, are worried that some are not picking environmentally-approved baselines. They are suspicious that the non-Enlightened are picking incorrect baselines so that the can downplay the decline of, say, certain fish stocks.

And they might be right. But they have an easy rejoinder to any that pick a suspicious baseline: just pick a different one and justify it. Voila! If their opponents are trying to goose the statistics disingenuously by cherry picking a baseline, they can point that out too.

None of this behavior yet qualifies as a “syndrome”, however. What makes it one—in their minds—is the idea that there is one, fixed, Platonic, pre-human baseline where the stock of fish species A, and every other plant and animal, was pure and unadulterated. By refusing to recognize this undefiled baseline, we are refusing to admit the obvious: that the world is growing worse and worse through human behavior.

We can then say that the syndrome is “the tendency for each new generation to accept a degraded environment as normal/natural.”

It is a simple biological observation, however, that through all of Earth’s history the quantity of any species has never been fixed or static. There have been the genesis of new species and the extinction of others long before humans came on the scene. And there isn’t any species on this planet that isn’t food for some other species. Life is in constant flux. All this, I imagine, Jacquet and Pauly would admit.

The period of time they are aiming at, as their shifted baseline, is the one right before people got here, say a couple of hundred thousand years ago. But even Jacquet and Pauly must admit that humans have to have some influence on the number of each species alive. Jacquet, as I gather from the picture on her web site, certainly looks healthy and well fed, so I conclude she is eating some of the other species. I presume Pauly is, too.

Thus, since humans must have some influence, and Jacquet and Pauly and the rest of us are currently influencing the environment, it becomes only a question of how much. How much is too much? How much is enough? What is permissible? What is not? And so on.

In other words, the baseline to use as a reference is a moving—or shifting—target that can only be defined by reference to the whole range of human behavior. This means, of course, the best baseline to use in any situation is a political and scientific question. Disagreements about baselines would then appear to be normal human behavior.

But Jacquet and Pauly want to medicalize these disagreements. Any that disagree with “experts”—which I suppose are people so designated by them—are not just making a mistake, they are exhibiting abnormal behavior.

In one way, of course, labeling disagreements a “syndrome” is cheering because it implies that being in the state of disagreement is not the sufferer’s fault. Some thing or somebody is responsible for leading the patient astray. This implies there is a cure, which is simple: remove the thing or body responsible for causing the dissention.

We can count ourselves lucky that they have not yet called for re-education camps or for medicating those inflicted.

If you haven’t seen Jackie and Dunlap before, you’ve been missing out. Here’s there take on the New Yorker’s terrorist Obamas cover. Hilarious.

They have an album coming out. The song “Too Much Lovin’” will undoubtedly sweep the nation.

The headline comes from this article at NASA, sent in by reader “Mike D.”

The gist of the article is “that there’s nothing to report.” Says David Hathaway:

“There have been some reports lately that Solar Minimum is lasting longer than it should. That’s not true. The ongoing lull in sunspot number is well within historic norms for the solar cycle.”…Although minima are a normal aspect of the solar cycle, some observers are questioning the length of the ongoing minimum, now slogging through its 3rd year…Hathaway has studied international sunspot counts stretching all the way back to 1749 and he offers these statistics: “The average period of a solar cycle is 131 months with a standard deviation of 14 months. Decaying solar cycle 23 (the one we are experiencing now) has so far lasted 142 months–well within the first standard deviation and thus not at all abnormal. The last available 13-month smoothed sunspot number was 5.70. This is bigger than 12 of the last 23 solar minimum values.”

In summary, “the current minimum is not abnormally low or long.”

Let’s take a look at the actual data and see if the statements about the “normalness” of the sunspot number are accurate. And let’s keep in mind the real reason NASA made this press release, the purpose of which is never directly stated—can you see it?. I’ll come back to this later.

Here is a picture from NASA showing the “Yearly Averaged Sunspot Numbers 1610-2007.”

Solar cycle “number 1″ peaked around 1760, the cycles and other behaviors before this time are ignored in the official counting. Well, that’s neither here nor there—the labels do not matter—but we should always remember that the sun’s sunspot activity has been taking place for at least 4 to 5 billion years, and we only have measurements on the last 400. Thus we are in a very poor position to say what is “normal” and what is not. We can, however, make statements conditional on the data observed so far.

Hathaway’s analysis starts with cycle number “1″ and ignores the previous data, which, given the extended period of low to no sunspots from 1650 to 1700, actually weakens his case. This is because, conditional on all the available evidence, periods of time with no or low sunspots are not that unusual. These quiescent periods are more likely given all the evidence than they are just using the data from 1749. This is true based on the simple observation that all the data has more quiescent periods than does the later half. It is true regardless of the periodicities or other structures present. Because we have seen periods in the past with few or no sunspots is excellent evidence, after all, that we will see these periods in the future.

So why would he purposely ignore evidence that would have strengthened his case? Part of the reason is that there is the possibility that the data before 1749 is measured with error, and so should be discounted somewhat. However, this error is not especially large. The real reason has to do with the “Maunder Minimum” (shown on the graph), the period with few or no sunspots. This period does not fit the probability model Hathaway has in mind, so it is ignored. NASA says this about the Maunder:

For reasons no one understands, the sunspot cycle revived itself in the early 18th century and has carried on since with the familiar 11-year period. Because solar physicists do not understand what triggered the Maunder Minimum or exactly how it influenced Earth’s climate, they are always on the look-out for signs that it might be happening again.

But Hathaway thinks the “quiet of 2008 is not the second coming of the Maunder Minimum.”

Thus we have gone from “For reasons no one understands” to “the solar cycle is progressing normally.” The path from one statement to the other is indeed rocky. This is why I believe Hathaway’s statements are too certain. I believe that periods of low to no sunspots are more likely. I am not, however, disagreeing with Hathaway in the sense that it does not appear that we are in another Maunder: there is only scant, at best, evidence for this.

As a technical note: It is not clear that the uncertainty in length of time in months that the cycles last is best represented by a normal distribution, as used by Hathaway. Ignoring the Maunder makes his approximation a better one, but there is never a good reason to ignore part of the data it does not fit your expectations.

Anyway, back to the real purpose of this press release. Why are people so interested in the length of the solar cycle? Easy. Because for years, most climatologists insisted that the role the sun plays in the climate was minimal. That is to say, changes in the behavior of the sun were not thought to be related to changes in the Earth’s climate. The sun, which alone supplies all the energy that goes into creating the climate, was thought not to be important. Obviously, this attitude is starting to change. This press release is a tacit admission that some now admit some role of the sun in climatology.

I do not have time to talk here of the actual methods to predict sunspot number, which is an important activity in space weather. But take a look at the first picture in the press release and see if you can not anything odd.