William M. Briggs

Statistician to the Stars!

Page 395 of 693

Autism Caused By Highways?

AutismEpidemiology is nothing if not a productive field. All that is needed for success is a database (larger the better), a disease (any will do), and some minor facility with statistical software.

Our latest example is the Environmental Health Perspectives1 paper “Residential Proximity to Freeways and Autism in the CHARGE Study” by Volk et al.

The authors found a group of mothers who lived in California. They measured the distance these mothers lived to “freeways and major roadways” for the majority of their pregnancies. They also took note whether their children developed autism. They posited that living closer to freeways increased the risk of autism. They also measured mothers’ education, age, and smoking status, the kids’ race and whether the kids were preemies.

They purposely identified 304 kids with autism and 259 without from a database “frequency matched by sex, age, and broad geographic area.” Ideally, since this data was hand-picked, they should have had equal numbers in each group, and equal frequencies of boys in each group. But the autism group had 87% boys, while the normal group had 81%. In other words, by design (purposeful or accidental), they put more boys in the autism group than they put in the control group. They gave this difference a “Chi-square p-value” of 0.10. What does that number mean? Well, nothing (see the footnote2).

As to the models:

Specifically, we included child’s sex and ethnicity, maximum education level of the parents, maternal age, gestational age at birth, and maternal smoking during pregnancy.

This was a logistic regression model, which here assumes the log-odds of developing autism is a linear function of the attributes just mentioned plus the distance (in meters) from freeways or major roadways. No plots of the freeway or roadway data are shown which indicate if this is a good assumptions.

Instead, the authors do a strange thing: they do not model the actual distance but chop up the distance into arbitrary bins. The first is living less than 309M from a freeway (about three football field’s distance). The next is living from 309M to 647M, then living from 647M to 1419M, and finally living greater than 1419M. They did the same thing for major roadways: less than 42M, 42-96M, 96-209M, and greater than 209M.

Two separate models were run: one for freeways, the other for major roadways. Only the less-than-309M group with respect to the greater-than-1419M group reached (classical) statistical significance. None of the other groups did. Nor did any bin in the roadways model. The (exponentiated) parameter associated with the freeway 309M-model was 1.86. This is incorrectly said to the the odds ratio for those to live withing 309M compared to those living farthest. It isn’t: it’s the parameter. To get the real odds, we’d have to “integrate out” the parameter, which would make the real odds ratio, assuming all else true and good, to be less than 1.86.

Remember when we talked about how changing the start date in time series analysis can lead to opposite conclusions? It’s the same here: why 309M and not, say, 308M or 310M? And the same for the other buckets. Different cuts will give different conclusions. Why not just leave distance in as a linear function? I mean, why chop it up at all?

Be generous and assume that these cuts are “real” and the “best”. Can we think of any other reason which might account for the results? Living within a football field or two of freeway in Los Angeles is a good indicator of what? Great medical care? Wealth? Health insurance? You’ll notice the authors left out any measure of economic importance.

In other words for this study, the effect is small, it is only for one small suspiciously chosen subset of the population (10% by the authors’ reckoning), and the posited cause is most likely an artifact caused by mismeasure and conflation of unmeasured socioeconomic variables. In short, the article gives no more than a vague suspicion that freeways are autism inducers: it even says they usually are not. It also says roadways are not autism inducers.

What makes this study interesting, then, is how it was reported in the press. The Wall Street Journal, not usually given to flights on fancy, reporting on this paper (and others) led with the headline:

The Hidden Toll of Traffic Jams

Scientists Increasingly Link Vehicle Exhaust With Brain-Cell Damage, Higher Rates of Autism

Lots of reasons given how exhaust might influence this or that biologic process, words like “Scientist believe”, a quote from the study author (“The evidence is growing that air pollution can affect the brain”), a quote or two from non-authors (“There is real cause for concern”).

CBS news, not content with the actual numbers, juiced them a little: “A new study shows that children in families who live near freeways are twice as likely to have autism as kids who live off the beaten path.”

No news source I could discover provided any analysis of how weak—and even nonexistent—the effects of this study were. Lesson for reporters: don’t trust scientists. We are no different than anybody else.

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1Volume 119, number 6, June 2011, pp. 873–877. Thanks to Willie Soon for suggesting this topic.

2Ordinarily, in frequentist statistics, a chi-square test is used to test for “differences in proportions” in groups. Here, there were two groups with proportions 87% and 81%. Are these different? This is not a trick question, but it also one which is not to be answered within classical theory. That is, the chi-square is not an answer to this obvious question. The test is not a test of difference in actual proportions, but something else. Okay?

Instead, the statistician asks, “Assuming the ‘true’ proportion of boys with autism and boys without autism is identical: if we sampled from these two groups indefinitely, what is the chance of seeing a certain mathematical function (the chi-square) of these two sampled proportions being larger than the chi-square we see for the actual data?” This is 10%.

And so? Well, again, well nothing. The statistic has no bearing or meaning to this data. The database was built by hand with the intent of matching by frequency the sex of kids with autism. It failed in this; slightly, but it still failed. The authors could have, just as they picked the other data by hand, tossed out a few of the boys in the autism group or added a few more in the control group. There was nothing “random” in these selections, not even in the classical sense.

Now this dull subject is important because, as all prior evidence indicates, boys are vastly more likely to develop autism than girls. Why this is so, while interesting, is not relevant to this study. Why is relevant is that this discrepancy, the actual difference in proportions in the sample, might account for the “significance” in the results even though the authors included sex in their models.

Stove On Unintended Consequences

A few quotations, incomplete, on this important subject from Stove’s On Enlightenment.

A primitive society is being devastated by a disease, so you bring modern medicine to bear, and wipe out the disease, only to find that by doing so you have brought on a population explosion…You guarantee a minimum wage, and find that you have extinguished, not only specific industries, but industry itself as a personal trait…This is the oldest and best argument for conservatism: the argument from the fact that our actions almost always have unforeseen and unwelcome consequences. It is an argument from so great and so mournful a fund of experience, that nothing can rationally outweigh it. Yet somehow, at any rate in societies like ours, this argument never is given its due weight. When what is called a “reform” proves to be, yet again, a cure worse than the disease, the assumption is always that what is needed is still more, and still more drastic, “reform.”

It does not follow ,from something’s being morally wrong, that i ought to be removed. It does not follow that it would be morally preferable if that thing did not exist. It does not even follow that we have any moral obligation to try to remove it. X might be wrong, yet every alternative to X be as wrong as X is, or or more wrong. It might be that even any attempt to remove X is as wrong as X is, or more so. It might be that every alternative to X, and any attempt to remove X, though not itself wrong, inevitably has effects which are as wrong as X, or worse. The inference fails yet again if (as most philosophers believe) “ought” implies “can.” For in that case there are at least some evils, namely the necessary evils, which no on can have any obligation to remove.

This means a state which takes money away from people in whose hands it might create wealth, and gives it instead to people in whose hands it cannot possibly do so: the unemployed, the earners of very low incomes, the aged, the sick, the handicapped, unmarried mothers, etc., etc., etc. Millions more people have to be paid, of course, merely for administering this immense redistribution of wealth…A system which rewards the economically dependent, and penalizes the independent, must be a “positive feed back system” (as engineers say) for the creation of poverty.

But Malthus was convinced that communism would replace the existing comparative poverty of most by the absolute poverty of all, and that it would in the process, destroy “everything which distinguishes the civilized by the savage state.”

For “They all laughed at Christopher Columbus” led, by a transition both natural and reasonable, to, “It’s an outrageous proposal, but we’ll certainly consider it.” That in turn led, naturally enough to “We must consider it because it’s an outrageous proposal.”…

As to the weakness of the Columbus argument, it is perfectly glaring. No doubt it is true that, for any change for the better to have taken place, either in thought or in practice, someone first had to make a new departure. But is is equally true that someone first had to make a new departure in order for any change for the worse ever to have taken place. And there must have been at least as many proposed innovations which were, or would have been, for the worse as ones which were, our would have been, for the better. But if in the past bad innovations have been at least as common as good ones, then we have at least as much reason to conclude that we ought to discourage innovators in the future as to conclude that we ought to encourage them…

In fact, of course, innovators-for-the-worse have always been far more numerous than innovators-for-the-better: they always must be so. Consider the practical side first. Do you understand television sets well enough to be able to repair a non-functioning one or to improve a malfunctioning one? Probably not: very few do. And if you, being one of the great majority, nevertheless do set out to repair or improve a TV set, it is a million to one, because of the complexity of the thing, that you will make it worse if you change it at all. Now human societies, at least ones as large and as rich as ours, are incomparably more complex than TV sets, and in fact no one understand them well enough to repair or improve them…

Mathematical Magic Trick: 8 4-Digit Numbers Summing To 35712?

Annemann Jinx!From reader Noble Abraham comes this question:

Is it possible to create a pool of distinct four digit numbers, so that the sum of 8 randomly chosen numbers from this pool is 35712? If yes, how?

I posted this in Quora also.

The basis of this question is actually a performance by a magician. He first wrote down his prediction on a sheet of paper. Then he picks someone from the audience to randomly select 8 four digit numbers from about 1000 (according to him) distinct four digit numbers kept in a bowl. The magician then adds these 8 numbers and finds the sum as 35712, which happens to be his prediction as well. I feel that the pool of numbers has a high probability that sum of any 8 numbers is 35712. Also, think 35712 can be replaced by any 5 digit number, and re-create the pool accordingly.

Am I wrong in asking the question. Or should I think that the fellow has got magical powers. He has chosen at least 11/12 numbers from the bowl that were distinct; 8 for performing the magic and 3/4 to show that they are distinct, before actually going in to the act.

Thank you so much for your valuable time.

You came to the right place because I have studied “Mentalism” i.e. mental magic, i.e. tricks which make it appear that one has paranormal powers, for some time. The top lesson gleaned from years of reading is that the audience never remembers what happened.

I have confirmed this wisdom time and again, both in my own “performances” and in the work of professional magicians. So I hope you won’t take it badly if I suggest you might not have perfectly recalled the exact sequence of events.

Now, there are three broad ways this trick can be accomplished. I won’t tell you exactly how the first two work, but we’ll try to figure out the third. It will be obvious that the methods in all three can be mixed.

The first is substitution. That is, the picking is genuine, as it appears. The magician really does have a bowl of many 4-digit numbers, all different. Eight are pulled out and somebody—probably not him—does the addition. Usually, the magician will have it done on a large chalkboard so that the audience can see the numbers, or he’ll have one or two people use calculators so that the sum can be verified. It helps (but it not necessary) the magician to be able to add rapidly. This is a skill that can be mastered easily.

The sum is announced, perhaps double-checked, then the magician reveals his “prediction”, which is found to match. Off the top of my head, I can name about a dozen ways that the magician “swaps” the prepared prediction with another “prediction” he made after learning the true sum.

The second is a force. Here, the picking is not genuine, despite appearances. There are literally hundreds of ways, with new ones invented monthly, whereby a magician can make it seem that you have a free choice where in reality the outcome is predetermined. (Sort of like how neurologists view all of human behavior.) Of course, he needn’t force every number of the eight picked. He would only have to force enough of them to cause the final solution to belong to a small set (a dozen or less) of possible sums. He could then use any number of methods to reveal the “prediction.” A cheesy, but effective, way to do this is to have, say, four different predictions in your suit pockets, two in the breast and two in the outside pockets: you pull out the one that was the final force. A miracle!

The third is mathematical. That is, the 4-digit numbers on the slips are designed such that picking eight of them force a predetermined single sum of 35712. There cannot be 10,000 slips with all the 4-digit numbers 1000, 1001, 1002,…, 9998, 9999 because, of course, by chance you could end up with the sum 8028 (the lowest possible) or 79964 (the highest possible). So the bowl must be loaded with slips such that the sum is fixed. If such a set of numbers exists, such a trick would be called “self working.” If this method is used, I’d lay my money on a set of sums, not just 35712, married to a substitution.

I saw the solution posted on Quora—the writer there suggests labeling all slips “4464”. This works mathematically, but it makes for a poor performance. You can get away with it only by walking to 8 different, widely separated audience members, have them silently pick a number, then have them add it to the sum shown on, say, a calculator. If you’re blustery enough you might get away with this, but chances are you’ll get caught.

So I leave it for a homework problem for everybody. Does a set of N different 4-digit numbers exist such that pulling 8 out of N leads to a sum of 35712 every time?

The Obama-HHS Diktat On Contraceptive Coverage: Non-Religious Arguments Against It

The government has decided that citizens who agree to work for other citizens must be given “free” coverage for contraceptives and drugs for auto-abortions. The “free” is a misnomer. Actually, the government has decided by fiat—there was no vote, no public deliberation, no input from the citizenry—that employers must pay for their employees’ birth control. Further, employers cannot ask anything for this largess; they are not allowed to require anything from their employees for this mandated “gift.”Gillibrand

In short, the government has decided that being an employer carries with it the obligation to pay for birth control to its employees. In other words, the Obama administration have discovered in the Constitution that it is the duty of employers to fund the reproductive choices of their employees. That is, Mr Obama has discovered the right to “morning after” and pregnancy-prevention pills, but only for those citizens who happen to work for someone. Employers themselves do not have this previously hidden (but always there, after all) “right.”

The strategy, then, for a poor woman who realized that she stayed out too late and woke up in the wrong bed is not to fret, but to instead ask for a job. The moment she is hired she can hold out her hand and demand cash for an abortifacient from her new employer. Sort of a reverse transaction, if you understand me. And the employer has to pay because he is an employer. The moral for the woman is: make sure you have your resume in order before slapping on the lipstick.

The principle is just as clear for the employer: don’t hire the woman.

But that would be an unexpected consequence, wouldn’t it? The reduction in the rate of hiring women of child-bearing years in order to save unnecessary costs? Not to worry: this can’t be because the modern Theory of Government insists that unintended consequences are impossible.

Senator Kirsten Gillibrand, unfortunately from New York, is livid that those who oppose this newly discovered right have had the temerity to question the government. In justifying the new right she said, “The power to decide whether or not to use contraception lies with a woman, not her boss. What is more intrusive than trying to allow an employer to make medical decisions for someone who works for them?”

The old way was that citizens had to take care of their own reproductive selves. If they wanted kids, they had them. If they didn’t want kids, they took care not to have them. This was called “choice.” Yet as Gillibrand has shown, that word has a new Orwellian spin. The woman now makes the “choice” of forcing her boss to pay for her contraception. Her boss has no say in the matter, not only in whether to pay for this “choice”, but in what the woman does with her contraceptive gift.

But let’s answer Gillibrand’s supposedly rhetorical question. I’ll tell her exactly what’s more intrusive: forcing employers to pay for what is none of their business—and giving them nothing in return. If a woman employee wants to do something with her body when she’s not on the clock, then she should be liable for her decisions, not her employer.

Time for unintended consequence number two from this new diktat: the deleterious increase into Us and Them. Most citizens are not employers, but all citizens have to negotiate life’s road. Through this new mandate, we are teaching, yet again, the majority of citizens to not look to family, to not look to their church or community, especially to not look to themselves, but to look to Them to fix their problems. People are routinely taught to ask the Government or the Rich (the overlap of individuals in these two sets is nearly complete) to take care of them, to tell them what to do.

And They will: tell them what to do, that is. We are creating, in the words of Kenneth Minogue, a servile class who who expect to be taken care of simply because they exist. In exchange for this cradle-to-grave caring, the servile must only follow simple rules. This works for now because most of these rules are made to extract wealth from the Rich who are not yet aligned with the Government (this reduces competition and increases the purse), and because, at first anyway, many of “rules” are actually loosenings of older cultural restrictions.

Yet the time is coming when these rules will be onerous even to the servile: eat this, don’t drink that, bring your kids here, teach them only this, do not travel without authorization, and on and on and on. Our lesson: there is no such thing as a free pill.

Update The One, apparently forgetting there is such a thing as Congress, has decided to “compromise” and force insurance companies to pay for contraceptives instead of employers. Every argument above is in force: just replace “employers” with “insurers.” So much for the idea of insurance as risk management.

Dear lefty reader: doesn’t it concern you, even a little, that the president has co-opted powers once belonging to Congress? You like it now, perhaps, because this president is dictating rules which you find reasonable. But imagine, say, George Bush—or Richard Nixon!—doing the same.

Update Just heard The One’s comments on this, featuring, “Women deserve this kind of free coverage…” If you don’t see the moral and economic problem with that, then please don’t vote next cycle.

Update Mr Obama yesterday said, in supposed favor of his new diktat, “No woman’s health should depend on who she is or where she works of how much money she makes.” He repeated the F-word: free, I mean. Women are special class of citizens? Well, long-time readers who were here when we discussed the reasons for not implementing Obamacare will recall that what is happening now was predicted. Stand by for further intrusions of liberty.

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