William M. Briggs, Statistician

Graph is here.

The headlines of today’s New York Daily News is

CURSES!

It seems the New York Giants will play the Green Bay Packers in some sort of sporting event this coming weekend. What makes this interesting is that Brett Favre, the star player of the Packers, has just appeared, much to the delight of the News, on the cover of Sports Illustrated, because the Daily News feels that this appearance will befoul Mr Favre, causing him to fail and so let the Giants win the game.

Got all that?

The News is hoping that Favre will fall pray to the so-called Sports Illustrated curse. What is supposed to happen is that the showing of an athlete on the front cover of that magazine applies a sort of black magic to that athlete’s capabilities, and that he will soon perform badly, or not up to expectations. The SI magazine itself is aware of its supposed talismanic powers, and wrote an article analyzing the statistics of the curse.

They examined 2,456 covers and found 913 jinxes, for a rate of 37%, which they intimate is a number high enough to conclude “something” is going on. Perhaps you think so, too.

Now, even though the editors said they listened to the advice of “sober statisticians” (if you attended any of our meetings, of Bayesians, anyway, you’d realize that this adjective is mistaken), they didn’t really take them seriously. Because it is true that mere numbers can remove the mystery and explain the curse. Take a look at this picture:

This describes that probability that Brett Favre’s performance will be way below, below, average, above average, and way above average. Higher levels of the curve indicate higher probability; the highest probability is for “average” performance. Now, that “average” is Favre’s average, not yours or mine. It applies to his lifetime performance capabilities and simply says that on most days he’ll perform at his average level.

Of course, there is some probability that he’ll perform “Way above” average and, judging by this year’s record, he has so far. But if you had to make a bet, and there is some evidence that people bet on football games, you’d do well to guess his performance in his next game will be just average. There is some correlation from game-to-game, meaning that if Favre played way above average last week, he’ll tend to also be above average this week, but this tendency is actually not that strong, and your best bet is still to say just average.

What about the curse? What happens is that some athlete somewhere in some sport will perform way above average. Sports Illustrated has to have something on its cover and so seeks out those athletes who are doing exceptionally well, and picks from among them the one that outperforms them all. In other words, this particular athlete will have performed way, way above average, a rare event. So their picture is shown. But, lo! In the coming weeks, our poor athlete slumps, disappointing all,? once again proving the validity of the curse.

All that has happened, however, is that the athlete has “regressed to his mean.” The overwhelming probability is for that athlete to perform near their average, which the athlete subsequently does. It’s no slump after all, just a return to regularity.

To say the SI has a “cover curse”, then, is no different than saying a coin has been hypnotized after a “Tail” finally shows up after a successful run of 20 “Heads” in a series of coin flips.

I realize, however, that showing the “curse” to be merely a banal expectation of statistics sucks the fun out of it. I don’t want you to go away depressed, so I’ll close by telling you that I am a Lions fan.

Who doesn’t love to read about statistics and statisticians? That’s a rhetorical question, my friends, so don’t bother answering. But I will allude to an answer, by telling you that I begin the statistics classes that I teach by asking the students whether they’d like to learn a magic trick. They always say yes. It goes like this:

Next time you are at a social gathering and somebody introduces themselves to you and asks what you do, say these magic words, “I am a statistician.” And…Poof! They will vanish before your eyes! It never fails.

So it’s not surprising that some of us feel left out from time to time. Which explains why the American Statistical Association (of which I am a member) has issued this statement “endorsing” the conclusions of the IPCC report while also admonishing climatologists to include more statisticians in their work.

The ASA recently convened a meeting of statisticians to ask them how they can be more involved with climate change. The statement was their answer. These sort of meetings do not always go well. The ASA had another such confab back in ‘95 and invited Chicago high school students to listen to the delights that awaited them if they chose a career in statistics. The lecture was by the distinguished ASA president, who was thorough, as all statisticians are. At the end of his talk, he opened the floor for questions. There was a period of silence when, finally, one brave young man shouted out, “Yeah. Why are you so goofy?” So you can see the danger.

Anyway, except for the blanket political* “endorsement”, given only to show that we’re willing to play along, the rest of the statement is pretty good, including this, “Over the course of four [IPCC] assessment reports, a small number of statisticians have served as authors or reviewers. Although this involvement is encouraging, it does not represent the full range of statistical expertise available.”

And this, “Even in the satellite era ? the best observed period in Earth?s climate history ? there are significant uncertainties in key observational datasets. Reduction of these uncertainties will be crucial for evaluating and better constraining climate models.”

Most importantly, this, “The design and analysis of computer experiments is an area of statistics that is appropriate for aiding the development and use of climate models. Statistically based experimental designs, not currently used in this field, could be more powerful. It is also important to understand how to combine the results of experiments performed with different climate models. Despite their sophistication, climate models remain approximations of a very complex system and systematic model errors must be identified and characterized.”

The main thrust is that climate scientists have not done as well as they could quantifying the uncertainty in their models, results, and speculations, and that statisticians should be more frequently consulted, because if we’re good at anything, this is it.

We’re also not too bad at magic.

*Of course it’s political, because you cannot simultaneously have a plea for statistical? analysis of climate models while at the same time concluding those analyses are proper.

Another one of those “studies” showing that guns might be unsafe (who knew?) has come out. Here’s a quote: “Over 70 percent of families surveyed reported not storing their firearms safely in their residence,” said Robert DuRant of the Wake Forest University Baptist Medical Center. “This concerns us a great deal because having guns in the home increases the likelihood that they will be used in a suicide or unintentional injury.”

The good doctor would have also wanted to point out, I am sure, that, if a family didn’t have a gun in the house, then of course that missing gun would not be very dangerous. Indeed, one of the “study’s” most prescient conclusions was that the “safest practice would be to remove guns from the house.”

These guys, these “researchers”, never seem to remember that Mark Twain was ahead of all of them, warning people way back in 1882 about the inherent dangerousness of guns in the house:

Don’t meddle with old unloaded firearms. They are the most deadly and unerring things that have ever been created by man. You don’t have to take any pains at all with them; you don’t have to have a rest, you don’t have to have any sights on the gun, you don’t have to take aim, even. No, you just pick out a relative and bang away, and you are sure to get him. A youth who can’t hit a cathedral at thirty yards with a Gatling gun in three-quarters of an hour, can take up an old empty musket and bag his mother every time at a hundred. Think what Waterloo would have been if one of the armies had been boys armed with old rusty muskets supposed not to be loaded, and the other army had been composed of their female relations. The very thought of it makes me shudder.

Anyway, this particular “study” estimates some 200 million guns are owned and, necessarily, stored by us. Just imagine the potential slaughter that awaits! Always remember: guns might be unsafe. Which is why you hear so many stories like this, again from Twain:

Never handle firearms carelessly. The sorrow and suffering that have been caused through the innocent but heedless handling of firearms by the young! Only four days ago, right in the next farmhouse to the one where I am spending the summer, a grandmother, old and gray and sweet, one of the loveliest spirits in the land, was sitting at her work, when her young grandson crept in and got down an old, battered, rusty gun which had not been touched for many years and was supposed not to be loaded, and pointed it at her, laughing and threatening to shoot. In her fright she ran screaming and pleading toward the door on the other side of the room; but as she passed him he placed the gun almost against her very breast and pulled the trigger! He had supposed it was not loaded. And he was right—it wasn’t. So there wasn’t any harm done. It is the only case of that kind I ever heard of.

Lest you think this new “study” didn’t find anything useful to say, we have this: “Our research shows that unsafe gun storage is associated with families who were raised with guns in the home,” DuRant said. “They tend to be more comfortable with guns…” I never would have guessed this, so it’s a good thing that this “study” was conducted.

I’m a veteran and haven’t killed anybody in years. But if you read the New York Times you’d be right to worry that I might.

The Sunday, 13 January 2008, edition of the Times spent four pages! detailing that, in the four and three-quarter years since the Iraq war began, returning soldiers, sailors, and airmen came home horribly scared—mentally, of course—and committed 121 murders. Which is a big number, no question; and probably some, or even most, of the people killed didn’t even have it coming to them.

Military writer Ralph Peters, in today’s column for the New York Post, shows that about 350,000 soldiers have come back from both the Iraqi and Afghanistani wars. That makes the per-year murder rate equal to about 7.3 per 100,000.

Time to seriously fret about the mental health of soldiers? Perhaps we should lock them down for a cooling off period until they loose their aggressiveness.

It was at this point that Peters did what any good statistician would have done: he refused to look at the statistic in isolation. He asked: is 7.3 a lot, or is it a little? How can you find out? It’s easy: by going to the Bureau of Justice web site and looking at the murder rates per 100,000 in a demographic most similar to that of GIs, which are 18-24 year-olds:

The civilian murder rate is 26.5 per 100,000

which is more than 3.5 times higher than for GIs! Incidentally, the murder rate for 14-17 year-olds is 9.3; and for those 25-34 it is 13.5, both higher rates than for GIs. It isn’t until you reach the the 35-49 year-olds do you find a lower rate at 5.1 per 100,000. As Peters says the Times

unwittingly makes the case that military service reduces the likelihood of a young man or woman committing a murder.

But his best work comes when he notes

In 2005 alone, 8,718 young Americans from the same age group [as GIs] were murdered in this country. That’s well over twice as many as the number of troops killed in all our foreign missions since 2001. Maybe military service not only prevents you from committing crimes, but also keeps you alive?

Peters has called on the Time’s “public editor” Clark Hoyt (who is in charge of correcting errors) to acknowledge the paper’s purposeful character assassination of our veterans. Add your voice to Peters’s: Hoyt’s email is public@nytimes.com.

Update: 16 January 2008.? Good thing I bought a bigger hat. NYPost.com

From the video where Mr Cruise identifies scientologists:? “You can see the look in their eyes, you know the ones who are doing it. And you know the spectators, the ones who are going, ‘It’s easy for you’ … I’ve canceled that in my area of my mind. So it’s our responsibility to educate, create the new reality. We have that responsibility to say, ‘Hey, this is how it should be done.’”

Be sure to watch the last minute.

From today’s Syndney Morning Herald comes the headline: “Global warming to impact health“.

First, by impact the reporter almost certainly means influence, a more accurate, but far less energetic and “actionable”, word. But never mind that. Our lesson instead comes from the story, one of a breed which appears almost daily in some major newspaper somewhere in the world.

But before we can get to it, you first have to learn, if you do not already know it, the definition of tautology. A tautology is a statement which is always true; that is, no matter what happens in the word, no matter what conditions eventually hold, a tautology will be true. Some examples: “Either it will rain tomorrow or it won’t” and “Marxism is a stupid theory or it is not.”

Here, from the article we are studying, is the lead sentence; it is a tautological fragment, “Rises in temperature produced by global warming could result in an increase in the number of people being admitted to hospital with kidney disease, heart disease and mental illness in Australian cities.” To make this into a grammatically correct tautology we need only add the implied clause “or the rise in temperature will not result in an increase, etc., etc.”

So the reporter has written something which is true, which will always be true, and will be true regardless whether mankind influences the climate or not. But he has written his tautology in such a way to show where his sympathies lie, much as I did in my second example. In any case, we have no grounds for criticizing the reporter on the grounds of accuracy. All such attempts, which I have seen from the skeptical community, are doomed to failure.

We now have to look at the “study” on which the reporter did his article. This will require some work from us, but it is exceedingly important that you understand this study, because it is entirely typical of academic work in this area. You will see more of its kind, and with increasing frequency, so it is imperative that you learn to recognize it and ascertain how to properly criticize it.

Here are the second and third sentences

The study, by a team of academics and senior health professionals from across the country, compared the number of hospital admissions, ambulance trips and the deaths in Adelaide during heat waves, with those in normal weather conditions.

The heat waves - defined as a periods of three days or more in which the average temperature exceeded 35 degrees - produced a seven per cent increase in admissions to hospital and a four per cent increase in ambulance trips.

They also tabulate rates of kidney disease and mental illness under non-heat wave and heat wave conditions, finding these maladies increase during heat waves.

Here is their argument: since, they conclude, more cases of some diseases are present during heat waves, and heat waves will increase with global warming, and that global warming is true, we will see more cases of these diseases.

The structure of their pleading is in perfect logical form, and is correct; that is, their conclusion is true given their premisses. I emphasize: you cannot criticize the form of their argument, since that form concludes something which is true. Or I should say, conditionally true. We will see more disease if it is also true that more cases of some diseases are present during heat waves, etc.

Are their premisses true? I will offer a series of alternate possibilities and likely faults, but I am sure to miss some, which I hope my readers will help supply.

Statistical sample criticisms:

• Did the authors look through the data to find diseases that increased in frequency during heat waves? If so, it is highly improbable that if we look at future heat wave data, we would see the same high levels of the diseases, most would have “regressed” to their mean level. And other diseases that they did not study will be found to have increased in frequency.
• What period of data was used?? Presumably, the epidemiology of these diseases have changed through time, certainly “ambulance driving” has.? The time series component to these data should have been accounted for.
• How many diseases did they find that did not increase in frequency during heat waves? These should have been noted.
• How many diseases did they find that decreased in frequency during heat waves? These should have been touted as benefits of warming.
• What were “non heat wave conditions”? Cold waves? All other periods of time? If cold waves, then how many diseases increased in frequency during cold waves? These should have been touted as benefits of warming. If all other periods of time, then they have chosen a poor sample: cold waves should have been separated out.

Medical criticisms:

• Are there rigorously clear and certain connections between humans living in heat waves and the diseases noted? If not, then the uncertainty associated with each should have been detailed.
• Again, the diseases increasing in frequency under cold waves were ignored.
• What benefits for other maladies are there for increased warming? It is foolish to say there are none, for, at the least, fewer people would die from extreme cold.

Technological criticisms:

• It is not at all certain that, given that heat waves will increase in frequency, people will suffer in them as they suffer now. It is highly probably that technological advances will, for example, increase the availability and efficiency of air conditioning.
• Medical science, too, will almost certainly increase in efficacy and, with high probability, lessen the number of people susceptible to the diseases under question, therefore, even if heat waves increase, the rate at which people suffer will decrease.

Global warming criticisms:

• Even if global warming is true, it is not certain, and even unlikely, that heat waves will increase in frequency. Assuming the models which predict warming are accurate, they predict more warming at nighttime and a more evening out of temperatures (reducing the diurnal swing of temperatures) than an increase in severe weather. In any case, the uncertainty inherent in these forecasts of increasing heat waves must be taken into account, and it was not.
• All other possible benefits of warming were ignored.
• And, finally, the uncertainty that global warming will continue was not accounted for.

Every criticism I offered did the same thing: increase the uncertainty, or decrease the certainty if you like, that we should have in the conclusions, in my view, to such an extent that the study is nearly worthless, and should not have seen publication.

But the authors were not content with their “findings”, they progressed to naked speculation: said one of them, warming “might also bring a significant increase in previously uncommon diseases such as Dengue and Ross River fever to Australia’s rural communities” and that we “could see both a worsening of existing diseases as well as the spread of diseases usually associated with warmer region.” Of course, we could; it is mere tautology to say we could, but to offer such a prediction without evidence and without an expression of uncertainty can rightly be called fear mongering.

I hope you have learned a little about how to properly criticize studies of this type. But whatever other criticism you offer, you cannot say this study, and others like it, are “not science.” It is science, but it is bad science, poorly executed science, and irresponsible science.

Take three-quarters of a hour and watch the following video interview with Anthony Daniels, a.k.a. Theodore Dalrymple.

Daniels is one of our most thoughtful, intelligent, and compassionate writers on culture. A quick Google search will bring you many of his books and articles.

The streaming video, first appearing on Dutch public television, is here.

It may finally be time to start worrying. The horrible effects of global warming look to have begun

It is estimated that at the Battle of the Somme in World War I, one million soldiers were killed or wounded. The men were subjected to continuous bombing and machine-gun fire, engaged in hand-to-hand combat, as well as endured poison gas attacks. On the most hideous day of the fight, the British lost over 50,000 troops. It has been called one of the bloodiest battles in all of history. It is not surprising, therefore, that a few of survivors reacted negatively, and experienced shell-shock, which is a complete mental breakdown. Incidentally, the term originated in that war.

Some of the distressing symptoms of men suffering from shell-shock are: shaking and tremors, sweating, nausea and vomiting, abdominal distress, urinary incontinence, palpitations, hyperventilation, dizziness, insomnia, nightmares, hyper-vigilance, heightened sense of threat, anxiety, irritability, depression, substance abuse, loss of adaptability, suicide and disruptive behavior, mistrust, confusion, and extreme feeling of losing control.

So it is with some anxiety that I read that Ted Scambos and his fellow glaciologists at the National Snow and Ice Data Center in Boulder, Colorado, were, he said, “shell-shocked” that the rate of loss of glaciers on Greenland might be occurring at a rate faster than some glaciologists have predicted.

This is worrying for at least two reasons. The first is that since it is well known that Boulder is one of the nation’s top spots for hand-wringing, the last thing the therapists who live there need is an increase in psychiatric cases. They will not be able to cope with the patient load and we might have to bus emergency relief shrinks in.

The second, and more important reason, is that, if Scambos’s statement is true, and not just an exaggeration said to a reporter over-eager to emphasize the possible dark side of the future, then we can officially count Scambos and his colleagues as the first casualties positively attributable to anthropogenic global warming! Even worse, this new form of shell-shock might be infectious, and could spread not just to other glaciologists, but to other climate scientists as well. There is already good evidence this is the case, judging by what you see printed daily in the headlines, so don’t be too quick to dismiss or scoff at the idea.

So get the word out, my friends, raise awareness of this new and debilitating form of illness, before it becomes epedemic in proportion, and before you find that you too have succumbed to this dread malady.

Most warm weekends, you can find me in Central Park by the Tavern on the Green playing the beautiful game of petanque. This is the French version of bocci, only unlike the Italian game, which uses effeminate wooden balls, we use manly balls of steel.

The game goes like this: each team takes turns throwing 800g balls six to ten meters towards a small colored ball, called the cochonette. The goal is to get as close to the cochonette as possible. When each team has thrown their six balls, we walk up to the cochonette and try to see which team’s balls is closer. Often, of course, it’s a narrow call whether my ball or my opponent’s ball is nearest.

Now, I have stood over the cochonette literally thousands of times—it helps to understand that I have perfect vision and have never needed glasses—and in a large fraction of those times I would have sworn, on my soul, that my ball was the closer of the two. Sometimes, of course, it is, but if you know me as a player, you know that is a rarity. Usually, my ball is the furthest, but it is often manifest, I pledge on my honor, that mine is best! Not only does my ball appear closer, but it is so obviously closer, that I cannot for the life of me see why there is an argument from my opponent.

But there is invariably a dispute, so out comes the stick, usually a telescoping radio antenna stripped from its base. Somebody bends down and measures the distance between all the balls and the cochonette. Once the objective results are in, there are usually groans from one side and calls of “It was obvious” from the other.

Psychologists are well familiar with this phenomena; in science it is called the experimenter effect. It describes what happens when an honest scientist carries out an experiment in the absolutely fairest way possible, looks at the results, and sees exactly what he expected to see, only to find that, later, other scientists have shown his result to be a statistical artifact or due to a forgotten, unaccounted variable. This is why, for example, double-blind trials in medicine are required, else the doctors would always find that the “active” pill beats the placebo.

You must understand that our scientist is a nice person, is kind to small animals, pays his taxes, and votes the proper way. He, with the best, and most honest, intentions carries out his experiments in the most meticulous manner he knows how. He is unbiased and exceptionally bright and in no way delusional or politically motivated. Only, it turns out, he is far too confident in his results. This is no dig against our scientist: most people in most things are overconfident; this is another thing that psychologists well understand.

It is true that greater than 99% of all climatologists are like our scientist, forthright, incredibly bright, and diligent. Too many “climate skeptics” have accused climate researchers as being driven by politics or by money (in the form of grants), and so seek to disregard results from these scientists on that account. But this is no different than the “green activist” denigrating findings from scientists whose research was funded by private companies. All results have to be analyzed on their own merit.

Climatologists are, I believe, too confident in their results: if there is any political temptation here, it is towards the tendency to make public statements that convey more certainty than research warrants; but there is no attempt to mislead. Without question, “activists” are annoyingly precise in their pronouncements, and since theirs is a political life, there is no temptation to which they will not give in. But many skeptics, too, could use a dose of humility. To say, for example, that “global warming is a hoax” is carrying constructive criticism too far.

I appreciate those folks who pay me the compliment of including my entire posts on their web sites, but please ask permission before you do so.