William M. Briggs

Statistician to the Stars!

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Stats On Extra-Terrestrial Life

From the mailbag comes this question.

Dear Professor Briggs,

Thanks for your astutely iconoclastic posts. I’m very interested on your opinion as regards the “there’s an infinite number of planets so there must be more intelligent life” meme. Disclosure: I am an Anti-Dawkins, “meme”-hating big fan of the late Stephen J. Gould, who thought the odds were greatly against anything like us on other planets, based upon the unlikelihood of so many crucial events in our evolutionary history. Thanks.

Michael Felong

Hey, me too! I also think memes are stupid, except as synonyms for “goofy ideas du jour“. As a scientific explanation for human behavior, they are at best asinine and useless and at worst a scurrilous, unjustified attack on human intelligence.

And I too enjoyed Stephen Gould’s writing and was with him all the way in his criticisms of the risible just-so stories “evolutionary psychologists” tease each other with.

But to your question. If there were an infinite number of planets, and given what we know about physics and biology as it pertains to evolution and so forth, then there would indeed be an infinite number of planets with life. Whether that life is “intelligent” is a separate question requiring the additional premise that all we (a sample of intelligent life) are is the result of “blind” forces. However, suppose that premise is true for the sake of this argument. Then given the other premises, there would be an infinite number of other planets with intelligent life, with “many” (by which I mean an infinite number) of these planets having life that looks and acts like us.

Depressing, no?

All this follows easily from simple probability calculus. Let the chance human-like beings evolve from scratch be some number, and let that number be as small as you like as long as it’s greater than zero. (It cannot be infinitesimally small given we already see us.) Then as long as we’re multiplying this small number against an infinite number, we must end up with infinity.

That means we must have an infinite number of planets that look just like ours (but are not ours) which contain beings who look us, who speak and act as we do, who are our doppelgangers in every respect, even to the point that there must exist at least one (other) plant where a being named “Felong” writes to another being named “Briggs” asking him questions about infinity.

There: An argument only a multi-worlds physicist could love. But also a demonstration that infinities are dangerous creatures not to be trifled with.

Anyway, there are not an infinite number of planets; in this universe there are not a infinite number of anything. I leave open the question whether there really are an infinite number of universes (with which no communication is possible). But inside this one, everything is finite. All is countable and limited.

This being so, it becomes crucial to nail the probability with which sentient life evolves. With an infinite number of planets, its size was irrelevant; here, it is everything. We can still say this probability is non-zero, and we can say this because we can say this. It is here that Gould’s observation that we are highly complex becomes relevant.

And we are complex; I’d say indescribably so, or at least incomprehensibly so. By which I mean that no one person can understand all that it is to be human, or can delineate the exact processes which were the causes of our evolution (an event which I do not deny). The best we can say is that there is nothing else like us; no other animal is even similar to us, especially with regards to thinking—and how that thinking relates to our ability to make tools which would make other intelligent life aware of our existence.

Since even identifying the premises which give us the probability our of evolution is difficult (or impossible), we can’t say with any certainty how many other planets with intelligent species exist. This remains true even if we could unambiguously say how many other planets there were which could support life and can support it for some identifiable length of time (for the universe is also finite in time).

The best we can do is to make the numbers up whole cloth, à la the Drake equation and its variants. This of course makes for a certain amount of fun, and for innumerable Star Trek episodes. But that’s about it.

Spanking Good For Future Education, Income: Researchers

                   Spanked as a child?
Spanking

A new peer-reviewed paper in the journal Pediatrics shows that girls are luckier than boys in avoiding spankings, that those who were spanked as children went on to greater education than those unfortunates biffed on the butts, and that those spanked had higher incomes as adults.

Yet in the paper’s abstract, we read

Harsh physical punishment in the absence of child maltreatment is associated with mood disorders, anxiety disorders, substance abuse/dependence, and personality disorders in a general population sample. These findings inform the ongoing debate around the use of physical punishment and provide evidence that harsh physical punishment independent of child maltreatment is related to mental disorders.

And then there are these summary headlines in the popular press:

The paper is “Physical Punishment and Mental Disorders: Results From a Nationally Representative US Sample” by Afifi and others. What Afifi did was to have a browse through the the National Epidemiologic Survey on Alcohol and Related Conditions and gleaned from that data those who had self-reported mental maladies and those who self-reported being spanked as a kid. This data was the result of face-to-face interviews with U.S. Census workers (surely government workers probing for intimate for-the-record details was no bar to honesty?).

Afifi, a Canuk, starts by telling us that, “The parent or caregiver’s right to use physical punishment has currently been abolished in 32 nations.” And is there a hint of lamentation when she continues, “Canada and the United States
are not included among these countries”?

Adults who answered at least “sometimes” to the question, “As a child how often were you ever pushed, grabbed, shoved, slapped or hit by your parents or any adult living in your house?” were classified as “having experienced harsh physical punishment.” Before questioning the use of harsh for something as small as being “grabbed”, let’s recall that Canada is a foreign country and they use words differently up there, eh?

A more rough-and-tumble interpretation of harsh would be “severe physical abuse, sexual abuse, emotional abuse, physical neglect, emotional neglect, or exposure to intimate partner violence” But we can’t use this definition because the poor folks who admitted to suffering this kind of “harsh” treatment “were excluded from the current sample.” Sigh.

Afifi and crew then checked off whether each remaining individual scored highly on various questionnaires for “major depression, dysthymia, mania, hypomania, any mood disorder, panic disorder with or without agoraphobia, social phobia, specific phobia, generalized anxiety disorder, posttraumatic stress disorder, agoraphobia, any anxiety disorder, any alcohol abuse/dependence, and any drug abuse/dependence.” She even grouped various of these into “clusters.” According to Tables 2 and 3 in the paper, they have 25 separate ways to be (to use a common Canadian phrase) a jelly donut short of a filling.

Anyway, the whole lot was fed into a series of logistic regression models, first adjusting for this, and then later adjusting for that. We can be grateful that Afifi eschewed the normally sacrosanct 0.95% confidence intervals and instead called “significant” those results which had p-values less than 0.01.

Unfortunately, after this promising start, Afifi forgot to adjust for all the different tests she ran. Using (for example), the Bonferroni method, to maintain that “0.01” level of significance, actual p-values would have to be 0.0004 or lower. That means a lot of the mental maladies Afifi thought were associated with mental maladies actually weren’t. Ah, well.

Then it appears she has sometimes mixed up the idea of confidence intervals and p-values. For example, in Table 1, “Widowed/divorced/separated” are given three asterisks (supposedly significant) with a confidence interval that includes 1 (which is not significant). And this happens in Table 2, too.

There were 20,607 individuals in the database (after culling). But only 1,258, or 6%, reported having remembered, or were willing to report to a government worker, “harsh” treatment. Only 6%? Really? I emphasize this to show that measurement error is in play here, which means (in frequentist theory) that p-values are too high.

The mean age of these folks was 48.4 plus-or-minus 0.2 years. Odd, that. And, for example, of those 1,258 “harshies” just 53 reported “Schizoid personality disorder”, yet this was “significantly” higher than the “un-grabbbed.” Small numbers here.

The authors also try to forget those results which appear at the start of this post: effects which show that “harsh” treatment can be good for some (the first link recognizes this). The big question any defender (even you) of this study must answer is: what other effects were positively associated with “harsh” treatment?

It is a disservice (at the least) to go into a database and look only for what you hope to find, to ignore evidence which does not support your theory. Yet that is what appears to have happened here.

July 4th: It’s Summer And It’s Hot


[To be sung to the obvious tune]

I have a sad story to tell you
It might upset you a bit
Last night I walked on the sidewalk
And it was hot.
Pity me!

Not exactly poetry, but it has a certain je ne sais quoi to it. The pathos encapsulated by the last line brings a tear to the ocular orifices every time I sing it. Doubtless you are welling up, too.

And that’s because it’s obvious this song of woe is a tale spun from reality. It actually happened to me! Yes. Last night I did walk out onto the sidewalk…and it was hot! Heat—raw heat—covered me instantly, soaking me, drenching me in waves of unwanted electromagnetic radiation. Layers of humidity, one upon the other, attached themselves to my clothing and my skin, making me feel as slimy as a Chicago alderman.

This went on block after block. The heat did not abate; no, not even in the shade. If anything, it grew hotter. And when I finally reached the bodega in which lay the amber, life-giving well-hopped fluid which my body so desperately craved, I realized to my horror that the air in the place was not conditioned! Avert your eyes if you don’t like graphic descriptions of bodily functions—but this final serving of blistering heat actually caused me to sweat!

I tell you the truth: I have never before suffered such minor inconveniences as this.

I should have listened to the radio, to the television, to the newspaper, to the media in every form which had dispatched scores of reporters to the far corners of the city, where to a man each of them reported that it was hot. These dedicated newsmen warned me to stay inside. They cautioned me to stay where the air was electrically cooled. They told me that sure death awaited me if I dared venture forth without saturating my bodily fluids.

Not satisfied with telling me the temperature, the journalists invented something called a “heat index.” I discovered (via statistical calculation) that this was actual temperature multiplied by three. The heat index isn’t therefore the temperature, but is a number to show what the temperature would be were it hotter than it is. It is a kind of maybe temperature, a temperature that isn’t, an index which can be adjusted up or down according to the importance the journalist gives the story.

When I went out onto the street, I naturally expected to see piles of bodies which had succumbed to the heat. But there were none. This was curious. Perhaps those that were to die had died already; their corpses efficiently removed by the Soylent Corporation. Still, I began to question if there was an element of exaggeration in the repeated dire warnings.

As I walked I recalled how I had lived for three years in San Antonio, Texas (average August high of 96 with liquid skies), and again in Okinawa, Japan (a degree or two cooler, but always wetter), and never had air conditioning. As far as I could ascertain, I had not died from this lack. I also remembered that in all the cars I ever owned, there was no air conditioning. Again, this did not kill me.

There may have been lasting damage, however, because I was for years after this an atheist (I have since recovered). Anyway—full disclosure—there was an air conditioning unit in the apartment in San Antonio, but the (so-labeled by Danny Stiles) blonde bombshell with whom I shared the rent would not allow me to turn it on because she was deathly afraid of contracting Legionnaires disease, which she was sure lurked in the recesses of the machine. Yes.

Who knows where the truth lies. But if there’s anything to this global warming we hear about, it’s likely to stay summer until at least September. Worse, sophisticated computer models say the whole cycle could repeat next year.

It’s the glorious 4th. Happy Birthday, America! Be careful, it’s Summer out there and hot. And since it’s never been Summer and hot before, heed the warnings of your elected and unelected leaders and stay away from any activity in which you might find enjoyment.

Would Finding E.T. Destroy Religion? Experts

Leave it to Live Science to ask Would Finding Aliens Shatter Religious Beliefs? Answer hint: maybe yes, maybe no. Experts say so.

The discovery of life beyond Earth would shake up our view of humanity’s place in the universe, but it probably wouldn’t seriously threaten organized religion, experts say.

Ah, experts. Presumably, given the subject matter, these experts have studied other inter-, and quite possibly intra-, galactic species, watched them develop through crude animism, to monotheism, to their first NPR station, to final stage enlightened atheism, and then waited until those species noticed that there were other species who were not their species. They then gauged how the still-religious aliens in the species that discovered there were other sentient species reacted to the discovery that there were other sentient species. The experts cataloged these reactions and then moved onto the next alien species that had not yet discovered there were other alien species. Do you follow?

Even if you don’t, it’s difficult to imagine what an “expert” in this kind of case is. Doug Vakoch, director of Interstellar Message Composition at the SETI, sure doesn’t seem like one. But he’s the first “researcher” in the story quoted. He said, “I think there are reasons that we might initially think there are going to be some problems. My own hunch is they’re probably not going to be as severe as we might initially think.” Problems? Like Mormons rioting in the street? Hindus queuing up at McDonald’s? Jews clamming on Jones Beach on Saturdays?

The writer of the story, Mike Wall, reveals his biases when he opines

Religious faith remains strong in much of the world despite scientific advances showing that Earth is not the center of the universe, and that our planet’s organisms were not created in their present form but rather evolved over billions of years. So it’s likely that religion would also weather any storms caused by the detection of E.T., researchers say.

The implicit theory is that once a theist is given knowledge that the Earth is not privileged and that newts were once newtosauruses (or whatever), he should wise up and buy a Richard Dawkins t-shirt (to announce to all how much he has grown).

What Wall, and many American non-theists are unaware of, is that the vast majority of theists—most Muslims, most Buddhists, most Christians, etc., etc.—are well in advance of secularists in accepting empirical observations. And they can even show how no empirical observation can be disproof of their religious beliefs.

So it is a wonderment that Wall writes “Nicolaus Copernicus made perhaps the first powerful case for it in 1543, when his seminal work ‘On the Revolutions of the Celestial Spheres’ showed that Earth revolves around the sun, rather than the other way around.” Wall might have learned this from astronomer Seth Shostak, who sagely said, “We haven’t been the center of the universe for a while now — four centuries.”

Both Shostak and Wall appear not to have known that Copernicus was a devout Catholic priest (there is also evidence that he might have only took minor orders), that he received a doctorate in Canon Law, and that his theory of the heavens in no way “challenged” his faith. The “experts” also failed to understand that while the Earth was indeed seen as a kind of center in Western life, it was the same kind of center as the hole in the middle of your commode. Instead of a privileged place, Earth was seen as something much lower.

The nearest thing Wall could find to a true expert—and I do not jest—was science-fiction author Robert Sawyer, a man used to thinking of how people would react to the “problematic” news that other sentient beings exist. He said, “If you ask most people whether there is alien life, most people say yes.”

They do, indeed. Even to the extent of believing that they are among us, snatching and probing with merry abandon. And this is for good reason, at least in those countries with movie screens. Alien life surrounds us on screen and in print. I myself have been in a dark room with strangers, many of them surely Christians, and watched as a spaceship full of alien slaves crash land in Los Angeles (that was before all movies had to be made in New York). I can report that absolutely none of those strangers ran amok and recanted their religion.

The real question is how would scientists react were they to discover a different metaphysics. Let he that readth understand.

Statistics Mailbag

Because of my new gig and then my two-week sojourn at Cornell I am way behind in acknowledging all the emails and blog tips I have received. Nearly all stories here originate as a link from readers, and for these I am very grateful. Thank you to all who send these in and apologies for not writing back to everybody personally.

Since I have no hope of writing a separate post on all these juicy tips, here today, in no order, are some of the older ones which deserve a wide audience. I might revisit some of these later and expand on them.

General Bad Statistics


Your Brain Scan Looks Different on Mac and PC

A team…took data from 30 brain scans and analyzed them using a package called FreeSurfer…to measure the size of different parts of the brain.

They ran the software on PCs, and also on Macs running different versions of Mac OS, each time using the software to measure the size and thickness of various structures of the brain…Across most sections there was at least a 2-5 percent variation in the answers.[other] answers diverged by as much as 15 percent.

Counties that enjoyed better weather on tax day had more people sign up to become Tea Party organizers. And the paper.

What’s more, the Tea Party experiment shows that the activism catalyzed by those sunny days translates into real political influence. Politicians whose districts were sunny on tax day voted in a more reliably conservative fashion throughout 2009 and 2010. Indeed, the absence of rain in a congressional district on April 15, 2009, made its representative 8.7 percentage points more likely to vote against the Affordable Care Act. Had the weather at those early rallies been sunnier, it’s possible that Obama’s signature legislation wouldn’t have passed.

Why Women Choose Bad Boys

Women choose bad boys because their hormones make them…

Doggy daydreams: brain scans reveal Fido’s thoughts

Now we can really begin to understand what dogs are thinking. We hope this opens a whole new door into canine cognition, social cognition of other species.

Climatological Bad Statistics

Climate Change Denial in the Classroom (pdf)

models suggest…

Climate sensitivity to the lower stratospheric ozone variations Looks like another smoothing before regression “study.” A naughty no-no and guarantor of over-certainty.

Doctored Data, Not U.S. Temperatures, Set a Record This Year

To most people, the hottest temperatures ever “recorded” would imply that quality controlled thermometers registered higher readings during the past year than had ever occurred before. If you believe that this is what the National Oceanic and Atmospheric Administration (NOAA) means by hottest temperatures ever “recorded,” then you are wrong.

Misc

Email from John Cook to which we can reply Amen, brother.

Matt,

I’ve started reading The Discarded Image by C. S. Lewis. Here’s a quote from it that sounded to me like something that might appear on your blog:

“In our age I think it would be fair to say that the ease with which a scientific theory assumes the dignity and rigidity of fact varies inversely with the individual’s scientific education.”

— John

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