William M. Briggs

Statistician to the Stars!

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Dawkins Gets It Wrong Again: Similar Is Not The Same

Oops.

Oops.

Richard Dawkins in an article to the New Statesman—the same issue which somebody who obviously wasn’t in full possession of his faculties assigned to Dawkins as editor—the Christmas issue, mind—an issue filled with unreason, prejudices, error, unexamined biases, and bizarre beliefs—e.g. Sam Harris pops up to say he has no free will, causing us to wonder if he demanded payment for his article; Michael Moore declares “We are animals” (who knew?); Daniel Dennett strokes his beard and inveighs against debutante balls (guess who never got asked to the prom)—in this article, I say, Dawkins demonstrates his astonishingly ability to think unclearly, while also convincing those willing and eager to be convinced that what he had to say was worth hearing and probably even true.

And they say there are no miracles. (There may be another; we’re praying for you, Richard.)

Crossing the line

Dawkins thinks lines are “tyrannical.” Why? Because he very cleverly noticed that some demarcations are capricious, such as voting age limits and college grades. He also discovered some discontinuities are matters of fact, such as admitting a beaver isn’t a coffee cup. He further, and wisely, opined that we shouldn’t reify capricious disjunctions, but we’re stuck with what nature hands us.

The only problem, and the reason for this response (besides that he just last week referenced this article), is that after this intellectual burst, Dawkins couldn’t keep straight the very categories he discovered. His irrationality probably entered because of his ulterior motive, his only real impetus, which was to proclaim his happiness with abortion—proving once again that bloodlust in blinding.

There are those who cannot distinguish a 16-cell embryo from a baby. They call abortion murder, and feel righteously justified in committing real murder against a doctor — a thinking, feeling, sentient adult, with a loving family to mourn him. The discontinuous mind is blind to intermediates. An embryo is either human or it isn’t. Everything is this or that, yes or no, black or white. But reality isn’t like that.

Abortion is murder if the 16-cell embryo is a human being. How many cells does it take before the collection becomes human? Dawkins, a collection of cells, will shortly claim that being human is entirely arbitrary. For now, he jumps into the silly stream.

Not all who call abortion murder because it is the killing of an innocent human being “feel righteously justified” in murdering abortion providers (I almost said “doctors”). Just as all those who guest edit issues of New Statesman and who despise religion do not “feel righteously justified” in killing innocent religion providers. But some do. And which side has more blood on its hands?

Not for the first time, Dawkins merely assumes what he wants to prove, and says something demonstrably false in the course of doing so.

It also does not follow that because an embryo is a human being that “everything” is black or white. Of course it doesn’t. But it also doesn’t follow that everything exists on the continuum, that all lines are subjective. Eagles are not sturgeons: yes is not no: true is not false.

But personhood doesn’t spring into existence at any one moment: it matures gradually, and it goes on maturing through childhood and beyond.

More bloodlust. Or ignorace. Or both. This statement appears to say that we never quite reach personhood, or that we can be partial people (not in body, but in essence), or that we do reach personshood but only after accumulating sufficient “maturity points” (perhaps doled out by some beneficent government). Human worth, to Dawkins, can be graded on a continuum, a horrifying view, instead of the old-fashioned view that all people have intrinsic value and in that sense are equal in the eyes of God.

What is human?

To the discontinuous mind, an entity either is a person or is not. The discontinuous mind cannot grasp the idea of half a person, or three quarters of a person.

To Dawkins, it seems, an entity such as my swift and sleek Dell Inspiron laptop might be characterized as partly a person (it does “mental” calculations); or that he, Dawkins himself, might be considered a shade volcanic (the lava-filled ones, I mean; his temples throb with hot fluid). Or would he snort and go all discontinuous on us in these matters of judgment? Does Dawkins not recognize the difference between metaphor and reality?

On the other hand, classicalists really can’t imagine what a three-quarters person is. Somebody missing a leg? Still a person. Somebody with an artificial heart? Still a person. Somebody with a pipe through his skull or strapped to a machine and declared a “vegetable”? Human, and eligible for employment in any university. All of these whole and in-pieces people all retain the essence of being a human, and are therefore people.

You won’t be surprised to learn that, to Dawkins, essentialism is “one of the most pernicious ideas in all history.” Sure it is. Look how much it holds fellows like him back. He and his gloomy band of New Statesman, loyal party members all, would delight to roll out the guillotine, at least figuratively, and start eliminating undesirables—improves the race and quells dissent, you see. They’d get away with it, too, if it weren’t for the majority still holding to essentialism and therefore frowning on wanton slaughter for eugenical and political purposes.

The danger of quotations

Some absolutists go right back to conception as the moment when the person comes into existence—the instant the soul is injected—so all abortion is murder by definition…[quote from Donum Vitae follows…]

It is amusing to tease such absolutists by confronting them with a pair of identical twins (they split after fertilisation, of course) and asking which twin got the soul, which twin is the non-person: the zombie. A puerile taunt? Maybe. But it hits home because the belief that it destroys is puerile, and ignorant.

Let me leap to agree with Dawkins: his words are puerile. And his quote from Donum Vitae was incomplete. Somehow he left out the best stuff, which is this:

This teaching [of human life] remains valid and is further confirmed, if confirmation were needed, by recent findings of human biological science which recognize that in the zygote resulting from fertilization the biological identity of a new human individual is already constituted.

Certainly no experimental datum can be in itself sufficient to bring us to the recognition of a spiritual soul; nevertheless, the conclusions of science regarding the human embryo provide a valuable indication for discerning by the use of reason a personal presence at the moment of this first appearance of a human life: how could a human individual not be a human person? The Magisterium has not expressly committed itself to an affirmation of a philosophical nature, but it constantly reaffirms the moral condemnation of any kind of procured abortion. This teaching has not been changed and is unchangeable. [emphasis added]

Empirical observation has, of course, guided the Church in deciding the question of human life. St Thomas Aquinas, lacking modern medicine, taught that ensoulment began some period after conception. It was the best he could do; now we know better. Plus, abortion was always said to be a moral evil and since the soul is the form of a human, identical twins pose no difficulty.

Essentially speaking

Back to Dawkins:

“It would never be made human if it were not human already.” Really? Are you serious? Nothing can become something if it is not that something already? Is an acorn an oak tree? Is a hurricane the barely perceptible zephyr that seeds it? Would you apply your doctrine to evolution too? Do you suppose there was a moment in evolutionary history when a non-person gave birth to the first person?

Yes, an acorn is, in essence, an oak tree. It is also an acorn. It is not a 1971 Mustang with “three on the tree”, nor is it a cheesecake nor a leopard. It is both an acorn and an oak tree, albeit a small, packed-up version of one. Just as the oak tree is still an acorn, but now fully grown. The caterpillar is the butterfly, and vicey versey.

Notice that the man can’t keep straight what he’s criticizing. A hurricane is neither puff nor zephyr: a hurricane is an organized system with winds exceeding an arbitrary level set by meteorologists. But breezes and gales are both wind, just as essentialism says.

And, yes, there must have been a moment in evolutionary history when a non-person gave birth to the first person; accepting, arguendo, evolution was responsible for producing the first human. See Mike Flynn’s instructive Adam & Eve & Ted & Alice. Why couldn’t evolution have done this? Dawkins only retort is that it’s not possible, again assuming what he’s hoping to prove. When you drive in a circle, you get nowhere.

If a time machine could serve up to you your 200 million greats grandfather, you would eat him with sauce tartare and a slice of lemon. He was a fish. Yet you are connected to him by an unbroken line of intermediate ancestors, every one of whom belonged to the same species as its parents and its children.

A question: is similar logically equivalent to the same or identical? I’m just asking.

From this quote we conclude that one should not guest edit magazines before dinner. Frames your thinking in terms of food, which might prove embarrassing. How often have you heard anybody speaking with relish of the relish he’d serve with his relative?

He speaks of a “connection” as it were a stout rope which if pulled upon at the base (by suitably equipped proto-slime) would jerk us back a few notches. Or something. Surely he realizes there is more than meat separating “Devonian fish” and humans. They weren’t rational: we are. Rationality is the essence of being human, as Aristotle taught us.

Dawkins eats his great grandfather

So it makes no sense to harp about eating each other or breeding with Jurassic Park recreations of species that came before humans, as Dawkins recommends as a desirable thought experiment. Ability to interbreed might be what biologists call a “species”, but that is neither here nor there for what is a human. And isn’t the doctrine of species, Richard, an arbitrary line? Are mules horses or are they donkeys? Or are they mules?

Who knows how he would answer, because no sooner has he declared for species, he declares against them, citing variously shaded gulls and their ability to interbreed or not. “Are they distinct species or not? Only those tyrannised by the discontinuous mind feel obliged to answer that question.” I don’t feel obliged, so I gather I’m not tyrannized. He doesn’t recognize that the problem is with the definition of species: if it doesn’t include essences, it is incomplete. A mule is essentially different than either of its parents, even though, I guess, it isn’t a “species” of anything since it can’t reproduce. Yet a mule may still be known by its essence.

I didn’t follow the rest of his article too well. Seems he was still angry with George Bush about something.


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We’re 88% Through The International Year Of Statistics

Keynes (right, a logical probabilist) reacting to the suggestion statistics is a branch of mathematics.

I hadn’t any idea we’d even started. But thanks to reader Dan Hughes and his link to the Wall Street Journal story Odds Lot: Statisticians Party Like It’s 2.013 x 10 Cubed, I now know our field is “sexy.”

Sure it is. At a conference last month a guy asked me what I did. I said I worked magic. He was incredulous. I said, Yes, as soon as I tell anybody what I do, they disappear. Magic.

He insisted on knowing anyway. I told him. “Oh, there’s Gary. I have to go say hi,” he said. I turned to my friend (a physicist) and said, “See? Magic.”

But I’d say that’s the second most common reaction. The first is, “I hated statistics,” meaning the person despised the class that somebody forced him to take. Now I, being a team player (right? right?), always accept responsibility and apologize for their experience. “Yes,” I admit, “It’s because we teach the subject badly.”

Most statisticians are under the impression that our subject is a branch of mathematics. An understandable mistake, but wrong. But because of this misconception we don’t feel we have taught our students anything unless we make them derive, and then memorize, a dozen or so formulas. Which, as we know, are of little value and often of great harm. We actually make them play with data before we say why and what it means. Strange.

The usefulness of this strategy, to any regular reader and to any who was made to suffer through a statistics class, will be obvious. Nobody ever remembers why they’re applying the formulas, nor can they recall how to derive them, but they do hold dear that wee p-values are magical.

Statistics is no more mathematical than physics. Sure, like physics statistics uses plenty of math, but it is all beside the point, not the point. Probability is a branch of logic, which is a branch of epistemology. Well, of course it is. We use probability to say how certain we are of things, right? And when we say how we know things, we are speaking epistemologically.

My idea is to eschew most mathematics when teaching statistics to newcomers. Speak more about what is means, how to understand, how to think. Particularly how to read and interpret evidence presented by others. Those who are intrigued—and I claim this will be a larger proportion than the old way—will stick around and learn the math.

Which, it must be admitted, isn’t easy. A minimum of calculus (a year or so) is required; having analysis is better. That’s a long haul. But then we don’t require the majority to derive results, prove theorems; we instead would like civilians to know when the wool is being pulled over their eyes.

If this panics you, don’t worry. My ideas are considered so outré that I am not trusted to be put in front of students (except for a handful two weeks a year). The old ways will continue.

From the article we learn that others have the same experiences Yours Truly does. Ron Wasserstein, a statistician, “recalls telling people back [in the 70s] about his studies and getting puzzled responses like, ‘Are there really enough numbers to memorize to get a Ph.D. in statistics?'”

Geert Molenberghs, a biostatistics professor at Belgium’s Hasselt University who helped organize the recent Belgian conference, says telling people at a cocktail party that he is a medical statistician sparks more interest than it would if he dropped the medical part.

Magic!


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Nonstatisticians Often Screw Up Statistics

Leland Teschler

Title stolen from article of same name by Leland Teschler in the trade journal Machine Design.

Update Statisticians often screw up statistics, too. See below.

The article is the result of an interview I gave Teschler a month ago. He called me up and asked about bad statistics, and I became that obnoxious guy in the bar who grabs your elbow and won’t let go until you understand his theory of life, the universe, and everything. Poor Teschler was panting by the time I finished with him.

Yet he must have recovered sufficiently to write:

Briggs’ argument for such a radical stance is that most nonexperts misapply these ideas and often use them to leap to bad conclusions. “The technical definition of a p-value is so difficult to remember that people just don’t keep it in mind. Even the Wikipedia page on p-value has a couple of small errors,” Briggs says. “People treat a p-value as a magical thing: If you get a p-value less than a magic number then your hypothesis is true. People don’t actually say it is 100% true, but they behave as though it is.”…

“P-values can and are used to prove anything and everything. The sole limitation is the imagination of the researcher,” he says. “To the civilian, the small p-value says that statistical significance has been found, and this, in turn, says that his hypothesis is not just probable, but true.”

Why not eliminate frequentist statistics for all but math PhD students and teach Bayes or, my preference, logical probability?

Nevertheless, there is only a slim chance a Bayesian revolution will sweep through statistics classrooms. The problem is one of inertia. “Most statistics classes are taught by nonstatisticians. They can’t teach Bayesian statistics because a lot of them have never heard of it,” says Briggs. Even worse, “Peer-review journal editors still want to see p-values in the papers they publish.”

Head on over to see the rest.

Update The interview I had with Teschler was wide ranging and did not focus on who was king of the statistical hill. I frankly do not care. The main complaint against me was that I am an academic. Ouch. I am so, it’s true, but only for two weeks of every year. The rest of the time I am on my own. Because why? Because the crazy ideas I espouse do not endear me to professional academics.

I didn’t appreciate that some people might take exception to the claim that professionals would be better at statistic than non-professionals. Of course, it is always possible that any non-trained person would do better than a trained one in statistics, or in any field.

My main point with Teschler was that statistics as a field was broken. Regular readers will understand just what I mean by this. Countless times I have showed that the further a field gets from the simple, the worse the evidence is handled. Most engineering is simple, and subject to much feedback, at least compared to the monstrous complexity which is human behavior.

If you’re new here, have a look around and you’ll see quickly what I mean.


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Johnson’s Revised Standards For Statistical Evidence

Valen Johnson: Notice how his shirt matches his hair.

Valen Johnson: Notice how his shirt matches his hair.

Thanks to the many readers who sent me Johnson’s paper, which is here (pdf). Those who haven’t will want to read “Everything Wrong With P-values Under One Roof“, the material of which is assumed known here.

Johnson’s and Our Concerns

A new paper1by Valen Johnson is creating a stir. Even the geek press is weighing in. Ars Technica writes, “Is it time to up the statistical standard for scientific results? A statistician says science’s test for significance falls short.” Johnson isn’t the only one. It’s time for “significance” tests to make their exit.

Why? Too easy, as we know, to claim that the “science shows” the sky is falling. Johnson says the “apparent lack of reproducibility threatens the credibility of the scientific enterprise.” Only thing wrong that sentiment is the word “apparent.”

The big not-so-secret is that most experiments in the so-called soft sciences, which—I’m going to shock you—philosopher David Stove called the “intellectual slums”, are never reproduced. Not in the sense that the exact same experiments are re-run looking for similar results. Instead, data is collected, models are fit, and pleasing theories generated. Soft scientists are too busy transgressing the boundaries to be bothered to replicate what they already know, or hope, is true.

What happens

I’ve written about how classical (frequentist) statistics works in detail many times and won’t do so again now (see the Classic Post page under Statistics). There is only one point to remember. Users glop data into a model, which accommodates that data by stretching sometimes into bizarre shapes. No matter. The only thing which concerns anybody is whether the model-data combination spits out a wee p-value, defined as a p-value less than the magic number.

Nobody ever remembers what a p-value is, and nobody cares that they do not remember. But everybody is sure that the p-value’s occult powers “prove” whatever it is the researcher wanted to prove.

Johnson, relying on some nifty mathematics which tie certain frequentist and Bayesian procedure together, claims the magic number is too high. He advises a New & Improved! magic number ten times smaller than the old magic number. He would accompany this smaller magic number with a (Bayesian) p-value-like measure, which says something technical, just the like p-value actually does, about how the data fits the model.

This is all fine (Johnson’s math is exemplary), and his wee-er p-value would pare back slightly the capers in which researchers engage. But only slightly. Problem is that wee p-values are as easy to discover as “outraged” Huffington Post writers. As explained in my above linked article, it will only be a small additional burden for researchers to churn up these new, wee-er p-values. Not much will be gained. But go for it.

What should happen

What’s needed is not a change in mathematics, but in philosophy.

First, researchers need to stop lying, stop exaggerating, restrain their goofball stunts, quit pretending they can plumb the depths of the human mind with questionnaires, and dump the masquerade that small samples of North American college students are representative of the human race. And when they pull these shenanigans, they ought to be called out for it.

But by whom? Press releases and news reports have little bearing to what happened in the data. The epidemiologist fallacy is epidemic. Policy makers are hungry for verification. Do you know how much money government spends on research? Scientists are people too and no better than civilians, it seems, at finding evidence contrary to their beliefs. Though they’re much better at confirming their opinions.

This is all meta-statistical, i.e. beyond the model, but it all affects the probability of questions at hand to a far greater degree than the formal mathematics. (Johnson understands this.) The reason we given abnormal attention to the model is that it is just that part of the process which we can quantify. And numbers sound scientific: they are magical. We ignore what can’t be quantified and fix out eyes on the pretty, pretty numbers.

Second: remember sliding wooden blocks down inclined planes back in high school? Everything set up just so and, lo, Newton’s physics popped out. And every time we threw a tiny chunk of sodium into water, festivities ensued, just like the equations said they would. Replication at work.

That’s what’s needed. Actual replication. The fancy models fitted by soft scientists should be used to make predictions, just like the models employed by physicists and chemists. Every probability model that spits out a p-value should instead spit out guesses about what data never2 seen before would look like. Those guesses could be checked against reality. Bad models unceremoniously would be dumped, modest ones fixed up and made to make new predictions, and good ones tentatively accepted.

“Tentatively” because scientists are people and we can’t trust them to do their own replication.

The technical name for predictive statistics is Bayesian posterior predictive analysis, where all memories of parameters disappear (they are “integrated out”). There are no such things as p-values or Bayes factors. All that is left is observables. A change in X causes this change in the probability of Y, the model says. So, we change X (or looked for a changed X in nature) and then see if the probability of Y accords with the actual appearance of Y. Simple!

This technique isn’t used because (a) the math is hard, (b) it is unknown except by mathematical statisticians, and (c) it scares the hell out of researchers who know they’d have far less to say. Even Johnson’s method will double current sample sizes. Predictive statistics requires a doubling of the doubling—and much more time. The initial data, as before, is used to fit the model. Then predictions are made and then we have to wait for new data and see if the predictions match.

Right climatologists? Ain’t that so educationists? Isn’t this right sociologists?

Caution: even if predictive statistics are used, it does not solve the meta-statistical problems. No math can. We will always be in danger of over-certainty.

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1Actually a summary paper. See his note 21 for directions to the real guts.

2This is not cross validation. There we re-use the same data multiple times.


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