William M. Briggs

Statistician to the Stars!

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A Depressing [Real Sad] Churchill Quotation—Contest

As I this morning scanned Facebook, I ran across the image below. Read it through and pause for a moment before continuing.

Churchill quote

Notice anything strange? I was so intrigued by the editor’s use of brackets that I responded with the following:

Love the quotation [words cited from source]! An insightful [cap full o' thinkin'] analysis [figurin' out] of a morally stunted [short people] heretical [believing bad stuff about God] sect [I forget this one].

Naturally, it’s time for another no-prize contest. Who can come up with the most helpful edited quotation? Your audience are degree holding—this is not synonymous with educated—United States citizens. Extra points awarded if edits are in the voice of a sorority or fraternity member.

Here is my entry.

Four score and seven [many] years ago our fathers [not our real fathers; other peoples' fathers] brought forth [after thirdth] on this continent [happy land mass] a new nation, conceived [thought of] in liberty [forget this word: vote Obama], and dedicated [given] to the proposition [business deal] that all men [and women] are created equal [must pay their fair share].

Now we are engaged [living together] in a great civil war, testing whether that nation, or any nation, so conceived and so dedicated, can long endure [make it]. We are met on a great battle-field [area outside club] of that war. We have come to dedicate a portion [bit] of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting [right size] and proper that we should do this.

But, in a larger sense, we can not dedicate, we can not consecrate [have sex with], we can not hallow [full of air] this ground. The brave men, living and dead, who struggled [worked hard] here, have consecrated [good grief!] it, far above our poor power to add or detract [insult]. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished [not done] work which they who fought here have thus far so nobly [lot of knowledge] advanced. It is rather for us to be here dedicated to the great task [minimum wage job] remaining before us—that from these honored [Facebook friended] dead we take increased devotion [follow on Twitter] to that cause for which they gave the last full measure of devotion—that we here highly resolve [see better] that these dead shall not have died in vain [self-centered]—that this nation, under God [or "god"], shall have a new birth of freedom–and that government of the people, by the people, for the people, shall not perish [Church place] from the earth.

Does Averaging Incorrect Data Give A Result That Is Less Incorrect? Climate Modeling

Another question from the statistics mailbag:

Dear Matt: I recently got into a discussion with a CAGW “believer” and of course the discussion turned to global average temperature (whatever that is) anomalies and that the predictions of climate catastrophe are based on computer model output. I then said, “If a computer model cannot predict regional changes, it cannot predict global changes. Averaging incorrect data does not give accurate data,” referring to the computer models. Was that a correct statement?

Although I once took statistics courses, about the only things I remember are median, mode, mean, and standard deviation so if you have time to respond to this e-mail, please do so in a ridiculously simple way that I might be able to understand.

Thanks. By the way, I like your new format.

Regards,

Chuck Lampert

Sort of Yes, Chuck. The part that’s tricky is your conditional: climate models necessarily do better at “higher” scales than “lower ones.” But your second part is right: averaging a Messerschmidt, no matter how large, still leaves you with a Messerschmidt, if I may abuse the punchline to the old joke.

First, a “climate” model is just a model of the atmosphere. What makes it “climate” is its scale and nothing more; what we call “climate” versus what we label “weather” is really a matter of custom. So imagine a model of climate of the Earth from the view of Alpha Centauri. From that vantage the Earth is indeed a pale blue dot and its “global mean” temperature can be modeled to high accuracy, as long as we don’t try for too many decimal places. We can even ignore seasonality at this distance. Heck, I’d even believe a forecast from James Hansen for “climate” as defined this way.

But now imagine the temperature and precipitation on a scale of a city block for each hour of the day and over the entire surface. This would be incredibly complex to model and verify. Even trying to write down the computing resources required produces a dull pain in the occipital lobe. To my knowledge nobody tries this for the globe as a whole, though it is done over very small areas for limited time frames. The hope that this scale of model would be accurate or useful as a climate model matches that of a Marxist who says to himself, “Next time it’ll be different.”

Here’s the tricky part. A climate model built for large-scale climate can do well, while another built for smaller-scale climate will fare more poorly, each verification considered at the scale intended of each model. We can, as you suggest, average the small-scale model so that the resultant output is on the same scale as its coarser brother.

Now it can happen that the averaged model judged on the coarser scale will outperform itself judged on its original scale. This could be simply because the model did well on the coarse scale but poorly on the fine scale. Of course, the averaged model may also perform poorly even on the large scale. There is no way to know in advance which will be the case (it all depends on the competence of the modelers and how well the models reproduce the physics).

But, all things equal, the variance (of the verification or the model itself) of the averaged model will be larger than the variance of the large-scale-from-birth model. That means we would have either more trust in the large-scale model, or in its verification statistics (even if those stats showed the model to be poor) or both.

The old tale of the Chinese Emperor’s Nose is somewhat relevant here. Nobody in China knew its length, but they desired to have the information. Why they wanted to know is a separate question we leave to competent psychologists. Anyway, many people each contributed a guess, each knowing that his answer was probably wrong. But they figured the average of all the wrong guesses would be better than any individual guess.

Wrong. Taking the mean of nonsense, as suggested above, only produces mean nonsense. So that if the small-scale model stunk at predicting small-scale climate, taking averages of itself (via ensemble forecasting, say) and then examining the average model on the same small (not large) scale will still leave you with a Messerschmidt.

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Photo source

“For who are a free people? Not those, over whom government is reasonably and equitably exercised, but those, who live under a government so constitutionally checked and controuled, that proper provision is made against its being otherwise exercised.” —John Dickinson, Letters From a Farmer in Pennsylvania (1768).

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.

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