Japanese Meltdown

No, not the reactors, the press. Ghouls, most of them. They always wish for the worst. The only class of people (besides Communists and morticians) for whom death not only delights, but offers a chance for personal advancement. The only folk who can speak the word “heartbreak” with a lilt to their voices. Their first thoughts upon hearing of a disaster is how they, and not their colleagues, can get their face in front of a camera.

Narrating the nauseating particulars of mass death is not a horrible duty that must be stomached, but is instead an opportunity. Not one in a hundred while jetting to the calamity would think to interrupt their prayers with a plea “take away this cup from me.” Instead they paraphrase Lenin, “It does not matter if three-fourths of mankind is destroyed: all that counts is that I am there to report it.”

It is true that ignorance is what drives much (there are exceptions) of the reporting on the nuclear reactors. After all, most of these reporters learned their physics from Hollywood movies. Nuclear reactors, when damaged, melt down blow up: that is what they do. And then all but a minuscule minority suffer from reporteritis, an epidemic psychiatric disorder whereby journalists assume they become as knowledgeable and important as the people they talk to.

They invite a nuclear physicist to offer a thirty-second soundbite, and that fraction of fact becomes All There Is To Know. The reporter assimilates the information and then opines sagely upon it; not repeating it word-for-word, but by creating variations on a theme, weaving it into their baseline ignorance.

Of course, in this case we cannot just blame reporters. Our Surgeon General has contributed to the unnecessary panic by starting a run on “radiation pills” on the west coast. She said of the hoarding that it was “definitely appropriate.” (Has the person in this office ever fulfilled a useful purpose?)

An anonymous but highly knowledgeable source gave this lament:

It has gotten to the point where I can barely watch the news. The hysteria driven media consistently endeavors to one-up itself on the terrors of radiation. You know, “significantly increased levels of radiation have been detected…” Of course, they fail to provide a baseline dose rate before the earthquake/accident and then do not say what is the significantly increased dose, so that sane, rational people can actually make comparisons and draw reasonable conclusions. I especially liked one commentator’s lame response. It went something like, “Well, you know…any exposure to radiation… even small increases, are known to not be good for you…”

Just like reporting on global warming, where it is always, just always, “Worse than we thought”, the radiation levels are always, ever always, increasing and increasing. What reporters should be doing is obvious: take as much time as necessary and, using actual experts, give as many facts as possible, even at the very real risk of talking over the heads of most of their audience. Difficult but correct material always trumps simplistic summaries.

A major component of the story, relevant to us, is over-certainty. According the the Nuclear Energy Institute, the reactor damage occurred because of “extraordinary natural forces that were outside the plant’s required design parameters.” In other words, the events that did occur were not foreseen, or were given such a low probability of occurrence that none thought it worth the trouble.

The people who design these plants are, to use the common phrase, rocket scientists. They are exceedingly bright, but they are still human. If these men can make a mistake in estimating risk on what are, after all, simple structures, just how over-confident are we in our understanding of systems as complex as Nature or the interactions between people and nations?

The disclaimer I have to, but should not have to, add is that I do not seek to minimize reporting on the dangers to those who live near the plants. But our choice is not a dichotomy: because we do not minimize does not mean we must maximize.

Freeman Dyson, NPR, TSA X-rays, Northwestern University’s Bachelor Party

The Lady Tasting Tea continues tomorrow.

Freeman Dyson Speaks

From our man-on-the-spot WS comes this link to an interview with Freeman Dyson regarding his work “In Praise of Heretics.” That word no longer has religious connotations, a milieu where the meaning is almost the opposite of what it is now. Warning: bad music alert (the intro to the program). Fun fact: Dyson was a statistician for the RAF in World War II! And he doesn’t have a PhD! (Therefore, how can he be smart?)

If you haven’t read his Infinite in All Dimensions, do so. There is also The Scientist as Rebel (which I have not yet read).

NPR Unbiased?

NPR’s interim CEO, Joyce Slocum, told the Associated Press, “I think if anyone believes that NPR’s coverage is biased in one direction or another, all they need to do to correct that misperception is turn on their radio or log onto their computer and listen or read for an hour or two. What they will find is balanced journalism that brings all relevant points of view to an issue and covers it in depth so that people understand the subtlety and the nuance.”

Slocum is statistically right: many NPR programs have nothing to do with politics and are not in danger of bias, except towards simplicity, our national curse. On the other hand, NPR member stations are often the only place that one can listen to free “classical” music on the radio (the word is a euphemism for “good” or “serious”). But of the shows, like news programs, that are politically tinged, it is absurd to claim NPR does not have a leftist bias. So the question, Mr Slocum, is this: why should I continue to give you money?

Quote from an unfortunately titled Cal Thomas piece.

TSA Body X-rays

From chief crank John Dvorak come a link to a TSA press release:

The Transportation Security Administration announced Friday that it would retest every full-body X-ray scanner that emits ionizing radiation — 247 machines at 38 airports — after maintenance records on some of the devices showed radiation levels 10 times higher than expected.

What a, uh, surprise.

Marxist, Feminist, Structuralist, Post-structuralist…

From an article by Alan Bekhor on scholasticism:

Consider, to take one example from many, the book Beginning Theory — an Introduction to Literary and Cultural Theory by Peter Barry, which has virtually become a set text for any humanities or literature undergraduate course in a British university today. Five rules, Barry affirms, are to be borne in mind for critical thinking about literature: “politics is pervasive, language is constitutive, truth is provisional, meaning is contingent, human nature is a myth.”

Each of those five rules are false (or have trivially true interpretations). Given these gross, even scurrilous, falsities as a base, is it therefore any wonder that our humanities departments are in the shape they are in?

They Are Too In Bad Shape

Via A&LD, comes Uncle Joseph Epstein’s “Lower Education: Sex toys and academic freedom at Northwestern.” After lamenting that Northwestern could do no better than invite commencement speakers like Stephen Colbert, Julia Louis-Dreyfus, or Dianne Sawyer, he writes of the Michael Bailey Dildo Scandal:

Because a subject exists in the world doesn’t mean that universities have to take it up, no matter how edgy it may seem. Let books be written about it, let research be done upon it, if the money to support it can be found, but the nature and quality and even the sociology of sexual conduct—all material available elsewhere in more than plentitude for the truly interested—does not cry out for classroom study. Students don’t need universities to learn about varying tastes in sex, or about the mechanics of human sexuality. They don’t need it because, first, epistemologically, human sexuality isn’t a body of knowledge upon which there is sufficient agreement to constitute reliable conclusions, for nearly everything on the subject is still in the flux of theorizing and speculation; and because, second, given the nature of the subject, it tends to be, as the Bailey case shows, exploitative, coarsening, demeaning, and squalid.

Vicar Of Vintage Vinyl Vanquished: Danny Stiles Dead At 87

It finally happened, though we thought, we hoped, he would go on forever. Danny Stiles, radio personality in the New York metro area for over 60 years, died on Friday, 11 March 2011 at age 87. Twenty-plus years, each Saturday night from 8 pm to 10 pm, Stiles broadcast the Music Museum, featuring the Great American Songbook on WNYC (820 AM), live from the “the east wing of the Art Deco penthouse” (as he described his quarters overlooking the picturesque Holland tunnel).

Stiles “on your dials” ranged over many stations in his long career; in recent month hosting a show—sponsored by John’s Pizzeria—on WPAT (930 AM). In the old style of radio, he would intersperse songs with laudatory comments about how savory, unique, and delicious the pizza was. He integrated the commercials so well that you didn’t always know you were hearing an ad.

Regular listeners knew something was wrong when Danny missed his broadcasts on WYNC for the past month. The station ran recordings of previous shows. They did so again on 12 March, in tribute (and it might have been the last). Even though he was ill, he continued to record his WPAT show with a voice cracked and tired. The week before he died, he sounded better and even boasted he would return to WYNC. Alas, he never made it.

 

WYNC tribute:

 

For many years, Stiles would host a Friday night get together at New York restaurants, starting at Meli Melo on Madison, and then at Seppi’s in the Parker Meridian Hotel. Seppi’s, a warm bistro chefed by the friendly Claude Solliard, unexpectedly closed over a year ago, and Stiles’s Friday nights ended soon after (he was briefly at another restaurant downtown).

People would come from all over to dine and have a chance to meet Mr Stiles. Cocktails to start (martinis, of course), then dinner, then music featuring Rick Bogart’s New Orleans trio. Danny would introduce the band with familiar, comfortable jokes. Bogart would play the clarinet and sing in an acquired-taste style. Danny would often spin records from Bogart on his Saturday night show, too.

It was at Seppi’s where I was introduced to the great-great-great (I’ve forgotten how many) grandson of John Quincy Adams who shared his relative’s name. I met many radio personalities. I even shook hands with the Kenilworth crooner. And was I busting with pride when, on the WNYC show after one Friday night, Mr Stiles mentioned that he met the “world-class statistician” and his “blond bombshell” companion?

Danny StilesHis life was devoted to preserving and playing the best of 20th century music. He played mostly original recordings on the original media. The sometimes scratchy recordings transported you back in time.

Stiles began each Music Museum with Cherokee from Charlie Barnet, followed closely by Glenn Miller, Artie Shaw, or some other big band piece. In third place was always an early recording of Frank Sinatra with the Tommy Dorsey band. Many casual Sinatra fans would do well to look these recordings up: many are a treat.

Right around 8:30 to 8:40 pm, Danny would slip into “mob music”, singers from the last 1950s with a distinct Italian bias. He would often spin a favorite record, week on week. Some of his choices—let’s face it—were a little schmaltzy, others were quirky. But you couldn’t hold it against him. And you didn’t just get the music, but you heard the stories behind the songs, the rich history.

Every show ended with Shirley Temple singing—and Danny signing—”Goodnight, My Love.” A goofy, playful exit.

Until this last year when, right before Shirley, Danny took to playing (and talking over) the very melancholy Acker Blik instrumental “Stranger on the Shore.” It wasn’t a good omen. He is now relieved of his having to carry those “excruciatingly heavy” 78s home from the studio.

We heard the door close for the last time tonight. Goodbye, Danny, we will miss you.

More:

Obituary from the New York Times. Nostalgia Alley interview with Danny. Danny Stiles had a website (currently still up) featuring continuous loops of his Friday night shows (they aren’t there now and are unlikely to return).

The Lady Tasting Tea will begin Monday.

Obama’s Faulty Pay Gap Statistics, Philosophy Of Abortion; Plus, The End Of The World

Deadline: 21 May 2011

Family Radio Worldwide has hit the road (in a bunch of mobile homes) to preach that the end shall come just over two months from now. end of the world On that date, “a massive earthquake will shake the world apart.”

According to the Daily Mail, “Those who believe in Jesus will be carried into heaven, while the rest of humanity will endure 153 days of ‘death and horror’ before the world ends on October 21.” This is the Rapture followed by the Tribulation spoken of by millennialists.

Harold Camping, the group’s leader, issued the definite forecast and for that I admire him. I do not believe him, but I approve of his concreteness. Most who preach doom and gloom haven’t the guts to put definite numbers, shape, or dates on their prognostications. Most are content to sit and wait for events “similar” to what they have vaguely predicted, and then take loose credit for having actually predicted those events.

Camping and his flock will have the chance to learn from their mistake. Not that Camping will take his failure to heart, but his followers might.

Of course, these sort of things often turn out badly. The evidence of a failed core belief is often too much for the devout to bear. Many in the group will not be able to face their ex-family and friends who they have abandoned to take up this cause. These poor people will not need our ridicule, but our prayers.

Obama: Women Earn Less

Mr Obama, in his radio address of today (which your intrepid reporter caught a portion of) said, “Today, women still earn on average only about 75 cents for every dollar a man earns. That’s a huge discrepancy.” He called this “troubling.” He also told us that March is women’s month. Oops: it’s National Women’s Month. (Men don’t get a month.)

Mr Obama’s statistics are faulty. I have done the numbers myself and can report that, within a job and age-matched with men, women not only earn as much as men, but sometimes more (on average). Particularly, women entering the workforce now earn more than men on average in most career fields. Yes, even engineering. At the very top, where gray hair abounds, men still, on average, have an edge. But these wrinklies are old and getting older and will be replaced by higher-earning women.

Another reason for the supposed “discrepancy” is that women do not enter the job force in the same proportion as men, but they are increasing that proportion. Thus, some fields are seeing dramatic increases in women; and, since these women are new employees, they tend to earn less than the older employees, who are more likely to be male.

Thus, Mr Obama, while quoting a (more or less) accurate statistic gave it the wrong interpretation; and not just the wrong interpretation, but one that is exactly the opposite of the truth. But one well in line with his call for more taxing, spending, and regulation to “correct the balance.”

Abortion Philosophy

Many philosophers have tried, in vain, to show that the only question about whether abortion should be legal depends on whether the fetus is human or not. To kill a human for convenience or personal gain is murder. Thus, if the fetus is human, then to abort it is to commit murder. Abortion is in no way an “issue” of women’s “rights.” Women do not have the “right” to murder simply because they are women.

You can argue that the fetus becomes human at a certain point in time. For example, it is not human at conception but becomes so at the beginning of the second trimester. (Never mind measurement; we are speaking purely philosophically.) Mark Mercer, chairperson of the philosophy department at Halifax’s St. Mary’s University, says the fetus does not become human until after it has been out of the woman’s womb for 18 months. Mercer says human-like creatures 18 months old or less are not human, but they become so after 18 months of life.

Mercer’s argument, while asinine, is, so far, philosophically sound. The only question is where to draw the line. He draws it rather late because being human is a “legal term which has had a changing definition throughout history.” Here is his mistake, a common one made by equality-mongers and multiculturalists. Just because a society commends or does not penalize some action, does not imply that that action is moral. The reason this is so should be obvious (hint: what is a society?).

Abortion “rights” supporters hate debate and tried “to disrupt a debate on abortion at Dalhousie University Tuesday night by ripping down ads, setting off stink-bombs, and covering the ceiling with helium balloons featuring pro-abortion slogans. In the end, they even turned on” Mercer. Why? Because he refused to acknowledge that abortion was an “issue” of women’s “rights.”

This proves that ignorance isn’t, or doesn’t produce, bliss, but perpetual outrage.

Update

See also this video where MSNBC’s Cenk Uygur argues (soundly) that the fetus’s first heartbeat cannot draw the line because the fetus “is not really a person.” But he also says, “Now, we reached out to the fetus to see if he or she wanted to come on the show, but it did not say anything, because it does not have a mouth. But if it could talk, I’m pretty sure it would say, could you please get out of my mother’s uterus.” How could a non-human say “Please abort me” or “Please let my mother decide whether to abort me”? Uygur’s fallacy is that he wants it both ways.

Earthquake Ghouls, Colleges As High Schools, The Robinson DeFazio Controversy, More

J-school Ghouls

On the radio, a female American reporter in Tokyo, unnecessarily breathless and somewhat disappointed. “I can only imagine if it were here, it would have been much worse and the, uh, the count would have been much higher.” Body count, of course.

Colleges Now Offer High School Degrees

From the—yes, really—New York Times, a story on how CUNY schools are having to teach college students what they should have learned in high school. The “tide of remedial students has now swelled so large that the university’s six community colleges — like other two-year schools across the country — are having to rethink what and how they teach, even as they reel from steep cuts in state and local aid. ”

Isn’t this the same paper that is siding with the Wisconsin (and New York) union teachers, saying that these teachers need more money for the find job they are doing? Thanks to long-time reader and contributer Ari Scwartz for bringing this to our attention.

Detroit Invaded By Hipsters

Under the We’re-not-sure-this-is-a-good-thing category, Detroit is being taken over by t-shirted, expensively shod hipsters. And why not, when you can buy a perfectly serviceable house for pocket change. Videos here.

Unintended Consequences of Obamacare

Who could have ever guessed that the you-can’t-know-what’s-in-it-until-you-pass-it Obamacare law would have provisions which actually cause health care costs to increase? Unprecedented. The Wall Street Journal is reporting on the comedic situation where parents are going to the doctor to ask for prescriptions for aspirin and others over-the-counter remedies. Why? The Obamacare law says that health care expenses drawn from flexible spending accounts can only be authorized via a doctor’s script. Result: costs increase.

Stuff Academics Like

Just when you thought the postmodern academic culture wars were over, we have a new site documenting the oddities of academics. In the vein as Stuff White People Like, Stuff Academics Like posts strange things ivory-tower inhabitants find important. Much fun can be had in their “Guess the Fake Title” game, where they display a list of titles from genuine peer-reviewed papers, one of which is fake. A brief excerpt:

Exemplarity – The Real: Some Problems of a Realist Exemplarity Exposed through the Channel of an Aesthetic Autopoeisis [conference paper]

Tragic Closure: A Genealogy of Creative-Destructive Desire [conference paper]

The True History of His Beard: Joaquin Phoenix and the Boundaries of Cinéma Vérité [conference paper]

Trying the Law: Critical Prosecutions of the Exception [conference paper]

Thinking the Pure Unformed [conference paper]

Alan Ball’s True Blood Antics: Queering the Southern Vampire [conference paper]

Antagonistic Corpo-Real-ities [conference paper]

This list is partial, so it is unknown which, if any, is fake. Be sure not to miss the link to the Write Your Own Academic Sentence site. My entry: “The epistemology of pop culture replays (in parodic form) the ideology of the nation-state.”

Democrat Peter DeFazio Meddles With Opponent’s Kids?

Many sites (one link) are reporting on the Oregon House race of MoveOn.org-supported Democrat Peter DeFazio (leader of the House “progressive” caucus) versus Republican Art Robinson (ex professor of chemistry and climate “skeptic”, a no-no in his corner of Oregon). The details are not clear, but Robinson accused DeFazio of conspiring to have three of Robinson’s children (he has six) booted from Oregon State University’s graduate school. Robinson writes of one of his sons:

Thus, Democrat activist David Hamby and militant feminist and chairman of the nuclear engineering department Kathryn Higley are expelling four-year Ph.D. student Joshua Robinson from OSU at the end of the current academic quarter and turning over the prompt neutron activation analysis facility Joshua built for his thesis work and all of his work in progress to Higley’s husband, Steven Reese. Reese, an instructor in the department, has stated that he will use these things for his own professional gain. Joshua’s apparatus, which he built and added to the OSU nuclear reactor with the guidance and ideas of his mentor, Michael Hartman, earned Joshua the award for best Masters of Nuclear Engineering thesis at OSU and has been widely complimented by scientists at prominent U.S. nuclear facilities.

Robinson lost to DeFazio. Oregon’s Gazette Times reports that OSU said there was “no factual basis” for Robinson’s claims. The paper also differs in the details saying Robinson didn’t claim his kids weren’t being kicked out, but that two, not three, were “given unfair deadlines to complete their Ph.D. projects.” Which is a very different thing.

Robinson also alleges the OSU has “ostracized” faculty member Jack Higginbotham (nuclear engineering) for telling Robinson of the conspiracy. OSU was forced to issue a press release which said Robinson’s claims are “baseless and without merit.”

Anybody have more details on this?

Update Somebody linked to the low-flow toilet story with this must-see video from Rand Paul spanking the Obama administrator’s “Ms. Hogan” on what “pro-choice” means. Busybody!

The Sorites Paradox Isn’t

Clearly, a guy with no hair on his head is bald. But so is a guy with just one—if and only if we define bald as “a man with little or no hair.” If the guy has one hair and we define bald to mean “a man with no hair” then the man with one hair is not bald. So let us use “a man with little or no hair” as our definition and see where that gets us.

We assume that if a man with one hair is bald (by our definition), then so is a man with just two hairs. And if a man with two hairs is bald, then so is a man with three. We can expand this: if a man has N hairs and is bald, then a man with N + 1 hairs is also bald. Thus (eventually) a man with a million (say) hairs on his head bald, too. Which is absurd. Any man which such a mane is clearly fully flocked. Yet our derivation is error free.

This is the Sorites, an ancient puzzle, also given with respect to grains and heaps of sand (the words is derived from the Greek heaped up). More than a few writers on this paradox, after reaching the gotcha!, now say something like the following:

“We seem to have reached the point where we say that a man with, say, 5,000 hairs is ‘bald’, but one with just one more tiny, wee hair is not. This is nuts. Nobody can see the difference between 5,000 and 5,001 hairs. Something must be wrong with our system of logic.”

The man who says this, or anything like it, makes (at least) two mistakes. I’ve already given a hint of the first error above. There is nothing wrong with logic, but there is with the definition of bald. That word, when used in this exceedingly formal logical argument itself becomes a formal creature. It is no longer the bald as used colloquially, it is instead like the X used in algebra. It is an abstract thing, it no longer means real baldness on real men. It means logical X-ness on fictional men.

Indeed, rewrite the Sorites to remove the pseudo-word bald and replace it with X. X now means a man with fewer than Y hairs. If the man with no hairs is X, then so is the man with one hair, and so forth. Now, at some point we either bump up against Y, in which case the man is no longer X, or Y is the limit and the man is always X except at the limit.

If I were to have originally written the Sorites in this algebraic form—with just Xs and Ys—there never would have been a gotcha!, we never would have questioned the foundations of logic, there would have been no paradox. That there felt like one when we do use bald instead of X can only mean that we are silently augmenting our argument with hidden premises (which define bald). We figure that because these premises are unstated, or do not appear in print, they are not truly there.

One hidden premise is that the word bald to me, and to me right now, means a man with a certain shape of head and a certain lack of hair. I need not know how many hairs this man has, but I will make the judgment bald or not by what I see. Of course, we may, after my judgment, count the man’s hair and thus reach a quantification. My premises fluctuate: they are different for different times and men, or for the same men but they change depending on what these men wear, or the properties of the light, my relations to these men, or even by how much I have drunk.

My premises are almost certainly different than yours. I may say bald when you do not. That our behavior is not constant or that our judgments do not agree is meaningless. Neither is it relevant—and here is the second mistake—that I cannot articulate my premises. All that I can do is to say bald or not. Quantification, as I said, can always be had after the fact. But all this will tell us, in any individual case, is that the man now in front of me has not yet reached Y, or that he has exceeded it. We will not be able to deduce Y (unless the man is willing to undergo experimentation; however, my premises might change as we add or subtract hair from our recruit).

Unacknowledged, hidden premises are the generator of many “paradoxes.” The most relevant to statistics are in (faulty) criticisms of Laplace’s Rule of Succession, which we can attack another day.

Group Differences: An Exceedingly Brief Introduction To Bayesian Predictive Inference

Read the first entry in this series. All of what follows will appear ridiculously obvious to those who have had no statistical training. Those who have must struggle.

In a recent study, a greater fraction of Whites than Blacks were found to have a trait thought desirable (or undesirable, or a trait thought worth tracking). Something caused this disparity to occur. It cannot be that nothing caused it to occur. “Chance” or “randomness” are not operative agents and thus cannot cause anything to occur. It might be that we cannot know what caused it to occur, or that we guess incorrectly about what caused it to occur. But, I repeat, something caused this difference.

If you like, substitute “Pill A” and “Pill B”, or “Study 1″ and “Study 2″, etc. for White and Black.

I observed a greater fraction of Whites than Blacks possessing some trait. Given this observation, what is the probability that a greater fraction of Whites than Blacks in my study possessed this trait? It is 1, or 100%. If you do not believe this, you might be a frequentist.

What is the probability that the proportion of trait-possessing Whites is twice—or thrice, or whatever—as high as Blacks in my study? It is either 1 or 0, depending on whether the proportion of trait-possessing Whites is twice (or whatever) as high as Blacks. All I have to do is look. No models are needed, no bizarre concepts of “statistical significance.” All we need do is count. We are done: any empirical question we have about the difference (or similarities) of Whites and Blacks in our study has probability 1 or 0. It is as simple as that.

Now suppose that we will see a certain number of Whites we have not seen before; likewise Blacks (they could even be the same Whites and Blacks if we believed the thing or things that caused the trait was non-constant). We have not yet measured this new group of Whites and Blacks so that we do not know whether a greater proportion of Whites than Blacks will be found to possess the trait. Intuition suggests that since we have already observed a group in which a greater proportion of Whites than Blacks possessed the trait, the new group will display the same disparity.

We can quantify this intuition with a model. There are many—many—to choose from. The choice of which one to use is ours. All the results derived from it assume that the model we have chosen is true.

One model simply says, “In any group of Whites and Blacks, a greater proportion of Whites than Blacks will be found to possess the trait.” Conditional on this model—that is, assuming this model is true—the probability there will be a greater proportion of trait-possessing Whites than Blacks in our new group is 1, or 100%. This simple model only makes a statement about Whites possessing the trait in higher frequency than Blacks. Thus, we cannot say what is the probability the proportion of trait-possessing Whites is twice (or whatever) as high as Blacks in my study.

Some models do not let you answer all possible questions.

We could create a model which dictates the probability that we find each multiple (from some set) of fractions of Whites than Blacks (e.g. twice, thrice, 1/2, 1/3, etc.), and then use this model to make probability statements about our new group. Since that would be difficult (and somewhat capricious), we could instead parameterize the differences in proportion.

We could use this model to answer the question, “Given this model is true, and given the observations we have made thus far, what is the probability that the parameters take a certain value?” This question is not terribly interesting and it does not answer what we really want to know, which is about the differences between Whites and Blacks in our new group. Why ask about some unobservable parameter? (The right answer is not, “Because everybody else does.”)

But given a fixed value of the parameters, we could answer the question, “Given this parameterized model is true, and given a fixed value of its parameters, and given the observations we have made thus far, What is the probability a greater fraction of Whites than Blacks will posses the trait?” This is almost what we want to know, but not quite, because it fixes the values of the unobservable parameters.

Simple mathematics allows us to answer this question for each possible value of the parameters, and then weighting the answers by the probability that the parameters take those values (this is from the parameter posterior distribution, which is conditional on the model being true and on the observations we have made thus far). The final number is the probability that the fraction of Whites is larger than Blacks in our new group. Which is what we wanted to know. (This is called the predictive posterior distribution.)

“Statistical significance” never once enters into this or any real decision. When you hear this term, it is always a dodge. It is an answer to a question nobody asks and nobody wants to know. It always assumes, as we do, on the truth of a model (though it remains silent about this, hoping by this silence to convince that no other models are possible). It tells us the probabilities of events that did not happen, and asks us to make decisions based on probabilities of these never-happened events. If you want to be mischievous, ask a frequentist why this makes sense. Homework: Locate Jeffreys’s relevant quote.

See the first in this series to discover what to do if we suspect our model is not true.