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Statistics for psychologists, sociologists, and political scientists

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In terms of mathematical structure, psychologists, sociologists, and poly-sci folks all do the same experiment, over and over, and all use the same simple statistical calculation, the ANOVA, to determine its significance. I thought I’d explain that experiment and the calculation below, walking you through an actual paper (one I find interesting) in psychology / poly-sci. The results are true at the 95% level (that’s the same as saying p >0.05) — a significant achievement in poly-sci, but that doesn’t mean the experiment means what the researchers think. I’ll then suggest another statistic measure, r-squared, that deserves to be used along with ANOVA.

The standard psychological or poly-sci research experiments involves taking a group of people (often students) and giving them a questionnaire or test to measure their feelings about something — the war in Iraq, their fear of flying, their degree of racism, etc. This is scored on some scale to get an average. Another, near-identical group of subjects is now brought in and given a prompt: shown a movie, or a picture, or asked to visualize something, and then given the same questionnaire or test as the first group. The prompt is shown to have changed to average score, up or down, an ANOVA (analysis of variation) is used to show if this change is one the researcher can have confidence in. If the confidence exceeds 95% the researcher goes on to discuss the significance, and submits the study for publication. I’ll now walk you through the analysis the old fashioned way: the way it would have been done in the days of hand calculators and slide-rules so you understand it. Even when done this way, it only takes 20 minutes or so: far less time than the experiment.

I’ll call the “off the street score” for the ith subject, Xi°. It would be nice if papers would publish these, but usually they do not. Instead, researchers publish the survey and the average score, something I’ll call X°-bar, or X°. they also publish a standard deviation, calculated from the above, something I’ll call, SD°. In older papers, it’s called sigma, σ. Sigma and SD are the same thing. Now, moving to the group that’s been given the prompt, I’ll call the score for the ith subject, Xi*. Similar to the above, the average for this prompted group is X*, or X°-bar, and the standard deviation SD*.

I have assumed that there is only one prompt, identified by an asterix, *, one particular movie, picture, or challenge. For some studies there will be different concentrations of the prompt (show half the movie, for example), and some researchers throw in completely different prompts. The more prompts, the more likely you get false positives with an ANOVA, and the more likely you are to need to go to r-squared. Warning: very few researchers do this, intentionally (and crookedly) or by complete obliviousness to the math. Either way, if you have a study with ten prompt variations, and you are testing to 95% confidence your result is meaningless. Random variation will give you this result 50% of the time. A crooked researcher used ANOVA and 20 prompt variations “to prove to 95% confidence” that genetic modified food caused cancer; I’ll assume (trust) you won’t fall into that mistake, and that you won’t use the ANOVA knowledge I provide to get notoriety and easy publication of total, un-reproducible nonsense. If you have more than one or two prompts, you’ve got to add r-squared (and it’s probably a good idea with one or two). I’d discuss r-squared at the end.

I’ll now show how you calculate X°-bar the old-fashioned way, as would be done with a hand calculator. I do this, not because I think social-scientists can’t calculate an average, nor because I don’t trust the ANOVA function on your laptop or calculator, but because this is a good way to familiarize yourself with the notation:

X°-bar = X° = 1/n° ∑ Xi°.

Here, n° is the total number of subjects who take the test but who have not seen the prompt. Typically, for professional studies, there are 30 to 50 of these. ∑ means sum, and Xi° is the score of the ith subject, as I’d mentioned. Thus, ∑ Xi° indicates the sum of all the scores in this group, and 1/n° is the average, X°-bar. Convince yourself that this is, indeed the formula. The same formula is used for X*-bar. For a hand calculation, you’d write numbers 1 to n° on the left column of some paper, and each Xi° value next to its number, leaving room for more work to follow. This used to be done in a note-book, nowadays a spreadsheet will make that easier. Write the value of X°-bar on a separate line on the bottom.

T-table

T-table

In virtually all cases you’ll find that X°-bar is different from X*-bar, but there will be a lot of variation among the scores in both groups. The ANOVA (analysis of variation) is a simple way to determine whether the difference is significant enough to mean anything. Statistics books make this calculation seem far too complicated — they go into too much math-theory, or consider too many types of ANOVA tests, most of which make no sense in psychology or poly-sci but were developed for ball-bearings and cement. The only ANOVA approach used involves the T-table shown and the 95% confidence (column this is the same as two-tailed p<0.05 column). Though 99% is nice, it isn’t necessary. Other significances are on the chart, but they’re not really useful for publication. If you do this on a calculator, the table is buried in there someplace. The confidence level is written across the bottom line of the cart. 95% here is seen to be the same as a two-tailed P value of 0.05 = 5% seen on the third from the top line of the chart. For about 60 subjects (two groups of 30, say) and 95% certainty, T= 2.000. This is a very useful number to carry about in your head. It allows you to eyeball your results.

In order to use this T value, you will have to calculate the standard deviation, SD for both groups and the standard variation between them, SV. Typically, the SDs will be similar, but large, and the SV will be much smaller. First lets calculate SD° by hand. To do this, you first calculate its square, SD°2; once you have that, you’ll take the square-root. Take each of the X°i scores, each of the scores of the first group, and calculate the difference between each score and the average, X°-bar. Square each number and divide by (n°-1). These numbers go into their own column, each in line with its own Xi. The sum of this column will be SD°2. Put in mathematical terms, for the original group (the ones that didn’t see the movie),

SD°2 = 1/(n°-1) ∑ (Xi°- X°)2

SD° = √SD°2.

Similarly for the group that saw the movie, SD*2 = 1/(n*-1) ∑ (Xi*- X*)2

SD* = √SD*2.

As before, n° and n* are the number of subjects in each of the two groups. Usually you’ll aim for these to be the same, but often they’ll be different. Some students will end up only seeing half the move, some will see it twice, even if you don’t plan it that way; these students’ scares can not be used with the above, but be sure to write them down; save them. They might have tremendous value later on.

Write down the standard deviations, SD for each group calculated above, and check that the SDs are similar, differing by less than a factor of 2. If so, you can take a weighted average and call it SD-bar, and move on with your work. There are formulas for this average, and in some cases you’ll need an F-table to help choose the formula, but for my purposes, I’ll assume that the SDs are similar enough that any weighted average will do. If they are not, it’s likely a sign that something very significant is going on, and you may want to re-think your study.

Once you calculate SD-bar, the weighted average of the SD’s above, you can move on to calculate the standard variation, the SV between the two groups. This is the average difference that you’d expect to see if there were no real differences. That is, if there were no movie, no prompt, no nothing, just random chance of who showed up for the test. SV is calculated as:

SV = SD-bar √(1/n° + 1/n*).

Now, go to your T-table and look up the T value for two tailed tests at 95% certainty and N = n° + n*. You probably learned that you should be using degrees of freedom where, in this case, df = N-2, but for normal group sizes used, the T value will be nearly the same. As an example, I’ll assume that N is 80, two groups of 40 subjects the degrees of freedom is N-2, or 78. I you look at the T-table for 95% confidence, you’ll notice that the T value for 80 df is 1.99. You can use this. The value for  62 subjects would be 2.000, and the true value for 80 is 1.991; the least of your problems is the difference between 1.991 and 1.990; it’s unlikely your test is ideal, or your data is normally distributed. Such things cause far more problems for your results. If you want to see how to deal with these, go here.

Assuming random variation, and 80 subjects tested, we can say that, so long as X°-bar differs from X*-bar by at least 1.99 times the SV calculated above, you’ve demonstrated a difference with enough confidence that you can go for a publication. In math terms, you can publish if and only if: |X°-X*| ≥ 1.99 SV where the vertical lines represent absolute value. This is all the statistics you need. Do the above, and you’re good to publish. The reviewers will look at your average score values, and your value for SV. If the difference between the two averages is more than 2 times the SV, most people will accept that you’ve found something.

If you want any of this to sink in, you should now do a worked problem with actual numbers, in this case two groups, 11 and 10 students. It’s not difficult, but you should try at least with these real numbers. When you are done, go here. I will grind through to the answer. I’ll also introduce r-squared.

The worked problem: Assume you have two groups of people tested for racism, or political views, or some allergic reaction. One group was given nothing more than the test, the other group is given some prompt: an advertisement, a drug, a lecture… We want to know if we had a significant effect at 95% confidence. Here are the test scores for both groups assuming a scale from 0 to 3.

Control group: 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3.  These are the Xi° s; there are 11 of them

Prompted group: 0, 1, 1, 1, 2, 2, 2, 2, 3, 3.  These are the Xi* s; there are 10 of them.

On a semi-humorous side: Here is the relationship between marriage and a PhD.

Robert Buxbaum, March 18, 2019. I also have an explanation of loaded dice and flipped coins; statistics for high school students.

Harvard Eunuchs

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Success is measured in different ways in different cultures. Among US academics, the first mark of success is going to a great college. If you graduate from Eureka college, as Ronald Reagan did, you are pretty-well assumed to be an idiot; if you went to Harvard and Princeton, as John Kennedy did, you’re off on a good start to popular acclaim, even if your entry essay was poor, and you got thrown out of one because of cheating. Graduation from a top college does not guarantee being seen as a success forever, though. You have to continue in the Harvard way: use big words — something that puts-off the less-educated; you have to win awards, write books or articles; have the right politics; work at a high power job and money, meet the right people, exercise regularly, etc. It’s hard work being successful; disposable income is tight, and one rarely has time for kids.

Fertility rates, 1950 and now

Fertility rates compared, world-wide, 1970 vs 2014.

By contrast, in ancient societies, success included food, leisure, land, and general respect. A successful person is seated at the front of the church, and consulted as few academics are. And there is another great measure: children. In traditional societies, children are valued, They are seen as a joy in your youth, and a comfort in your old age. They are you and your wife reborn, with reborn wonder. They are your future, and the defenders of your legacy; ready to take on the world with an outlook of their own, but one that you had a unique chance to mold. In the Bible, children are a sign of blessing, and the opposite is explicitly stated as a punishment for violating God’s commands.

I have come to wonder why rich countries have so few children, and why successful people in rich countries have yet fewer than the average. These people and countries are no worse than others, yet they are common. Harvard produces a surprising number of “Legal Eunuchs” — people with a refined place in society, but no time or children; people who work tirelessly for the pleasure and success of others. Harvard couples marry late, or not at all. If they marry, they usually produce childless households, DINKs — Double Income No Kids.

The same pattern is seen in Europe, UK, Japan, Canada, Russia, and China, as the map above shows. Particularly among the élite, the great works are being created for the deplorables and their children. Could anything be more depressing?

The seven things include that Eunuchs can be trusted, that they love to serve, that they are compassionate, that they are passionate (for excellence) and that they have fewer distractions.

There’s and organization for everything these days. In this case, the seven things you didn’t know include that Eunuchs can be trusted, that they love to serve, that they are compassionate, that they are passionate for excellence, and that they have fewer distractions. This is the opposite of toxic masculinity, but it comes at a cost. 

I think one reason for the growing ranks of Harvard Eunuchs is a dislike of masculinity; masculinity is sort-of toxic,  associated with war, revolution, and selfishness. In the 1800s, only Republicans and Communists had beards; the more-refined gentleman did not. The eunuch qualities listed above, are considered noble, charitable, and selfless. Clearly it helps others if you are selfless, but why do it? I think the answer is self-doubt about ones worthiness to enjoy the fruits of your labor. To get to Harvard takes striving, and that relates to a degree of self-doubt and loathing about your worthiness today.

I graduated from Cooper Union, and went to Princeton for graduate school. It was a magical place, I became machines chairman, then chairman of the Graduate College House Committee. I dealt with a lot of very bright, accomplished people, and a pattern I saw often was self-doubt and loathing. And the most accomplished students were the ones with the most self-loathing. It made them strive to be better; it drove the innovative research and the grant writing. It motivated graduates to try to become professors (only a few would succeed) or judges, or financiers, or politicians. All that takes time, striving, and putting off your wants in the here-and-now, for a reward to the future you that is worthy. It’s a system that produces greatness, but at great personal cost.

So what’s to be done? How do you help yourself, or some other, the bright, educated fellow see that he or she is good enough. Unfortunately, for those in the system, good enough equals bad. I found it helped to say, in my own words, the words or Solomon:”Eat, drink, and enjoy yourself.” “It is not good to be over-wise… Why wear yourself out?” Not that these words changed them, but they did seem to give comfort. I’d suggest the write things that were honest; that people understand, and that they take time for themselves. “May your fountain be blessed, and enjoy the wife of your youth.” (Ps.127:3-4, Ecc.8:15, Pr.5:18…) It suffices to retell old truths and raise a new generation. Only make sure that what you have to say is honest and logical, and trust your own value. As for toxic masculinity, it can have its own charm.

Robert E. Buxbaum, January 29, 2019. I got the title for this article, and the idea, from the phrase, “Legal Eunuchs” in this wonderful book review (2005) by Alan Dershowitz.

A Pastor to Trump’s Soul

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Trump’s religious connection is so different from the norm that most people think it must be fake, but the truth of his connection to Christianity, as best I can determine it, is even more bizarre than the assumption that there is none. From the time that he was six years old, Donald Trump attended a famous church in New York City, The Marble Collegiate Presbyterian Church. He attended along with his grandfather, his parents, his brother, and his sisters. He was married in this church as was his sister. Both his parents funerals were in the sanctuary, and unlike most children in a family church, he seems to have been generally moved by the sermons — moved to change his life.

Trump and NVP

Various scenes of Trump and his family with Dr. Norma Vincent Peale.

The pastor of the church and the author of these sermons was not a standard Christian, though. It was Norman Vincent Peele, author of “The Power of Positive Thinking.” According to President Trump, he loved the sermons almost from the beginning. They went on for an hour or so and as Trump remembers it, the Reverend Peele could have spoken for twice as long at least. Dr. Peale did not talk fo sin, but rather of success and other of the most positive things. Peale claimed that you could do anything you wanted with the help of God and proving you believed in your self and didn’t let anything anyone said interfere. He backed up this take on the bible by a cherry-picked selection from all the positive lines in the Bible — Lines that are really there, but that most pastors avoid because they can make a person arrogant (or seem arrogant). A source for all of president Trumps bizarre self-image ideas can be found in Peele’s “The power of positive thinking,”I  find.presidents-billy-right-960x640BG-Kennedy-960x640

Dwight Eishenhouer

Some other US presidents with Reverend Billy Graham.

Most other American pastors have emphasized self reflection and humility. They would pray for the power to avoid bragging or other forms of puffing one’s self up —  the very opposite approach of Dr. Peale’s. The most popular of the alternates approaches, one embraced by virtually every president from 1952 to today was Billy Graham’s fire humility.

Eisenhower golfed with Graham regularly, as did Kennedy, Johnson, Nixon, Ford, and G. H.W. Bush. Graham was a feature at prayer breakfasts with Johnson and Reagan, and Carter. In time of trouble it was Billy Graham who counseled Carter, Clinton, and Nixon, and it was Graham who got George W. Bush to give up drinking. After a time, one could imagine that Billy Graham’s quiet humility and fiery faith was the real American belief. Or at least that this was the form of American soul that one associated with success.bill graham reagan BG-JOHNSON

After decades of seeing Billy Graham at the White House, one began to believe that his was the image of the believing American. To believe meant to see oneself as a sinner who often made mistakes but was genuinely sorry for these failures. A believing American was genuinely penitent, but not too loudly. Was reborn, but didn’t make too much fuss of it. Thus it’s more than a little shock to find believer in God’s plan who claims to believes that God wants him to have success, money, and power, and who claims, as Trump does, that those who criticize him are “fake news”.

I’ve mentioned before that a strong belief in ones self has a positive side for leaders, but it strikes me that perhaps it’s also good for religion. These lines really do appear in the Bible, Humility is there too, of course, but we could all use a reminder that “God gives to all who believe in Him.”

Robert Buxbaum, September 3, 2018

West’s Batman vs Zen Batmen

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“Holy kleenex Batman, it was right under our noses and we blew it.” I came of age with Adam West’s Batman on TV and a relatively sane Batman in the comic books. Batman was a sort of urban cowboy: a loner, but a law-abiding, honest loner. A proud American who was polite to the police and to the ordinary citizen. He was both good, and “nice.” Back then, as today, no one died by the hand of Batman, but that was largely because he worked with the police who made the final arrests

bat-buddah

More recent Batmen have been not nice, and arguably not good either. They do not work with the police but act above the law. Their ethos is not from US civics class, but from dark training in eastern monasteries by masters of kung fu. It’s a morality no one quite understands, not least himself. Quite literally, ‘He is a dark and stormy knight.’

A few days ago, I found this plastic Batman-Buddah for sale on e-Bay and I started wondering about how far our current movie Batmen have moved from those of the 60s. And on the deep, Zen thoughts that Batman now expounds on life and crime. These zen thoughts are pretty messed up, as psychologists have noted.

Example. In a recent Batman movie, Batman beats up an invasive wannabe wearing hockey pads. He gets asked: “What gives you the right? What’s the difference between you and me?” The response, “I’m not wearing hockey pads.” This is to say, the current Batman believe his physical prowess makes him above the law. Some more comments:
“Sometimes it’s only madness that makes us what we are.”
“That mask — it’s not to hide who I am, but to create what I am.”
“I won’t kill you, but I don’t have to save you.”

When he speaks to the Joker, it’s not clear which one is crazier. E.g.. Batman tells the Joker that he doesn’t kill because, “If you kill a killer, the number of killers remains the same.” To which Joker replies: “Unless you kill more than one….” That sounds sane to me.

By contrast. consider Adam West as Batman in the 1960s: “Underneath this garb, we’re perfectly ordinary Americans.” Another quote: “A reporter’s lot is not easy, making exciting stories out of plain, average, ordinary people like Robin and me.” Though this comment is “off” it’s nice to see that this Batman feels for peoples’ problems, respects their professions, and does not profess to be better than they are. He’s weird, but not a psychopath, and he leaves Gotham city pretty much the way you find it at the beginning of a comic or episode.

Not a classic Batmobile, but I like the concept.

Not a classic Batmobile, but I like it. Adam West’s Batman always strove to be socially responsible. 

By contrast, the current, dark, depressive Batmen always leave Gotham City in shambles, with piles of dead and destroyed buildings and infrastructure. Given the damage Batman does, you wonder why anyone calls for Batman; current Batmen never works with the police, quite.

And where’s Robin. To the extent that Robin appears at all, his relationship with Batman is more frenemy than ally. Batgirl too is mostly absent, and has changed. The original Batgirl was connected to the police. She was Barbara Gordon, Police Commissioner Gordon’s daughter, a positive female with a good relationship with her supportive, non-sexist father (an early version of Kim Possible’s dad) and with society as a whole. The current Batgirl appears is the butler’s daughter, and except for one brief appearance, you never see her, not at Wayne Manor, not anywhere. Somehow she’s Batgirl though it’s presented that didn’t know what her dad was up to.

Here are some real interactions between Adam West as Batman with Robin. He shows an interest in Robin’s education and well-being, something currently lacking:

AW Batman: “Haven’t you noticed how we always escape the vicious ensnarements of our enemies?” Robin: “Yeah, because we’re smarter than they are!”  Batman: “I like to think it’s because our hearts are pure.”

AW Batman: “Better put 5 cents in the meter.” Robin: “No policeman’s going to give the Batmobile a ticket.” Batman: “This money goes to building better roads. We all must do our part.”

Robin: “You can’t get away from Batman that easy!” AW Batman: “Easily.” Robin: “Easily.”
“Good grammar is essential, Robin.” Robin: “Thank you.” Batman: “You’re welcome.”

Robin/Dick: “What’s so important about Chopin?” Batman: “All music is important, Dick. It’s the universal language. One of our best hopes for the eventual realization of the brotherhood of man.” Dick: “Gosh Bruce, yes, you’re right. I’ll practice harder from now on.”

AW Batman: “That’s one trouble with dual identities, Robin. Dual responsibilities.”

“Even crime fighters must eat. And especially you. You’re a growing boy and you need your nutrition.”

“What took you so long, Batgirl?” Batgirl: “Rush hour traffic, plus all the lights were against me. And you wouldn’t want me to speed, would you?” Robin: “Your good driving habits almost cost us our lives!” Batman: “Rules are rules, Robin. But you do have a point.”

And finally, AW Batman: “I think you should acquire a taste for opera, Robin, as one does for poetry and olives.”

Clearly this Batman takes an interest in Robin’s health and education, and in Batgirl’s. Robin is his ward, after all, a foster child. And Batgirl is a protege, as well as the daughter of a friend.

The modern Batman claims, “It’s not who I am underneath, but what I do that defines me.” It’s, more or less, a quote from Karl Jung that shows pride in one’s art, but it also shows an attachment to job over self. This approach appeared in the olden days, in the form of Catwoman, a woman with her own moral code, and proud of it. Batman found her odious, abhorrent, and “insegrievious”. The only difference between her and the Joker, he says, is the amount of damage done. I’m sorry to find that recent, Zen Batmen and Supermen might as well be Cat-women, or Jokers. To quote Robin: “Holy strawberries, Batman, we’re in a jam.”

Robert Buxbaum, June 26, 2017. Insegeivious is a made-up word, and I love it. I also love the humor of Robin’s “holy xxx” comments.

Narcissism, a horrible disease except in presidents.

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Perhaps the worst sort of employee is a narcissist. A narcissist is in love with an image of himself that he sees, and that he has created. Though his behavior does not match the image — it can not –the narcissist can not, or will not accept the damage he’s caused by insubordination and undercutting. The typical narcissist is always right, and is confident of being right, even when seriously wrong. He can take some (little) advice because he sees himself as humble, but he will not take blame, and thus does not change. He can be charming in his love of you and your ideas. Still, you’ll notice his complete disdain for others and of ideas that (to you) look equally brilliant. And once he accepts your first idea as brilliant, he’s unlikely to change to accept your second, or modified version.

The Great Gatsby created an image of himself, and strove to live it. "He looked at you like the moon and the stars shone out of your eyes."

The Great Gatsby created an image of himself, and strove to live it. “He looked at you like the moon and the stars shone out of your eyes.”

The narcissist friend or boss is somewhat better. He creates a positive mental image of those around him, usually seeing them as kind, holy, or smart people. The Great Gatsby was a classic example of this. It’s nice to be in his presence, “seen as you’d wish to be seen, as if the moon and the stars shone in your eyes”. It’s an image the narcissist does his best maintain, both of you and of him, even if it kills you and him together. This is still a damaging, false image, but it has a tremendous up-side or two in a friend or boss. It’s nice to work with someone who sees you as God’s gift even if you know it’s false. Besides that, the narcissist usually has some general plan of action or knows how to get one (e.g. hire the best, consult the iChing, build a wall). The plan might not be great, but it’s usually better than having no-plan or waiting to consult the consultants at every turn. And unlike most folks, the narcissist knows he must stick to the plan or he looks like a loser. It also helps that he or she, by force of charisma, has the ability to make others stick to the plan. In times of trouble or confusion, that’s usually far better than hopeless paralysis. Also good is that narcissists tend to collect solid followers — a plus when leading a big organization where decisions are important. The leader can not hope to manage all the details of a big organization, and needs to be able to rely on loyal minions to follow general his orders and get the details right.

There are few bigger organizations than government. Government leadership has seen an uncommon concentration of narcissists, and these have done rather well, considering. In the US and elsewhere the best (and worst) leaders have been narcissists, mostly. Napoleon, FDR, Stalin, Churchill, Christ, Mohammed, Hitler, Bill Clinton, Gandhi, and Genghis Kahn; all narcissists as best I can tell. They all saw themselves as great, behaved accordingly, and got people to follow. They made grand plans and carried them out by convincing others to go along: the others providing the necessary blood, sweat, tears, and death. Their approach may appall when seen in quiet times, but it’s absolutely necessary in troubled times when the normal alternatives are confusion and despair. Jimmy Carter, a more-normal type, folded in times of trouble; he dithered in the face of the Ayatollah and of Idi Amin. Twice he started Iranian rescue operations, then called them off — in both cases at the worst possible moments. People died, friends lost hope. Carter was a normal person in a situation that required a narcissist. Meanwhile, the Ayatollah and Idi Amin did as narcissist do, for better or worse.

It’s been pointed out that Donald Trump is a narcissist (he is, congratulations). I strongly suspect that’s true of Cruz, and Sanders too. Trump’s narcissism is unusually blatant because his vision of himself is unusually brash. Cruz and Sanders, have quieter visions of themselves mixing feigned humility with their firm resolve. I don’t see these visions as better, just more normal-looking. Brash visions can be a negative, of course, both in a US president, and in a corporate president, but to have no vision is worse. Apple computer company seems to have no vision now that Steve Jobs is dead, and it’s floundering. Jeb! Bush, similarly seemed to have had no firm vision, and he ended his run as a washed-up flotsam. As for HRC, I don’t know. Fortunately, the US government has the power to rein in any (I think) narcissist, via the constitution’s balance of power. Congress and the supreme court, if they choose to use it, have the power to stop any excess of a narcissist president. The narcissist will fight, but will eventually will bend to them; the one thing the narcissist does not wish is to see himself as, is as a loser, and they have the power to portray him that way. The US will survive whoever gets elected.

Robert Buxbaum, April 10, 2016. I’m not a psychologist and might be dead wrong here, but how I see things at the moment is that Trump’s narcissism is manageable and perhaps advantageous. Besides, I’ve argued in favor of tariffs for some time, so we have some policy agreement. For April Fools day, last year, I described the duel of a famous narcissist president, Andrew Jackson, with his lawyer.

if everyone agrees, something is wrong

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I thought I’d try to semi-derive, and explain a remarkable mathematical paper that was published last month in The Proceedings of the Royal Society A (see full paper here). The paper demonstrates that too much agreement about a thing is counter-indicative of the thing being true. Unless an observation is blindingly obvious, near 100% agreement suggests there is a hidden flaw or conspiracy, perhaps unknown to the observers. This paper has broad application, but I thought the presentation was too confusing for most people to make use of, even those with a background in mathematics, science, or engineering. And the popular versions press versions didn’t even try to be useful. So here’s my shot:

Figure 2 from the original paper. For a method that is 80% accurate, you get your maximum reliability at the third to fifth witness. Beyond that, more agreement suggest a flaw in the people or procedure.

Figure 2 from the original paper. For a method that is 80% accurate, you get your maximum reliability at 3-5 witnesses. More agreement suggests a flaw in the people or procedure.

I will discuss only on specific application, the second one mentioned in the paper, crime (read the paper for others). Lets say there’s been a crime with several witnesses. The police line up a half-dozen, equal (?) suspects, and show them to the first witness. Lets say the first witness points to one of the suspects, the police will not arrest on this because they know that people correctly identify suspects only about 40% of the time, and incorrectly identify perhaps 10% (the say they don’t know or can’t remember the remaining 50% of time). The original paper includes the actual factions here; they’re similar. Since the witness pointed to someone, you already know he/she isn’t among the 50% who don’t know. But you don’t know if this witness is among the 40% who identify right or the 10% who identify wrong. Our confidence that this is the criminal is thus .4/(.4 +.1) = .8, or 80%.

Now you bring in the second witness. If this person identifies the same suspect, your confidence increases; to roughly (.4)2/(.42+.12) = .941,  or 94.1%. This is enough to make an arrest, but let’s say you have ten more witnesses, and all identify this same person. You might first think that this must be the guy with a confidence of (.4)10/(.410+.110) = 99.99999%, but then you wonder how unlikely it is to find ten people who identify correctly when, as we mentioned, each person has only a 40% chance. The chance of all ten witnesses identifying a suspect right is small: (.4)10 = .000104 or 0.01%. This fraction is smaller than the likelihood of having a crooked cop or a screw up the line-up (only one suspect had the right jacket, say). If crooked cops and systemic errors show up 1% of the time, and point to the correct fellow only 15% of these, we find that the chance of being right if ten out of ten agree is (0.0015 +(.4)10)/( .01+ .410+.110) = .16%. Total agreement on guilt suggests the fellow is innocent!

The graph above, the second in the paper, presents a generalization of the math I just presented: n identical tests of 80% accuracy and three different likelihoods of systemic failure. If this systemic failure rate is 1% and the chance of the error pointing right or wrong is 50/50, the chance of being right is P = (.005+ .4n)/(.01 +.4n+.1n), and is the red curve in the graph above. The authors find you get your maximum reliability when there are two to four agreeing witness.

Confidence of guilt as related to the number of judges that agree and your confidence in the integrity of the judges.

Confidence of guilt as related to the number of judges that agree and the integrity of the judges.

The Royal Society article went on to a approve of a feature of Jewish capital-punishment law. In Jewish law, capital cases are tried by 23 judges. To convict a super majority (13) must find guilty, but if all 23 judges agree on guilt the court pronounces innocent (see chart, or an anecdote about Justice Antonin Scalia). My suspicion, by the way, is that more than 1% of judges and police are crooked or inept, and that the same applies to scientific analysis of mental diseases like diagnosing ADHD or autism, and predictions about stocks or climate change. (Do 98% of scientists really agree independently?). Perhaps there are so many people in US prisons, because of excessive agreement and inaccurate witnesses, e.g Ruben Carter. I suspect the agreement on climate experts is a similar sham.

Robert Buxbaum, March 11, 2016. Here are some thoughts on how to do science right. Here is some climate data: can you spot a clear pattern of man-made change?

In praise of openable windows and leaky construction

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It’s summer in Detroit, and in all the tall buildings the air conditioners are humming. They have to run at near-full power even on evenings and weekends when the buildings are near empty, and on cool days. This would seem to waste a lot of power and it does, but it’s needed for ventilation. Tall buildings are made air-tight with windows that don’t open — without the AC, there’s be no heat leaving at all, no way for air to get in, and no way for smells to get out.

The windows don’t open because of the conceit of modern architecture; air tight building are believed to be good design because they have improved air-conditioner efficiency when the buildings are full, and use less heat when the outside world is very cold. That’s, perhaps 10% of the year. 

No openable windows, but someone figured you should suffer for art

Modern architecture with no openable windows. Someone wants you to suffer for his/her art.

Another reason closed buildings are popular is that they reduce the owners’ liability in terms of things flying in or falling out. Owners don’t rain coming in, or rocks (or people) falling out. Not that windows can’t be made with small openings that angle to avoid these problems, but that’s work and money and architects like to spend time and money only on fancy facades that look nice (and are often impractical). Besides, open windows can ruin the cool lines of their modern designs, and there’s nothing worse, to them, than a building that looks uncool despite the energy cost or the suffering of the inmates of their art.

Most workers find sealed buildings claustrophobic, musty, and isolating. That pain leads to lost productivity: Fast Company reported that natural ventilation can increase productivity by up to 11 percent. But, as with leading clothes stylists, leading building designers prefer uncomfortable and uneconomic to uncool. If people in the building can’t smell an ocean breeze, or can’t vent their area in a fire (or following a burnt burrito), that’s a small price to pay for art. Art is absurd, and it’s OK with the architect if fire fumes have to circulate through the entire building before they’re slowly vented. Smells add character, and the architect is gone before the stench gets really bad. 

No one dreams of working in an unventilated glass box.

No one dreams of working in a glass box. If it’s got to be an office, give some ventilation.

So what’s to be done? One can demand openable windows and hope the architect begrudgingly obliges. Some of the newest buildings have gone this route. A simpler, engineering option is to go for leaky construction — cracks in the masonry, windows that don’t quite seal. I’ve maintained and enlarged the gap under the doors of my laboratory buildings to increase air leakage; I like to have passive venting for toxic or flammable vapors. I’m happy to not worry about air circulation failing at the worst moment, and I’m happy to not have to ventilate at night when few people are here. To save some money, I increase the temperature range at night and weekends so that the buildings is allowed to get as hot as 82°F before the AC goes on, or as cold as 55°F without the heat. Folks who show up on weekends may need a sweater, but normally no one is here. 

A bit of air leakage and a few openable windows won’t mess up the air-conditioning control because most heat loss is through the walls and black body radiation. And what you lose in heat infiltration you gain by being able to turn off the AC circulation system when you know there are few people in the building (It helps to have a key-entry system to tell you how many people are there) and the productivity advantage of occasional outdoor smells coming in, or nasty indoor smells going out.

One irrational fear of openable windows is that some people will not close the windows in the summer or in the dead of winter. But people are quite happy in the older skyscrapers (like the empire state building) built before universal AC. Most people are nice — or most people you’d want to employ are. They will respond to others feelings to keep everyone comfortable. If necessary a boss or building manager may enforce this, or may have to move a particularly crusty miscreant from the window. But most people are nice, and even a degree of discomfort is worth the boost to your psyche when someone in management trusts you to control something of the building environment.

Robert E. Buxbaum, July 18, 2014. Curtains are a plus too — far better than self-darkening glass. They save energy, and let you think that management trusts you to have power over your environment. And that’s nice.

Is ADHD a real disorder

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When I was in school, ADHD hadn’t been invented. There were kids who didn’t pay attention for a good part of the day, or who couldn’t sit in their seats, but the first activity was called day-dreaming and the second “shpilkas” or “ants in your pants.” These problems were recognized but were considered “normal.” Though we were sometimes disorderly, the cause wasn’t labeled a disorder. It’s now an epidemic.

There were always plenty of kids, me included, who were day-dreamers. Mostly these were boys who would get bored after a while and would start to look around the room, or doodle, or gaze into space thinking of this or that. Perhaps I’d do some writing or math in the margin of a notebook while listening with one ear; perhaps I’d work on my handwriting, or I’d read something in another textbook. This was not called a disorder or even an attention deficit (AD), but rather day-dreaming, wool-gathering, napping, or just not paying attention. Sometimes teachers got annoyed, other times not. They went on teaching, but sometimes tossed chalk or erasers at us to get us to wake up. Kids like me took enough notes to do OK on tests and homework, though I was never at the top of the class in elementary or middle school. The report cards tended to say things like “he could do better if he really concentrated.”  It’s something that could apply to everyone.

Then there were the boys who would now be labeled HD, or “hyperactive disordered.” These were always boys: those who didn’t sit well in their chairs, or fidgeted, or were motor mouths and got up and walked about, or got into fights, or went to the bathroom; these were the class clowns, and the trouble makers — not me except for the fidgeting. Girls would fidget or talk too, and they’d pass notes to each other, but they didn’t get into fights, and they weren’t as disruptive. They tended to have great handwriting, and took lots of notes in class: every single word from the board, plus quite a bit more.

There are different measures of education, if you measure a fish's intelligence by the ability to climb a tree it will spend its life thinking it's stupid.

There are different measures of education, if you measure a fish’s skill level by the ability to climb a tree you’ll conclude the fish is ADD or worse.

Elementary and middle schools had activities to work out the excess energy that caused hyper-activity. We had dancing, shop, fire drills, art, some music, and sports. None of these helped all that much, but they did some good. I think the fire drills helped the most because we all went outside even in the winter, and eventually we calmed down without drugs. Sometimes a kid didn’t calm down, got worse, and did real damage; these kids were not called hyperactive disordered, but “bad kids” or “juvenile delinquents.” Nowadays, schools have far less art and music, and no shop or dancing. There are a lot more hyperactive kids, and the claim nowadays is that these hyperactive kids, violent or not, are disordered, ADHD, and should be given drugs. With drugs, the daydreamers take better notes, the nappers wake up, and the hyperactive kids calm down. Today about 30% of high-school seniors are given either a version of amphetamine, e.g. Adderall, or of Methylphenidate (Ritalin, etc.) The violent ones, the juvenile delinquents, are given stronger versions of the same drugs, e.g. methamphetamine, the drug at the heart of “breaking bad.”

Giving drugs to the kids seems to help the teacher a lot more than it helps the kids. According to a famous joke, giving the Ritalin to the teacher would be the best solution. When the kids are given drugs the disorderly boys (it’s usually given to boys) begin to act more like “goodie goodies”. They sit better and pay attention more; they take better notes and don’t interrupt, but I’m not sure they are learning more, or that the class is, or that they are socializing any better than before. The “goodie-goodies” in elementary school (mostly girls) did great in the early grades, but their good habits seemed to hold them back later. They worked too hard to please and tended to not notice, or pretended to not notice, when the teacher said nonsense. When it came time for independent or creative endeavors, their diligent acceptance of authority stood in the way of excellence.Venn diagram of ADHD

The hyperactive and daydreamers were more used to thinking for themselves, a prerequisite of leadership. The AD ones had gotten used to half-ignoring the teacher, and the HD ones were more openly opinionated and oppositional: obstreperous, in a word. Those bright enough to get by got more out of their education, perhaps because it was more theirs. To the extent that education was supposed to make you a leader and a thinker, the goodie-goodie behavior was a distraction and a disorder. This might be expected if education is supposed to be the lighting of a fire, not the filling of a pit. If everyone thinks the same, it’s a sign that few are thinking.

Map of ADHD variation with location for US kids ages 6-18, Scrips Research.

Map of ADHD variation with location for US kids ages 6-18, Scrips Research. Boys are 2-3 times more often diagnosed as ADHD; diagnosis and medication increase with grade, peaking currently in early college.

This is not to say that there is no such disorder as ADHD, or no benefit from the drugs. My sense, though, is that the label is given too widely, and that the drugs are given too freely. Today drugs are pushed on virtually any kid who’s distracted, napping or hyperactive — to all the members of the big circles in the Venn diagram above, plus to athletes and others who feign ADD to get these, otherwise illegal, performance enhancing drugs. Currently, about 10% of US kids between 6 and 18 are diagnosed ADHD and given drugs, see figure. The numbers higher for boys than girls, higher in the US than abroad, and higher as the kids progress through school. It’s estimated that about 25% of US, 12th grade boys are given amphetamine or Ritalin and its homologs. My sense is that only a small fraction of these deserve drugs, only those with severe social problems, the violent or narcoleptic: those in the smaller circles of the Venn diagram. The test should not be that the kid’s behavior improves on them. Everyone’s attention improves when taking speed. ADHD appears more as an epidemic of overworked, undertrained, underfunded teachers, and a lack of outlets, not of disordered kids, or of real learning, and real learning is never pretty or easy (on all involved).

Robert Buxbaum, April 18, 2014. In general, I think people would be happier if they’d do more art, music, dance and shop, and if they’d embrace their inner weirdo. It would also help if doctors and teachers would use words rather than initials to describe people. It’s far better to be told you’re hyperactive, or that you’re not paying attention, then to be called ADD, HD, or ADHD. There’s far more room for gradation and improvement. I’m not an expert, just an observant observer.

Einstein’s fuzzy slippers — and a fetish lawyer joke

First, the joke about the fetishistic lawyer: He got off on a technicality.

It’s funny because  ….  it’s a double entendre, a multi-word, sexual homophone (no insult  to the homophone community). It also relates to a fact as true and significant as any in life. What a person considers enjoyable, fun (or not) depends mostly on what’s in his mind. Whether judging sexy or scary; pleasant or disagreeable, it has relatively little to do with a physical reality, and is mostly in the imagination of the person. As a result, the happiest people seem to be those who embrace their inner weirdness. They try to find jobs that they are good at, that allow them to take perverse pleasure in their own weird way within the bounds of a civil society.

Take pleasure in your own weirdness.

Einstein in fuzzy slippers outside of his Princeton home; take pleasure in your own weirdness.

Einstein, at left, seems to have enjoyed doing physics, playing the violin, and wearing odd clothes: sweaters, and these (pink) fuzzy slippers. the odd clothes didn’t detract from his physics, and may have even helped him think. Boris Spassky (the Russian chess champion) was asked which he preferred: sex or chess, he said: “it very much depends on the position.” Do what you like, and like what you do. As the old joke goes, “I don’t suffer from insanity: I enjoy every moment.”

Robert Buxbaum. April 1, 2014; I mostly blog about science and hydrogen, but sometimes, like here, about personal relations, or last week economics (dismal). Here’s a thermodynamic look at life. And a picture of an odd sculpture I made. I take my own advice, by the way: this blog doesn’t get me any money but it’s fun, and maybe I’ll help some day — e.g. maybe it’ll spark my creativity. Here’s a bit about Einstein’s mustache, and the universe being curved in.