I see that Charles "I Don't Like My Regression Results so I'm Going to Drop All Education Variables From My Equation" Murray--one of the main reasons why the AEI's reputation is so low among social scientists--is on the New York Tmes op-ed page. Shame on the editors: we really do deserve a better press corps.
Let's review this guy's record a bit:
Posted by DeLong at October 13, 2004 11:40 AM | TrackBackCharles Murray Can't Multiply: David Brooks writes, "Think of your twelve closest friends, Richard J. Herrnstein and Charles Murray write. If you had chosen them randomly from the American population, the odds that half of your twelve closest friends would be college graduates would be six in a thousand. The odds that half of the twelve would have advanced degrees would be less than one in a million..."
Ummm... No. Definitely not. Back when The Bell Curve was published, 22.2% of Americans over 25 had bachelor's degrees (an additional 7% had associate's degrees) and 7.5% of Americans over 25 had advanced degrees. Draw 12 people at random from this set*... the odds that half of them will have college degrees is 2.5% (7.2% if we are counting not just bachelor's but associate's degrees)--not "six in a thousand." The odds that half of 12 people drawn at random from this set will have advanced degrees is 0.1%--not "less than one in a million." I can't for the life of me figure out what calculations Murray was trying to make that would produce his numbers. But whatever calculations he made, he is off by a factor of 4 (or 12, if we are counting associate's degrees) for the college-educated and off by a factor of more than 100 for those with advanced degrees.
"Does being off by a factor of a hundred (or four) really matter?" you ask. "2.5% or 0.6%, 0.1% or 0.0001%, the odds are still low--and the point that American society is not well-mixed is still true. " But Murray's (and Brooks's) point is not that American society is not well mixed. Their point is that American society is totally stratified--and that is false.... [N]othing Charles Murray writes can be trusted without being independently verified, and that even the first chapter of The Bell Curve is "controversial"--that is, flat-out wrong.
*Suppose we draw twelve people at random. The chance that all of the first six we draw will have college degrees is 0.222^6. The chance that all of the last six we draw will not have college degrees is 0.778^6. The chance that both of these things will happen together is the product of those two numbers--0.0000265. But we don't care about the order: we would be perfectly happy if numbers 2, 4, 7,8,9, and 12 had college degrees. So we need to multiply 0.0000265 by the number of possible ways in which six college and six non-college graduates can be ordered. There are (12!)/((6!)(6!)) such ways--924 such ways. Multiplying 0.0000265 by 924 gives us 0.025--our 2.5% number.
AEI-Quality Research: : [T]he impeccably right-wing Jim Heckman's [review of The Bell Curve] flay[s] Murray and Herrnstein alive and [hangs] their skins on his office door:
James Heckman in Reason: ...The book fails for four main reasons. First, too much space is devoted to discussions of intrinsically irrelevant issues. Nothing central to the case for recognizing diversity in human abilities hinges on the issue of whether there is one "true ability" or whether there are multiple abilities--as common sense, much psychometric research, and the authors' own evidence indicate is the actual state of affairs. Despite this evidence, Murray and Herrnstein devote many pages to justifying a one-ability, or "g," model of human intelligence....
The second, more fundamental, reason why this book fails to provide an effective challenge to contemporary egalitarian social policy... [is that] the authors choose an empirical approach... [and] fail to develop the empirical case in a satisfactory or coherent manner.... [T]he authors do not discuss the costs and benefits of various interventions.... The authors seek to short-circuit all of the hard work required to make credible cost-benefit calculations by claiming that there is a genetic basis for skill differences. But estimates of a genetic component of skills are irrelevant to the requisite cost-benefit analysis unless it can be established that all differences are genetic. No one, including the authors, claims that this is so.... The Bell Curve fails to present the hard information required to settle these matters on the factual grounds chosen by the authors. This point is particularly telling for their assessment of education. The authors offer an inconsistent treatment of education throughout the book.... They acknowledge--and then go on to forget--that the relationship between education and ability is far from exact... throughout much of the book, they equate ability and education and implicitly assume that the economic returns to ability drive the economic returns to education....
[T]his implicit assumption is false. Their own evidence (buried in Appendix 6), as well as a vast literature in empirical social science, clearly indicates that controlling for ability lowers but does not eliminate the return to schooling measured in terms of earnings.... Ability and education are not the same thing, and both have economic rewards... Their implicit claim that ability drives the economic return to education, and the recent increase in the economic return to education, fails to pass empirical muster.
The third source of The Bell Curve's failure lies in the details of its analysis of the impact of ability on measured outcomes such as earnings. In their empirical research, the authors examine how well one measure of ability explains a variety of economic and social behaviors. They pit their ability measure against a measure of the socioeconomic status of persons when they were children. The authors intend this contrast to reveal the relative importance of "genes" and "environment" in accounting for behavior. Outcomes are much more sensitive to their measure of ability than to their measure of socioeconomic status. Large changes in the socioeconomic variables have weak effects on the outcome measures, while small changes in ability have large effects on the same outcome measures. This sort of empirical exercise prospers--or founders--on the details. The credibility of any empirical study depends on the care taken by the analyst in defining and measuring concepts, and in interpreting conclusions drawn from the data. It is at this point that the book becomes a policy polemic rather than a scholarly study of human differences....
Finally, the book fails due to a lack of coherence. The argument does not cumulate in a convincing way. Too many seams are visible...
Notes: What Thomas Sowell Thinks of The Bell Curve: Atrios laments: "Every time I refer disparagingly to [Herrnstein and Murray's] The Bell Curve some true believer expects me to write a 50,000 word critique of the book to justify my opinion of it. Frankly, it's as if every time I spoke disparagingly of The Protocols of the Elders of Zion someone expected me to write a 50,000 word critique of it."
You don't have to write a 50,000 word critique. All you have to do is point them to Thomas Sowell's American Spectator review of The Bell Curve. Sowell pulls his punches--no book that goes to the lengths The Bell Curve does to keep from considering education as an independent influence on people's life-paths can possibly be, as Sowell calls it, "very sober, very thorough, and very honest." But even Sowell's pulled punches are absolutely devastating. And no one can call Thomas Sowell a politically-correct left-wing hack:Upstream: Issues: Bell Curve: Thomas Sowell : Vol. 28, American Spectator, 02-01-1995, pp 32: [Herrnstein and Murray] seem to conclude... that... biological inheritance of IQ... among members of the general society may also explain IQ differences between different racial and ethnic groups.... Such a conclusion goes... much beyond what the facts will support....
[T]he greatest black-white differences are not on the questions which presuppose middle-class vocabulary or experiences, but on abstract questions such as spatial perceptual ability.... [Herrnstein and Murray's] conclusion that this "phenomenon seems peculiarly concentrated in comparisons of ethnic groups" is simply wrong. When European immigrant groups in the United States scored below the national average on mental tests, they scored lowest on the abstract parts of those tests. So did white mountaineer children in the United States tested back in the early 1930s. So did canal boat children in Britain, and so did rural British children compared to their urban counterparts, at a time before Britain had any significant non-white population. So did Gaelic-speaking children as compared to English-speaking children in the Hebrides Islands. This is neither a racial nor an ethnic peculiarity. It is a characteristic found among low-scoring groups of European as well as African ancestry.
In short, groups outside the cultural mainstream of contemporary Western society tend to do their worst on abstract questions, whatever their race might be....
Perhaps the strongest evidence against a genetic basis for intergroup differences in IQ is that the average level of mental test performance has changed very significantly for whole populations over time and, moreover, particular ethnic groups within the population have changed their relative positions during a period when there was very little intermarriage to change the genetic makeup of these groups.
While The Bell Curve cites the work of James R. Flynn, who found substantial increases in mental test performances from one generation to the next in a number of countries around the world, the authors seem not to acknowledge the devastating implications of that finding for the genetic theory of intergroup differences, or for their own reiteration of long-standing claims that the higher fertility of low-IQ groups implies a declining national IQ level. This latter claim is indeed logically consistent with the assumption that genetics is a major factor in interracial differences in IQ scores. But ultimately this too is an empirical issue--and empirical evidence has likewise refuted the claim that IQ test performance would decline over time.
Even before Professor Flynn's studies, mental test results from American soldiers tested in World War II showed that their performances on these tests were higher than the performances of American soldiers in World War I by the equivalent of about 12 IQ points. Perhaps the most dramatic changes were those in the mental test performances of Jews in the United States. The results of World War I mental tests conducted among American soldiers born in Russia--the great majority of whom were Jews--showed such low scores as to cause Carl Brigham, creator of the Scholastic Aptitude Test, to declare that these results "disprove the popular belief that the Jew is highly intelligent." Within a decade, however, Jews in the United States were scoring above the national average on mental tests, and the data in The Bell Curve indicate that they are now far above the national average in IQ.
Strangely, Herrnstein and Murray refer to "folklore" that "Jews and other immigrant groups were thought to be below average in intelligence. " It was neither folklore nor anything as subjective as thoughts. It was based on hard data, as hard as any data in The Bell Curve. These groups repeatedly tested below average on the mental tests of the World War I era, both in the army and in civilian life. For Jews, it is clear that later tests showed radically different results--during an era when there was very little intermarriage to change the genetic makeup of American Jews.
My own research of twenty years ago showed that the IQs of both Italian-Americans and Polish-Americans also rose substantially over a period of decades. Unfortunately, there are many statistical problems with these particular data, growing out of the conditions under which they were collected. However, while my data could never be used to compare the IQs of Polish and Italian children, whose IQ scores came from different schools, nevertheless the close similarity of their general patterns of IQ scores rising over time seems indicative--especially since it follows the rising patterns found among Jews and among American soldiers in general between the two world wars, as well as rising IQ scores in other countries around the world.
The implications of such rising patterns of mental test performance is devastating to the central hypothesis of those who have long expressed the same fear as Herrnstein and Murray, that the greater fertility of low-IQ groups would lower the national (and international) IQ over time. The logic of their argument seems so clear and compelling that the opposite empirical result should be considered a refutation of the assumptions behind that logic....
A man who scores 100 on an IQ test today is answering more questions correctly than his grandfather with the same IQ answered two-generations ago, then someone else who answers the same number of questions correctly today as this man's grandfather answered two generations ago may have an IQ of 85.
Herrnstein and Murray openly acknowledge such rises in IQ and christen them "the Flynn effect," in honor of Professor Flynn who discovered it. But they seem not to see how crucially it undermines the case for a genetic explanation of interracial IQ differences. They say: "The national averages have in fact changed by amounts that are comparable to the fifteen or so IQ points separating blacks and whites in America. To put it another way, on the average, whites today differ from whites, say, two generations ago as much as whites today differ from blacks today. Given their size and speed, the shifts in time necessarily have been due more to changes in the environment than to changes in the genes."
While this open presentation of evidence against the genetic basis of interracial IQ differences is admirable, the failure to draw the logical inference seems puzzling. Blacks today are just as racially different from whites of two generations ago as they are from whites today. Yet the data suggest that the number of questions that blacks answer correctly on IQ tests today is very similar to the number answered correctly by past generations of whites. If race A differs from race B in IQ, and two generations of race A differ from each other by the same amount, where is the logic in suggesting that the IQ differences are even partly racial?
Herrnstein and Murray do not address this question, but instead shift to a discussion of public policy: "Couldn't the mean of blacks move 15 points as well through environmental changes? There seems no reason why not--but also no reason to believe that white and Asian means can be made to stand still while the Flynn effect works its magic."
But the issue is not solely one of either predicting or controlling the future. It is a question of the validity of the conclusion that differences between genetically different groups are due to those genetic differences, whether in whole or in part. When any factor differs as much from Al to A2 as it does from A2 to B2, why should one conclude that this factor is due to the difference between A in general and B in general?...
A remarkable phenomenon commented on in the Moynihan report of thirty years ago goes unnoticed in The Bell Curve--the prevalence of females among blacks who score high on mental tests. Others who have done studies of high- IQ blacks have found several times as many females as males above the 120 IQ level. Since black males and black females have the same genetic inheritance, this substantial disparity must have some other roots, especially since it is not found in studies of high-IQ individuals in the general society, such as the famous Terman studies, which followed high-IQ children into adulthood and later life. If IQ differences of this magnitude can occur with no genetic difference at all, then it is more than mere speculation to say that some unusual environmental effects must be at work among blacks. However, these environmental effects need not be limited to blacks, for other low-IQ groups of European or other ancestries have likewise tended to have females over-represented among their higher scorers, even though the Terman studies of the general population found no such patterns.
One possibility is that females are more resistant to bad environmental conditions, as some other studies suggest. In any event, large sexual disparities in high-IQ individuals where there are no genetic or socioeconomic differences present a challenge to both the Herrnstein- Murray thesis and most of their critics.
Black males and black females are not the only groups to have significant IQ differences without any genetic differences. Identical twins with significantly different birthweights also have IQ differences, with the heavier twin averaging nearly 9 points higher IQ than the lighter one. This effect is not found where the lighter twin weighs at least six and a half pounds, suggesting that deprivation of nutrition must reach some threshold level before it has a permanent effect on the brain during its crucial early development.
Perhaps the most intellectually troubling aspect of The Bell Curve is the authors' uncritical approach to statistical correlations. One of the first things taught in introductory statistics is that correlation is not causation. It is also one of the first things forgotten, and one of the most widely ignored facts in public policy research. The statistical term "multicollinearity," dealing with spurious correlations, appears only once in this massive book.
Multicollinearity refers to the fact that many variables are highly correlated with one another, so that it is very easy to believe that a certain result comes from variable A, when in fact it is due to variable Z, with which A happens to be correlated. In real life, innumerable factors go together. An example I liked to use in class when teaching economics involved a study showing that economists with only a bachelor's degree had higher incomes than economists with a master's degree and that these in turn had higher incomes than economists with Ph.D.'s. The implication that more education in economics leads to lower incomes would lead me to speculate as to how much money it was costing a student just to be enrolled in my course. In this case, when other variables were taken into account, these spurious correlations disappeared. In many other cases, however, variables such as cultural influences cannot even be quantified, much less have their effects tested statistically....
I have always wondered who first said:
"There are three kinds of social scientists. Those who can count and those who can't."
It must have been Murray.
Posted by: Dwight meredith at October 13, 2004 12:00 PMhttp://www.nytimes.com/2004/10/12/opinion/13forkerry-final.html
Questions for Kerry
By CHARLES MURRAY
Five percent of Americans pay 54 percent of all personal income taxes. They do not use more government services than other Americans; they use fewer. Why is this fair?
Would you be willing to sponsor tort reform that requires plaintiffs to have used common sense before being eligible for damages?
You promise to create millions of jobs, but many people who run businesses say that nothing in your life has taught you how much effort, risk and sometimes heartbreak goes into creating one real job. Could you describe your experiences when you last had to meet a payroll, or when your boss had to meet a payroll?
Not to mention the regular and odious presence of the source of the gaffe, Mr. Brooks himself. To quote my pal Robin, "he's Andy Rooney trying to be H.L. Mencken." And if I have to read another Brooks column that takes the form, "some people like coke, and some people like pepsi", and passes it off for analysis, I'm going to tear my thinning hair out. Sometimes, I think the worst casualty of L'affaire Blair is the NY Times' effort to attain some sort of ostensible parity on the op-ed page (which contributed I believe to the selection of bobo bozo Brooks.) And what's up with them printing that Tim Kane column a while back? I think it's reasonable to expect a diversity of viewpoints, but diversity needn't require that we include the stupid and disingenuous.
Posted by: Dan at October 13, 2004 12:14 PMMinor nitpick:
He probably actually meant "at least 6 out of twelve," so the probability is over 3%.
Posted by: Bernard Yomtov at October 13, 2004 12:18 PMUnless the editors are stupid and disingenuous.
Murray's questions are both. 1)show me that on a per capita basis the wealthy don't use more government services than do the poor (the argument for the obverse is obvious: greater coverage of their assets via governmental insurance, armed forces going in to rescue their companies, subsidies to businesses the wealthy are involved in, various corporate bailouts when said corporations go belly up due to mismanangement by wealthy CEOs and so forth ad nauseam) 2) the law already has a "common sense" basis, and most lawyers will discourage a claim based on idiocy on the plaintiffs' part; this is a red herring to make people think that most claims are idiotic and that all plaintiffs have no one but themselves to blame if they don't know every single bit of information about every single product that they might use over their lifetime 3) say what? what many people in business? and GWB is supposed to have created a single job (and don't tell me about his so-called real world experience where he ran buinesses into the ground, obviously he has the qualifications to destory jobs) ? what the hell kind of question is that? Has Murray created a single job?
Now, why did I do this?
Posted by: Carol at October 13, 2004 12:24 PMI think Murray's third question for Kerry was meant for Bush.
Posted by: Charles Kinbote at October 13, 2004 12:25 PMOn =The Bell Curve=, note also Stephen Jay Gould's demolition of it in the revised (1996) edition of =The Mismeasure of Man=.
Posted by: David Moles at October 13, 2004 12:33 PMPerhaps it all comes to a supposed balance. A Democrat watches the sun rise in the east, and there must be a Republican found who knows it rises is the west.
Posted by: anne at October 13, 2004 12:40 PMAs far as tort reform goes, what happened to all the states' rights advocates? Why do they want to deprive the states of their traditional power to police the health and welfare of their citizens?
If I were cynical, I would say that they admire "states' rights" only when they want to block the federal government from providing some protection to consumers, employees, civil rights victims, etc.
Posted by: joe at October 13, 2004 12:45 PMNote also that wealth would be impossible without a complex government and society.
Look at hunter-gathering societies (about 99% of human existance).
* No Crime.
* No government.
* Very little war.
* No wealth, you had what you could carry.
Try carrying that McMansion on your back.
Posted by: Matthew Saroff at October 13, 2004 12:46 PMIt's pointed out at Atrios (http://atrios.blogspot.com/2004/10/hackery.html) that Kerry founded a small business, which eviscerates Murray's attack.
Posted by: rilkefan at October 13, 2004 12:47 PMOT, but still in the economic vein: sghort of a last-minute rally, the Dow will close under 10,000 today. Germany has as much admitted that it will come to the table under a Kerry administration. The GOP is linked to scandal after scandal. It goes on and on.
If America doesn't soundly reject Bush, I will loose what respect I have left for the American sheeple.
Yeah, the Dow # is just a one day occurence, and I have nearly all savings in the market (I'm young enough to be looking very long term), but it still gives me a warm feeling inside on the eve of the last debate....
Posted by: Gregory at October 13, 2004 12:49 PMCarol wrote, "1)show me that on a per capita basis the wealthy don't use more government services than do the poor (the argument for the obverse is obvious: greater coverage of their assets via governmental insurance, armed forces going in to rescue their companies, subsidies to businesses the wealthy are involved in, various corporate bailouts when said corporations go belly up due to mismanangement by wealthy CEOs and so forth ad nauseam)..."
Presumably this is why the classical liberals thought that people should be taxed in proportion to their wealth. (Note that's *wealth*, not income.)
Posted by: liberal at October 13, 2004 12:50 PMI think his third question is hilarious - typical right-wing posing. How many of our previous Presidents had any real small business experience - Reagan? Maybe in the 1920s. Bush I? Ha-ha. LBJ? Nope. JFK? Never worked. FDR? No again. Teddy Roosevelt? Uh, no. Abraham Lincoln? Well, if you consider a small law practice a business.
Posted by: Harry O'Nihan at October 13, 2004 12:51 PMBest compilation of critiques of _The Bell Curve_ I've seen is _The Bell Curve: History, Documents, Opinions_, R. Jacoby and N. Glauberman, eds, 1995.
Check out Goldberger and Manski's review of the Bell Curve
http://www.ssc.wisc.edu/irp/featured/bellcurv.htm
Not only a double damnation of the whole business, but good for an intermediate stats refresher.
I agree with posters above -how would we determine whether high income individuals do or do not receive more "government services"? Or are some government services inherently good and noble to right thinking people and others are just bread and circuses for leeches? And if so, which ones are which? If you include financial rule of law and other government enforcers who protect financial wealth, then is it clear that high earners pay a disproportionate share?
Call in Benjamin Franklin on this one.
There is nothing wrong with the Gaussian curve, when applied to the proper sorts of data.(?Datums)
Posted by: old ari at October 13, 2004 01:18 PMYears ago, I was asked to meet Richard Herrnstein about a research position. I had no idea who he was. I remember sitting in the office and listening to him begin to explain how he had come to discern differences in intricacy of the thoughts of racial groups. Since I had no idea how he could determine the bounds of any racial or ethnic group or isolate genetic from social potentials, I was lost through the explanation. So much for the position. From the beginning of the Herrnstein-Murray work, it never occured to me there was a research design that allowed the least of the conclusions to be relied on. They were never even able to explain how we are to identify ourselves.
Posted by: anne at October 13, 2004 01:24 PMSigh...I will add that IQ tests are scaled and adjusted to produce results designed to guide education and are only reliable within relatively narrow (5-10 year) age cohorts. Every so often the empirical tables used to convert raw scores to the familiar bell-curve scores are revised; over the past 50 years revised to account for a large rise in raw scores.
In plain, direct English, as far as we know, IQ tests don't tell much about genetics; results are too heavily influenced by unknown factors for the the tests to be useful outside of education planning, which is after all what the tests are designed for.
Posted by: Randolph Fritz at October 13, 2004 01:28 PM
As rilkefan notes, Kerry started a company in 1976, a cookie company that apparently operated at Quincy Market in Boston. (It's part of an area full of various small food counters, kind of like an early food court but less commercialized.)
Kerry bought his partner's share of the business in 1982, and sold them on to another buyer. A few years later, Kerry sold his own share to the same buyer.
This means that the company survived for a good long while, longer than most startups, and was in good enough shape for it to be bought out.
(Also, it suggests that Kerry knew about exit strategies, even then. That's something which has eluded Bush his whole life.)
It seems to still be a going concern.
http://www.kilvertandforbesbakeshop.com/history.html
(The "forbes" is from Kerry's mother's name. The shop was named for the partners' mothers.)
Bernard Yomtov is clearly right that "the odds that half of the 12 have college degrees" means at least half, not exactly half. (If I have $30 in my wallet and my wife asks me, do you have $20, I say yes.) But he greatly underestimates how much Brad has underestimated Murray's error. The right calculation is the sum of the odds of 6 out of 12, plus 7 out of 12, plus 8 out of 12, etc. So the number will be way more than double Brad's 2.5%. The only way I know how to do this is to make a big 12x12 grid, fill in the percentages, multiply out every possible combination, and add them up - I might finish by Friday and I would certainly make an error somewhere. Anyone have enough statistics to do this in a couple of minutes?
Posted by: jr at October 13, 2004 02:00 PMI suppose it's just me, but the main message I personally got from The Bell Curve is that life is very difficult and very hazardous for people with poor intellectual gifts, and the concentration of political and economic power into the hands of the more intellectually talented has tended to complicate life for everyone. That complication is not much of a problem for smart people, but it makes a difficult life even more difficult for unintelligent people.
Reading that book left me rather more sympathetic to the plight of the folks toward the left side of that curve than I had been before.
jr,
Thanks, but I believe I did it correctly, unless Excel has let me down. The trouble is that as the number increases the probability drops dramatically because you're dealing with a p of only .222. For exactly seven successes I get .6% , for eight I get .1%,and for nine about .01%. The rest are negligible. The total is 3.17%.
Posted by: Bernard Yomtov at October 13, 2004 02:14 PMBest I can tell, the only businessman presidents in this century have been Warren Harding (newspaper publisher) and Herbert Hoover (mining company executive).
Posted by: jr at October 13, 2004 02:18 PMI suppose it's just me, but the main message I personally got from The Bell Curve is that life is very difficult and very hazardous for people with poor intellectual gifts, and the concentration of political and economic power into the hands of the more intellectually talented has tended to complicate life for everyone. That complication is not much of a problem for smart people, but it makes a difficult life even more difficult for unintelligent people.
Reading that book left me rather more sympathetic to the plight of the folks toward the left side of that curve than I had been before.
It was Adam Smith who first suggested that the wealthy should pay more in taxes because they derive the most benefit from the state's protection of their property. I always liked thyat guy. (See The Wealth of Nations).
Posted by: Lawrence at October 13, 2004 05:00 PMIt was Adam Smith who first suggested that the wealthy should pay more in taxes because they derive the most benefit from the state's protection of their property. I always liked thyat guy. (See The Wealth of Nations).
Posted by: Lawrence at October 13, 2004 05:05 PMI am very familar with books edited by Bernie Yomtov that involve a great deal of probability analysis. A good rule of thumb in these discussions is that if Bernie makes a comment concerning probabilities, you can take it to the bank.
Posted by: dwight meredith at October 13, 2004 06:04 PMMatthew Saroff: Hunter-gatherer societies have very little war? Doesn't that depend on which hunter-gatherer society one looks at? Personally, I can't think of the Yanomami without thinking of widespread institutionalized violence, whereas !Kung are fairly peaceful, as far as I know. I know little about hunter-gatherer societies, though, generally or specifically. I'm just surprised at this.
I'm a college kid who thinks the world started circa 1995. Tell me, is it true that the AEI was once one of the most respected think tanks, up there with Brookings?
jr: the basic formula for the probability of a r successes (each success having probability p) for a series of n Bernoulli trials is, as Brad showed, (n C r)*p^r*(1 - p)^(n - r), where (n C r) = n!/((n - r)! * r!). Since the larger factorial in the denominator cancels out a lot of the factorial in the numerator, (12 C 6) ends up looking like (12 * 11 * 10 * 9 * 8 * 7)/(6 * 5 * 4 * 3 * 2 * 1), and (12 C 3) and (12 C 9) are the same (since ((12 - 9)! * 9!) must be the same as ((12 - 3)! * 3!), and are equal to (12 * 11 * 10)/(3 * 2 * 1). So, applying this to college students in a sample of 12:
(12 C 6)*0.222^6*0.778^6 = (12 * 11 * 10 * 9 * 8 * 7)/(6 * 5 * 4 * 3 * 2 * 1)*0.00012*0.2218 = (665280/720 = 924)* 0.00012 * 0.2218 = 0.0245
(12 C 7)*0.222^7*0.778^5 = 0.0060
(12 C 8)*0.222^8*0.778^4 = 0.00107
(12 C 9)*0.222^9*0.778^3 = 0.00014
(12 C 10)*0.222^10*0.778^2 = 0.0000116
(12 C 11)*0.222^11*0.778 = 0.000000603
(12 C 12)*0.222^12 = 0.000000014
Now, since you having 6 out of 12 college-educated friends and 6 out of 12 non-college-educated friends and you having 7 out of 12 college-educated friends and 5 out of 12 non-college-educated friends are mutually exclusive, you add 'em up. The result is 0.0317. If you can understand everything I did, then you now know more about statistics than Charles Murray, who, after all, wrote a learned tome based on the subject.
Conservatives like William Blackstone would be infuriated by the tort reform issue: not only are Republicans intent on circumscribing common law and precedent with statutory law, but they're doing so with no attempt to make that statute fair by, for example, tightening regulation on doctors in exchange for reducing patients' right to sue. It's like conservatives have now acquired all the vices of sum-ranking Benthamite radicals (like, willingness to circumscribe minority rights for the sake of majority gain), but without any of the virtues (like, say, thinking a typical poor person needs a given amount of money more than a typical rich person on folk-psychological grounds).
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