Chance News 19
Quotations
Like dreams, statistics are a form of wish fulfillment. - Jean Baudrillard
Everyone believes in the normal law of errors: the mathematicians, because they think it is an experimental fact; and the experimenters, because they suppose it is a theorem of mathematics. However, it is neither an experimental fact nor a theorem of mathematics - Garbriel Lippmann.
Forsooth
This Forsooth was suggested by Paul Alper.
The Auburn football team appeared to be the biggest benefactor of Professor Petee's directed-reading offerings. The 18 football players received an average G.P.A. of 3.31 in the classes ...In all of their other credit hours at Auburn, their average was 2.14.
Top grades and no class time.
New York Times, July 14, 2006
Pete Thamel
P.S. The star running back Carnell (Cadillac) Williams, now playing in the National Football League, said the only two classes he took during the spring semester of his senior year were one-on-one courses with Professor Petee. One of these two courses was a statistics class. Williams described the class this way: 'You're just studying different kinds of math. It's one of those things where you write a report about the different theories and things like that.'"
forsooth2
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Another Look at "The Kindness of Strangers?"
In a recent wiki, The Kindness of Strangers, based on a paper ["Study of the Therapeutic Effects of Intercessory Prayer (STEP)in cardiac bypass patients"] by Herbert Benson et al., you will find a commentary regarding this latest statistical attempt to foist intercessory prayer--IP as it is now known--into the realm of science. Nevertheless, despite the excellence of the wiki, some additional comment is in order. As stated, the $2.4 million dollar waste of time was sponsored by the foundation of the billionaire John Templeton; for more on the individual, his son and the foundation, and why so many "American medical schools now offer courses on links between health and spirituality," the reader is directed to The Templeton Foundation: A Skeptic's Take. In short, the answer is money for the asking.
The same issue of The American Heart Journal [vol. 151, Issue 4, April 2006, Pages 934-942] which contained the paper by Benson--there are, believe it or not, 15 other authors!--also has an editorial by Krucoff, Crater and Lee [Pages 762-764] which states "the STEP investigators' interpretation of the study results appears to reflect more the cultural bias that healing prayer...is only capable of doing good if it does anything at all." Unfortunately, the editorial while being skeptical, fails to note some other failures inherent in the article.
For one thing, unlike real medicine, there is no notion of dosage as in amount of time spent per individual praying. For another, in defiance of physical laws, distance between patient and prayers [St. Paul, MN, Worcester, MA and Lee's Summit, MO] appears to be irrelevant. And then, there is the statistical difficulty of going from a sample to a population. As is virtually always true, the people doing the praying are Christians. Consequently, while the patients who were prayed for in this study did worse than those who weren't prayed for, it is conceivable that other religions would score higher. However, Templeton is not a Moslem, Shintoist or a Hindu so we will never know because I suspect his foundation is not eager to pursue this line of reasoning.
The Annals of Behavioral Medicine, June 13, 2006 has an excellent article, "Are There Demonstrable Effects of Distant Intercessory Prayer? A Meta-Analytic Review" by Masters, Spielmans and Goodson. STEP is not included but 14 other studies are, including the discredited one by Lobo, Cha and Worth--Lobo withdrew his name and Worth is in prison. Based on their meta-analysis, Masters, Spielmans and Goodson write,
There is no scientifically discernable effect for IP as assessed in controlled studies. Given that the IP literature lacks a theoretical or theological base and has failed to produce significant findings in controlled trials, we recommend that further resources not be allocated to this line of research.
Discussion
1. Why is the following phrase cherished by statisticians and other scientists? "Extraordinary claims demand extraordinary evidence."
2. If one assumes that IP is absurd, what is it about conventional prayer--prayer by the patient, prayer by his loved ones, etc.--that distinguishes it from IP?
3. If IP has some effect, is it ethical to prayer for someone without his knowledge?
4. Benson claims "We were unable to locate other Christian, Jewish or non-Christian groups that could receive the daily prayer list of this multiyear study." Suppose they did locate these other groups. Speculate on the outcome if these other groups were included.
5. According to The Columbia University 'Miracle' Story when referring to Daniel Worth, "A good rule of thumb for a medical journal is that anyone who uses the names of dead children in order to fraudulently obtain bank loans, jobs and passports is not a reliable source of data." However, the other two authors are medical doctors so should suspicion diminish?
6. Steven Weinberg is a Nobel Laureate in Physics and an atheist. He once said, I am all in favor of a dialogue between science and religion, but not a constructive dialogue." What do you think he means?
7. Discuss how the interest in IP reflects the shift to the right in American politics and religion.
8. What sort of pardox is implied when people of faith need statistics to buttress their beliefs?
Submited by Paul Alper
The IQ of Aahkenazi Jews
The Lessons of the Ashkenazim, Groups and Genes
The New Republic, June 26, 2006
Steven Pinker
Readers comments
Natural History of Ashkanzi Intelligence
Gregory Cochran Jason Hardy and Henry Harpending
Journal of Biosocial Science to appear in 2006 and available now at Journal's website.
La Griffe du Lion La Griffe du Lion
Steven Pinker is a well known Harvard Psychologist. In his New Republic article he discusses: "Are Ashkenazi more intellegent than non Jews?
Ashkenazi Jews are Jews descended from the medieval Jewish communities of the Rhineland. You can obtain more information about the history of Ashkenazi Jews here. According to Wikopedia there are about 6 million Jews in the US of which about 5 million are Ashkenazi Jews.
Pinker writes:
The appearance of an advantage in average intelligence among Ashkenazi Jews is easier to establish than its causes. Jews are remarkably over-represented in benchmarks of brainpower. Though never exceeding 3 percent of the American population, Jews account for 37 percent of the winners of the U.S. National Medal of Science, 25 percent of the American Nobel Prize winners in literature, 40 percent of the American Nobel Prize winners in science and economics, and so on. On the world stage, we find that 54 percent of the world chess champions have had one or two Jewish parents.
Does this mean that Jews are a nation of meinsteins? It does not. Their average IQ has been measured at 108 to 115, one-half to one standard deviation above the mean. But statisticians have long known that a moderate difference in the means of two distributions translates into a large difference at the tails. In the simplest case, if we have two groups of the same size, and the average of Group A exceeds the average of Group B by fifteen IQ points (one standard deviation), then among people with an IQ of 115 or higher the As will outnumber the Bs by a ratio of three to one, but among people with an IQ of 160 or higher the As will outnumber the Bs by a ratio of forty-two to one. Even if Group A was a fraction of the size of Group B to begin with, it would contribute a substantial proportion of the people who had the highest scores.
We found it easiest to understand all this in terms of one of the many studies carried out to compare the IQ's of Jews with Gentiles ( white non-Jews). For this we use a study The Intelligence of American Jews reported on the web in 2004 by Richard Lynn Lynn. Lynn is a well known researcher in the field of Intelligence. You can read about his work here.
In his article Lynn reviews the results of studies carried out to compare the IQ's of Jews and Gentiles. He summarizes this by writing:
The existing state of the research literature on the IQ of American Jews is
therefore that some studies have shown that their verbal IQ is about the same as that of gentile whites while other studies have shown that it is considerably higher at 107.8 (Backman, 1972), 112.6 (Herrnstein and Murray, 1994) and 112.8 (Bachman, 1970). However, the last of two of these studies have sample sizes of fewer than 100. There is room for more data on the IQ of American Jews, and it is to the presentation of this that we now turn. <\blockquote>
For his study Flynn uses data from the annual surveys on approximately 1,600 individuals in continental United States carried out by the American National Opinion research Center (NORC). Previous studies suggest that Jews tend to excel in verbal and numerical ability but not unexceptionally in spatial or percptual problems with most convincing advantage is in verbal ability. In the years 1900,1991, 1992, 1994 aand 1996 NORC servays included a 10 word vocabulary test. Previous studies sugget that vocabulary is a good measure of both general intelligence and verbal intelligence. Flynn compared the results for Jews, Gentiles, and Blacks. Here are the results for Jews and Gentiles:
It is customary when comparing IQ's for different groups to normalize the scores by a linear transformation so that one reference group to have mean 100 and standard deviation 15. Here Lynn chose the Gentiles as the reference group. The standard deviation of the Gentiles was 2.03. Thus to make their standard deviation 15 we multiply the numbes by a = 15/2/03. Their mean was 6.28 so it is now 6.28 x a. Thus to make their mean 100 we add to their scores b = 100 - 6.28 * a = 53.5961. Then the Gentiles have mean 100 and standard deviation 15.
Now we use the same normalization for the Jews. Their standard deviation was 2.16 so now it is c = 2.16*a = 15.9606. The Jews had a mean of 7.32 so now their mean is d = 7.32Xa + b = 107.685. Thus the Jews have mean 107.69 and standard deviation 15.96.
Pinker makes the point that a modest difference in means can lead to a significant difference in the probability of tail events. For example consider probability that a member of one of the two groups has an IQ greater that 145. Using one of the many normal distribution applets we find that this probability is .0013 for the Gentile group and .0095 for the Jew group. Thus we can expect about 10 times more Jews that Gentiels to have an IQ at least 145.
This method of comparing the IQ and permforance of different groups is used in a number of essays on a web site named La Griffe de Lion (The claw of the lion).These essays are written by one or more anonymous people. We shall call the authors Griffe. In the essay called [ http://www.lagriffedulion.f2s.com/ashkenaz.htm Assessing the Ashkenazic IQ, Griffe compares Aahkenazi Jews with wite male non-jews using data from the annual USSR Chess Championships and the mathematitions who were awareded Fields medals. He summers his conclusions by writing: <blocquote> In sum, from the frequency of appearance of Ashkenazic Jews in the annual USSR Chess Championships, we assess the mean Ashkenazic IQ to be 116. And from the frequency of Ashkenazic Fields medallists, we infer an Ashkenazic "math IQ" of 111. On these numbers, gentlemen, you can hang your yarmulkes.<block quote>
Giffe's essays are fun to read. They have interesting data, math, and graphics. Here is a graphic from an essay called http://www.lagriffedulion.f2s.com/DP.htm The Color of death row which shows the suprising results that when it comes to death penelties southern states have a bias against whites.
Probability of Pregnancy
On June 24th, the UK newspaper The Guardian contained the following quote:
A friend of mine got pregnant the first time she slept with her (now) husband, at the age of 43; this was after she had made a documentary on infertility and had been repeatedly told by fertility experts that her chances of conceiving naturally were "less than 5%". This may be right as a general statistic, but it wasn't right in her case: her chances of conceiving, provided she had sex at the right time of the month, were 100%.
(Full article available here).
Discussion
- What do you think the author meant by "a general statistic". What other sorts are there?
- Any person's chance of getting pregnant is 0% or 100%, so what does a 5% chance of getting pregnant mean?
- Are there different (but equally correct) interpretations of that 5% probability?
Depressing News
Financial ties to industry cloud depression study.
Wall Streat Journal, Tues. July 11, 2006
David ArmstrongAnother example of what the most important question a consumer of statistical information should ask can be found in this Wall Streat Journal article. The front-page piece is a lengthy commentary on a JAMA article dealing with the desirability of prescribing antidepressant medication to pregnant women. ("Relapse of major depression during pregnancy in women who maintain or discontinue antidepressant treatment", Cohen LS, Altshuler LL, Harlow BL, et al JAMA. 2006; 295: 499-507).
Turns out that "most of the 13 authors are paid as consultants or lecturers by the makers of antidepressants." And apparently paid well, although none chooses to reveal the amount to the WSJ. Further, as the lead author, Dr. Lee S. Cohen, of the JAMA article put it, "'it didn't seem relevant' for him and several of his co-authors to disclose their industry relationships in the JAMA paper in part because the study was funded by the government, not drug makers." JAMA's editor-in-chief "says the journal wasn't aware of the relationships" to the pharmaceutical industry but Dr. Cohn's explanation "will be published very soon in an upcoming issue of JAMA." In any event, he says, "we are not talking about megabucks" although "He declined to specify what he does in his consulting role for the companies or how much he is paid."
Discussion
1. Defend Dr. Cohn's distinction regarding source of funding. Criticize Dr. Cohen's distinction regarding source of funding.
2. Justify JAMA's editor-in-chief's delay in publishing Dr.Cohen's explanation.
3. Speculate on why there are so many authors.
4. Suppose a medical doctor with ties to antidepressant pharmaceutical companies would publish a study which revealed that antidepressants were harmful in certain situations. What, if any financial consequences would he suffer?
5. The JAMA article states, "the current investigation used a nonrandomized design." Further, the study was completely without blinds, that is, the physicians and the patients were aware of which arm of the study was applicable. How do these facts affect the faith in the study?
Submited by Paul Alper
