Chance News 19
Quotation
Like dreams, statistics are a form of wish fulfillment. - Jean Baudrillard
Forsooths
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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?
The IQ of Aahkenazim Jews
The Lessons of the Ashkenazim, Groups and Genes
The New Republic, June 26, 2006
Steven Pinker
[http://www.tnr.com/doc_posts.mhtml?i=20060626&s=pinker062606
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.
Steven Pinker is a well known Harvard Psychologist. In his article in the New Republic he discusses a
La Griffe du Lion La Griffe du Lion
La Griffe du Lion is a website prepared by an anonymous author or authors. In the absence of a names we we shall assume one author named La Griffe.
Since September 1999 the La Griffe has discssed 21 problems many of the following form. We have two groups of people who have different abilities as measured by a standardized test, IQ, or some other kind of test. The distribution of the scores for the two groups are assume to be normal with means and variances estimated from data. The problem is to estimate the numbers from each group who will be in high positions such as an elite college, Nobel prize winner, captains of industry etc. Here is a typical problem.
A random selection of Nm men and Nw women compete for Ns available slots. If the slots are filled in rank order of mathematical ability, what is the most probable gender composition of the winners' circle?
The La Griffe du lion solves this problem using data from Project Talent1 study of 1960 which showed a mean (male-female) difference of .12 standard deviations and a 1.20 (male/female) variance ratio. Using his solution the La Griffe finds that the most probable number of women in the group of 143 Nantional Academy mathematicians is 7.1 with a confidence interval [2,12]. The La Griffe comments "At this time there are precisely 7 women in the mathematics sections of the Academy. The agreement is almost embarrassing. "
The key to the authors solutions is that two normal distributions with a smaller difference in means can have a significant difference in the tails when the variances differ.
La Griffe also applies his method to solve the mystery of how an "otherwise unremarkable college ( City College of New York) managed to produce eight Nobel Prize winners in 21 years".
The success of American Jews in winning Nobel prises is also the subject of Steven Pinker's New Republic article. Steven is a well known Professor of Psychology at Harvard. Pinker writes:
The apearance of an advantage in the average intelligence among Ashkenazi Jews is easier to establish than its causes. Jews are remarkable over-represented in benchmarks of brainpower. Though never exceeding 3 percent of the American population, Jews account for 37% 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 econmics, and so on. On the world stage we find that 54 percent of the world chess champions have had one or two Jewish parents.
The Ashkenaz iJews are those whose ancestors are from Eastern and Central Europe. About 80 percent of the six million ethnic Jews in the U.S. are of Ashkenazi Jewish descent.
Pinker goes on to say:
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 statiscians have long known that a moderate difference in the means of two distributions translates into a large dlifference at the tails. In the simplest case, if we have two groups of the same size, and the aaverage of Group A exceeds the average of Group B by fifteen IQ points (one standard deviation), then among people with an IQ or 115 or higher the As will outnumber the Bs by a ratio of three to one, but amoung 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 sustantial proportiion of the people who had the highest scores.
To be continued
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 at: http://www.guardian.co.uk/comment/story/0,,1804775,00.html).
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?