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2D:4D<br>
==Autism Statistics Lesson==


If you put 2D:4D into a Google search, you will obtain 11,700,000 hits so you know that something is missing in your life if 2D:4D doesn’t ring a bellFrom [http://en.wikipedia.org/wiki/Digit_ratio Wikipedia] we are informed that “It has been suggested by some scientists that the ratio of two digits in particular, the 2nd (index finger) and 4th (ring finger) is affected by exposure to androgens such as testosterone while in the uterus and that this 2D:4D ratio can be used as a crude measure for prenatal androgen exposure, with lower 2D:4D ratios pointing to higher androgen exposure.”  Because “Some authors suggest that digit ratio [is] correlated to health, behavior, and even sexuality,” there is a great deal of finger measurements all over the globe.  For a previous Chance News wiki on the subject, see [http://chance.dartmouth.edu/chancewiki/index.php/Chance_News_43#Nature_vs_Nurture_and_Sexuality here]; in that wiki, according to those who subscribe to the relevance of 2D:4D, “the 2D:4D ratio is able to explain such disparate entities as sex and population difference, assertiveness, status, aggression, attractiveness, the wearing of rings, reproductive success, hand preference, verbal fluency, autism, depression, birth weight, breast cancer, sex dependent diseases, mate choice, sporting ability, running speed, spatial perception, homosexuality and more.
Autism is a devastating diseaseRecent attempts to pinpoint a cause have been recently in the news in the United States: [http://www.nytimes.com/2009/02/13/health/13vaccine.html?scp=1&sq=donald%20g.%20mcneil%20autism&st=cse New York Times article] by Donald G. McNeil, Jr.] and [http://www.nytimes.com/2009/02/13/opinion/13fri2.html?scp=1&sq=editorial%20vaccines&st=cse a follow-on New York Times editorial].  The focus of these articles is on law suits regarding the measles, mumps and rubella (MMR) vaccine “or its combination with thimerosal, a mercury-based preservative that was used in most childhood vaccines until 2001,” as a cause of autismAfter “5000 pages of testimony from experts and 939 medical articles,” judges concluded the plaintiffs failed to prove their assertionsOne judge “ruled that the evidence was ‘overwhelmingly contrary’ to their argument.”
One of the latest extensions of the importance of 2D:4D phenomenon is to financial trading and may be unearthed [http://www.pnas.org/content/106/2/623.full.pdf+html here].  The startling conclusion is “We found that 2D:4D predicted the traders' long-term profitability as well as the number of years they remained in the business.”  More specifically, “traders with a lower 2D:4D would make greater long-term profits and would remain in the business for a longer period of time. Numerically, “a trader in the lowest tertile of the 2D:4D range makes 11 times the P&L of a trader in the highest tertile. With regard to experienced traders only, “low 2D:4D traders make, on average 5.4 times the P&L of high 2D:4D traders.”


Discussion
Coincidentally, in England autism was also in the news in February, [http://briandeer.com/mmr/lancet-summary.htm here] and [http://briandeer.com/mmr-lancet.htm here].  In this instance, the story begins back in 1998 [http://download.videohelp.com/vitualis/downloads/Wakefield_%20LancetVolume%20351(9103)February28-1998.pdf The Lancet, February, 1998] and ignores thimerosal but introduces a problem additional to autism due to the MMR vaccine, Crohn’s disease (inflammatory bowel disease).  The Lancet article had an extraordinary impact on the general public in England as the following graph indicates:


1.  The article looked at 44 traders over a 20 month period who “specialize in noise or high-frequency trading: they buy and sell securities, specifically futures contracts, sometimes in sizes of up to £1 billion, but hold their positions for only a few minutes, sometimes mere seconds. Comment upon (a) the sample size, (b) whether the traders represent a random sample, (c) what population the traders might represent and (d) whether this is an experiment or an observational study.
MMR inoculation rates fall off sharply after the Lancet article and start to rise in 2004 because of a (London) Sunday Times investigation which revealed serious deficiencies in the Lancet studyThese deficiencies often fall under the rubric of “follow the money,a concept not given enough attention when discussing what constitutes statistical literacy.


2. Compare high-frequency trading with outright gambling.
The phrase, “follow the money,” is often thought to have originated in the book, All the President’s Men. According to [http://newsmine.org/content.php?ol=deceptions/deep-throat/follow-the-money-phrase-written-by-princess-bride-author.txt Frank Rich] the book never uses that phrase.  It is however, from the film of the same name.  Obviously, the pharmaceutical industry has a vested financial interest in vaccines and [http://www.huffingtonpost.com/deirdre-imus/on-vaccinations-consider_b_165347.html?show_comment_id=20767201 Deirdre Imus] is suspicious of any “big pharma” vaccine and any doctor who sides with it.  The main author of the Lancet article, Andrew Wakefield, unbeknownst to the twelve other authors of the Lancet study, had been paid “about $780,000 plus expenses, for his role in backing the generic case against MMR.”  Further, he had a patent on “a single vaccine against measles—a potential competitor to MMR” which he claimed would cure “both inflammatory bowel disease and autism.”  As cited by [http://www.washingtonpost.com/wp-dyn/articles/A41450-2004Jul10.htm Glenn Frankel] ten of the twelve other authors in 2004 issued a “Retraction of an interpretation” because “no causal link was established between MMR vaccine and autism.”  Wakefield has since moved to the U.S. and according to a supporter of Wakefield, “The United States, with its privatized health care system and entrepreneurial spirit is much more fertile ground than Britain for a medical pioneer like Wakefield.”  According to [http://www.timesonline.co.uk/tol/life_and_style/health/article5683671.ece Brian Deer] official figures showed that 1,348 confirmed cases of measles in England and Wales were reported last year [2008], compared with 56 in 1998. Two children have died of the disease.


3. The article looked at the performance of traders several years ago before the economic downturn.  Speculate on how performance might be different in 2008-2009.
Discussion
 
4.  The 2D:4D ratio of the 44 traders ranged from about .9 to 1.02.  If you are a male, look at your right hand—somehow, the left hand is irrelevant--and comment on the difficulty of accurately measuring the ratio over that small range.
 
5.  The approximate annual P&L for the 44 traders ranged from -£2000 to +£4,200,000 and was heavily skewed to the right. 
 
<center>
<table width="86%" border="1">
  <tr>
    <td width="9%"><div align="center"></div></td>
    <td width="18%"><p align="center">Age</p>
      <p align="center"> (years)</p></td>
    <td width="35%"><p align="center">Trading experience</p>
      <p align="center"> (years)</p></td>
    <td width="38%"><div align="center">Aproximation Annual Income (&pound;1-&pound;2)</div></td>
  </tr>
  <tr>
    <td><div align="center">Mean</div></td>
    <td><div align="center">28.99</div></td>
    <td><div align="center">2.77</div></td>
    <td><div align="center">&pound;285,000</div></td>
  </tr>
  <tr>
    <td><div align="center">Std</div></td>
    <td><div align="center">4.14</div></td>
    <td><div align="center">1.9</div></td>
    <td><div align="center">&pound;259,000</div></td>
  </tr>
  <tr>
    <td><div align="center">Range</div></td>
    <td><div align="center">19 to 38</div></td>
    <td><div align="center">1 to 12</div></td>
    <td><div align="center">&pound;-2,000 to &pound;4,200,000</div></td>
  </tr>
</table>
</center>
 
<center>http://www.dartmouth.edu/~chance/forwiki/2d-4da.gif </center>
 
That is, a very small number of the 44 traders made a great deal more money than the others.  The graph below is for the average P&L.
 
How would this affect regression assumptions of P&L vs. 2D:4D.
 
6.  Naturally, this 2D:4D investigation catches the eye of the media.  Typical is [http://sciencenow.sciencemag.org/cgi/content/full/2009/112/1 Are You a Moneymaker? Look at Your Hands].  This article quotes Tim Harford, a columnist for the Financial Times and author of The Logic of Life: The Rational Economics of an Irrational World, who calls the study "fascinating."  Harford “says he's glad to see that economists have started looking at financial markets in terms of natural selection instead of looking at them in terms of rational people making rational decisions.”  Why would Harford be glad?
 
7.  Because P&L of these traders is far from being normally distributed, the investigators did a Box-Cox transformation (cube root of P&L)  in order to induce normality.  As can be seen from below with this transformation, p-value is very low and the magnitude of the correlation coefficient is far from zero indicating that this model has some validity. 
 
<center>http://www.dartmouth.edu/~chance/forwiki/2d-4d.gif </center>
 
However, what is the physical meaning of the units of this y variable? 


8The investigators note that high-frequency trading is different from ordinary trading where the emphasis is on the “long-term approach to the markets.  For example, arbitrage traders at the investment banks and hedge funds are increasingly hired from the math and science departments of universities, and one study, which looked at average digit ratios in university departments found that faculty from math, science, and engineering exhibited higher, more feminine digit ratios.  A similar result may well be found among traders with a long-term holding period.”  As a possible statistics project, verify that the 2D:4D ratio for your math, science and engineering faculty is higher and thus, more feminine.
1If the medical profession overwhelmingly believes the MMR vaccine to be safe, why are parents of autistic children actively seeking litigation? That is, what element of emotional guilt might there be?


9Bearing in mind that statistical research can be costly and time consuming, what is the special appeal of 2D:4D?
2Although there were 13 authors of the Lancet article, there were only twelve children in the study.  A multiplicity of authors is a common phenomenon in medical journals.  Why is this so?


Submitted by Paul Alper
3.  The Lancet article claims that in eight of the twelve children, “the average exposure to first behavioral symptoms was 6.3 days (range 1-14)” after receiving the MMR vaccine.  An earlier version of the paper, not unearthed until 2005, puts the average at 14 days with the maximum time as 56 days.  Further, it was later revealed that there was “no trace of measles virus [or mumps and rubella viruses] in any of the children.”  Subsequent investigation indicated that instead of Crohn’s disease, the children were suffering from a benign condition, severe constipation.  Moreover, the children were not randomly referred by general practitioners but were recruited from a lawyer “who had been attempting to raise a speculative lawsuit.”  In 2007, Wakefield abandoned a libel claim, and agreed to pay costs, “estimated at about £500,000.”  Assuming all of this is factually correct, explain why some parents still view Wakefield as a hero.

Revision as of 18:55, 24 February 2009

Autism Statistics Lesson

Autism is a devastating disease. Recent attempts to pinpoint a cause have been recently in the news in the United States: New York Times article by Donald G. McNeil, Jr.] and a follow-on New York Times editorial. The focus of these articles is on law suits regarding the measles, mumps and rubella (MMR) vaccine “or its combination with thimerosal, a mercury-based preservative that was used in most childhood vaccines until 2001,” as a cause of autism. After “5000 pages of testimony from experts and 939 medical articles,” judges concluded the plaintiffs failed to prove their assertions. One judge “ruled that the evidence was ‘overwhelmingly contrary’ to their argument.”

Coincidentally, in England autism was also in the news in February, here and here. In this instance, the story begins back in 1998 The Lancet, February, 1998 and ignores thimerosal but introduces a problem additional to autism due to the MMR vaccine, Crohn’s disease (inflammatory bowel disease). The Lancet article had an extraordinary impact on the general public in England as the following graph indicates:


MMR inoculation rates fall off sharply after the Lancet article and start to rise in 2004 because of a (London) Sunday Times investigation which revealed serious deficiencies in the Lancet study. These deficiencies often fall under the rubric of “follow the money,” a concept not given enough attention when discussing what constitutes statistical literacy.

The phrase, “follow the money,” is often thought to have originated in the book, All the President’s Men. According to Frank Rich the book never uses that phrase. It is however, from the film of the same name. Obviously, the pharmaceutical industry has a vested financial interest in vaccines and Deirdre Imus is suspicious of any “big pharma” vaccine and any doctor who sides with it. The main author of the Lancet article, Andrew Wakefield, unbeknownst to the twelve other authors of the Lancet study, had been paid “about $780,000 plus expenses, for his role in backing the generic case against MMR.” Further, he had a patent on “a single vaccine against measles—a potential competitor to MMR” which he claimed would cure “both inflammatory bowel disease and autism.” As cited by Glenn Frankel ten of the twelve other authors in 2004 issued a “Retraction of an interpretation” because “no causal link was established between MMR vaccine and autism.” Wakefield has since moved to the U.S. and according to a supporter of Wakefield, “The United States, with its privatized health care system and entrepreneurial spirit is much more fertile ground than Britain for a medical pioneer like Wakefield.” According to Brian Deer official figures showed that 1,348 confirmed cases of measles in England and Wales were reported last year [2008], compared with 56 in 1998. Two children have died of the disease.”

Discussion

1. If the medical profession overwhelmingly believes the MMR vaccine to be safe, why are parents of autistic children actively seeking litigation? That is, what element of emotional guilt might there be?

2. Although there were 13 authors of the Lancet article, there were only twelve children in the study. A multiplicity of authors is a common phenomenon in medical journals. Why is this so?

3. The Lancet article claims that in eight of the twelve children, “the average exposure to first behavioral symptoms was 6.3 days (range 1-14)” after receiving the MMR vaccine. An earlier version of the paper, not unearthed until 2005, puts the average at 14 days with the maximum time as 56 days. Further, it was later revealed that there was “no trace of measles virus [or mumps and rubella viruses] in any of the children.” Subsequent investigation indicated that instead of Crohn’s disease, the children were suffering from a benign condition, severe constipation. Moreover, the children were not randomly referred by general practitioners but were recruited from a lawyer “who had been attempting to raise a speculative lawsuit.” In 2007, Wakefield abandoned a libel claim, and agreed to pay costs, “estimated at about £500,000.” Assuming all of this is factually correct, explain why some parents still view Wakefield as a hero.