Chance News 62
Quotations
"It is a very sad thing that nowadays there is so little useless information."
--Oscar Wilde
Quoted in All too much: Monstrous amounts of data
The Economist, 25 February 2010
"Statisticians are engaged in an exhausting but exhilarating struggle with the biggest challenge that philosophy makes to science: how do we translate information into knowledge? ...
"If you think that statistics has nothing to say about what you do or how you could do it better, then you are either wrong or in need of a more interesting job."
--Stephen Senn, Dicing With Death
Suggested by Paul Alper
"Of course, there are plenty of veteran basketball decision-makers who don't believe that stats are the only key to success. They'll tell you the difference in winning percentages has less to do with statistical analysis than with statistical freaks. 'If you took LeBron off the Cavaliers, you could give them 10,000 number crunchers, and it wouldn't make a difference,' says [one team executive]."
--David Biderman, “Are Statheads the NBA’s Secret Weapon?”, The Wall Street Journal, March 12, 2010
The article indicates that the 15 NBA teams with data analysts have won 59% of their combined games this season, while the 15 teams without data analysts have won only 41% of their games.
Submitted by Margaret Cibes
“In order for an economy to have an adequate system of financial reporting, it is not enough that companies make disclosures of financial information. …. In addition, it is vital that there be a set of financial intermediaries, who are at least as competent and sophisticated at receiving, processing, and interpreting financial information … as the companies are at delivering it.’”
--Malcolm Gladwell, quoting a Yale law professor, in “Open Secrets”, The New Yorker, January 8, 2007
Submitted by Margaret Cibes
Chance moves to CAUSEweb
Chance Project Moves to CAUSEweb
Amstat News, 1 March 2010
This story announces that the Chance materials will be moving to a new home at CAUSEweb, effective March 15. Actually, the Chance News Wiki quietly moved a week earlier--you will see a new URL in your browser! If (by chance) you didn't notice, it was because of the wonderful work by the technical experts at Dartmouth College and CAUSEweb, who enabled a very smooth transition and redirect of links from the Dartmouth site.
Submitted by Bill Peterson
Media highlights
The College Mathematics Journal has a column called "Media Highlights". Norton Starr is one of the editors and his contributions are usually of interest to Chance News readers. The March issue has two such items.
(1) For decades, puzzling people with mathematics
by John Tierney, New York Times, 19 October 2009
Norton writes:
This article gives an inspiring portrait of Martin Gardner, the premier exponent of recreational mathematics for over 50 years. It invites readers to see mathematics vastly richer and more interesting than they may recall from their classrooms exercise.
Norton says more about Martin and ends with a quote from Ronald Graham:
Martin has turned thousands of children into mathematicians, and thousand of mathematicians into children.
From this article we also learn that Martin Gardner recently had his 95th birthday and is still publishing new books.
(2) Do we need a 37-cent coin?
by Steven D. Levitt, New York Times, Freakonomics blog, 6 October 2009
Here Norton Writes:
This article reports on the work of economist Patrick DeJarnette, who developed some unusual results in probabilistic integer arithmetic. We can combine pennies, nickels, dimes and quarters to pay for any item costing below a dollar (freebies included, so (0.99 cents) is the relevant range). With the assumption that each of these 100 prices is equally likely to occur and that a purchaser uses the fewest possible coins, then on average each purchase requires 4.70 coins. DeJarnette asked if some other set of four coins, perhaps including one worth 8 or 61 or 37 cents would yield a lower average. He found that the optimal result uses an average of 4.10 coins per purchase, and is achieved by the sets (1, 3, 11, 37) or (1, 3, 11, 38).
Norton concludes his discussion with "there is a lot of play in this curious study." This is verified by looking at the 116 comments at the end of the blog.
Submitted by Laurie Snell
Back of the envelope calculations about Toyota
Toyotas are safe (enough).
by Robert Wright, The New York Times Blog, March 9, 2010.
How worried are you about driving a Toyota? Robert Wright is not that worried.
My back-of-the-envelope calculations (explained in a footnote below) suggest that if you drive one of the Toyotas recalled for acceleration problems and don’t bother to comply with the recall, your chances of being involved in a fatal accident over the next two years because of the unfixed problem are a bit worse than one in a million — 2.8 in a million, to be more exact. Meanwhile, your chances of being killed in a car accident during the next two years just by virtue of being an American are one in 5,244. So driving one of these suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent).
Of course, the type of risk involved is part of the problem.
But lots of Americans seem to disagree with me. Why? I think one reason is that not all deaths are created equal. A fatal brake failure is scary, but not as scary as your car seizing control of itself and taking you on a harrowing death ride. It’s almost as if the car is a living, malicious being.
Robert Wright includes an appendix (entitled "Tedious methodological footnote for statistics nerds") with all of the computations and assumptions that went into these numbers.
Submitted by Steve Simon
Questions
1. People seem to make a distinctions between risks that they place upon themselves (e.g., talking on a cell phone while driving) and risks that are imposed upon them by an outsider (e.g., accidents caused by faulty manufacturing). Is this fair?
2. Contrast the absolute change in risk (.01935-.01907=.00028) with the relative change in risk (.01935/.01907=1.0147). Which way seems to better reflect the change in risk?
3. Examine the assumptions that Robert Wright uses. Do these seem reasonable?
Placebos getting stronger?
The growing power of the sugar pill
by Alix Spiegel, NPR, 8 March 2010
The randomized double-blind placebo-controlled experiment is regarded as the "gold standard" in medical research. This story describes new research indicating that our response to placebo treatments may be getting stronger over time. One example of this so-called "placebo drift" phenomenon is provided by Arthur Barsky, the director of psychiatric research at Brigham and Women's Hospital in Boston. Barsky compared trials on antidepressants from the 1980s with studies done in 2005, and found that the reactions to placebos had become twice as strong.
Ted Kaptchuk of the Harvard Medical School suggested a number of possible explanations. First, antidepressants have become more widely accepted in society. To the extent that people come to expect treatment to be successful, they may react more positively to being treated, even with a placebo. Another possibility relates to funding, which increasingly comes from pharmaceutical companies. This creates pressure for the research to succeed, which could potentially bias the evaluation of the treatment. Finally, Kaptchuk notes that increased demand for research subjects may lead to the enrollment of marginally depressed people in the studies. Such subjects, who require less help to begin with, might plausibly be more responsive to placebos.
Kaptchuk has conducted earlier research on placebos. In a 2006 report entitled All placebos not created equal, Kaptchuk demonstrated that a fake acupuncture treatment could exhibit a stronger placebo effect than a fake pill in treating pain. In this case, Kaptchuk attributed the difference to the "medical ritual" associated with the acupuncture treatment.
Last summer, Wired Magazine had an article describing a number of drug trials that were cancelled at various stages when the drugs failed to outperform placebos. Among these was an anti-depressant that had been under development by the pharmaceutical company Merck.
Discussion Question
In the Wired article we read:
Two comprehensive analyses of antidepressant trials have uncovered a dramatic increase in placebo response since the 1980s. One estimated that the so-called effect size (a measure of statistical significance) in placebo groups had nearly doubled over that time.
What is being confused here?
Submitted by Bill Peterson
Ranking Olympics countries: The first may be last
Not all countries are rich and snowbound
by David Biderman, The Wall Street Journal, February 18, 2010
WSJ staff came up with an alternative system for ranking a country’s success in the Olympics, based on eight factors that they felt could affect a country’s performance. They then analyzed and ranked ten Winter Olympics 2010 countries as of February 16, based on the factors of population, per-capita GDP, average temperature, infant mortality rate, per-capita number of cars bought per month, percent of smokers, per-capita daily protein consumption, and per-capita yearly alcohol consumption.
A chart, “Another Way to Measure Olympic Aptitude”, shows the data for the eight factors, the medal counts, and the WSJ scores for the ten countries.
Italy came out on top, with 3 medals and a WSJ score of 0.942, while Germany came in last with 9 medals and a WSJ score of 0.750.
Submitted by Margaret Cibes
Athletes' birthdays
Born late year? Choose another sport
by David Biderman, The Wall Street Journal, March 21, 2010
A researcher at Queensland University of Technology compared the distribution of birthdays of the 617 Australian-born Australian Football League 2009 players in particular, to Australian birth statistics in general.
He found the following quarterly data on expected number of birthdays, actual number of birthdays, and percent more/less than expected :
| Expected | Actual | ||
| Jan-Mar | 153 | 196 | +28.1% |
| Apr-Jun | 155 | 162 | +4.5% |
| Jul-Sep | 157 | 137 | -12.7% |
| Oct-Dec | 152 | 122 | -19.7% |
He suggested that the decreasing percent changes could be explained by the January 1 cut-off date for youth-sports leagues, which “means players born near or after that date grow up with physical advantages over their competitors, likely influencing them to keep playing.” (Biderman reports that other studies have found similar results in European soccer and Canadian hockey.)
Questions
1. If Australian birthdays, in general, were uniformly distributed in any year, how many AFL player birthdays would you have expected in each quarter of a leap year? Of a non-leap year?
2. In what way(s) does the shape of either quarterly distribution in question 1 differ from the researcher’s quarterly distribution of expected AFL player birthdays?
3. How do you think the researcher calculated the expected number of AFL player birthdays in each quarter? What, if anything, might his distribution of expected AFL player birthdays tell you about the distribution of Australian birthdays in general?
4. Would/should this data discourage a young Australian-born person from aiming for an AFL career because he has a late-year birthday? What are some other considerations in making such a career decision?
Submitted by Margaret Cibes
Stock market bubble-predictor
“The Professor Who Chases Financial Bubbles”
by Eleanor Laise, The Wall Street Journal, March 13, 2010
Didier Sornette, director of the six-person Financial Crisis Observatory at the Swiss Federal Institute of Technology in Zurich, last year “launched the bubble experiment by identifying four developing bubbles and forecasting when they'll peak. His predictions are locked away in encrypted files that can't be altered, to be revealed only when the forecasted bubble peaks have passed, on May 1.”
Formerly a geophysics professor at UCLA, Sornette is now a professor of finance, physics and geophysics with a “passion for predicting events in complex systems” such as earthquakes, epileptic seizures, and the popularity of YouTube videos. He applies his work on rocket-tank ruptures to market fluctuations.
While there's lots of complex math behind it, one key pattern is essentially this: periods of unsustainable growth, in which the growth rate is itself accelerating, punctuated by waves of panicky selling. Key elements are the "positive feedback" generated by optimistic investors pushing the price ever higher into bubble territory even as more pessimistic investors produce waves of selling. In the midst of this tug of war, there's an accelerated development of the bubble. …. Only about two-thirds of bubbles end in a crash …. But in his view, as the bubble develops, it becomes increasingly unstable so that any number of small disturbances could cause it to pop. …. So while market-watchers often seek the causes of a crash in the events immediately preceding it, he believes the fundamental origin is in the longer-term build-up of instability.
Nassim Taleb, of “black swan” fame, says that Sornette’s work “is vastly more useful to me than anything else in economics."
Submitted by Margaret Cibes
Tiger’s average better than average
“Tiger Can Win by Just Playing ‘Average’”
by Austin Kelley, The Wall Street Journal, March 20, 2010
Two finance professors at Dartmouth’s Tuck School of Business have “used data from 83,823 rounds of golf on the [PGA] Tour between 2004 and 2008 and created a statistical model that calculate[s] every golfer's skill level” and estimates “each player’s average score for an average round on an average course.”
In that span, they found that [Tiger] Woods could have won 13 of the 72 PGA Tour stroke-play events he entered just by playing his "normal" game (he actually won 24). No other golfer on the tour could have won a single title without a little help from the golf gods. …. [They] estimate that if Mr. Woods can cope with the media maelstrom and put in a few run-of-the-mill days at Augusta National, he has about an 18.1% chance of winning. If Phil Mickelson does the same, he has no shot.
Based on the 2004-2008 data, they estimate Woods’ projected average round on an average course at 68.07, Phil Mickelson’s at 69.19, and Vijay Singh’s at 69.21. According to Kelley, the professors are not sure “how Mr. Woods’s hiatus will affect the statistics, but [guess] that Tiger will return to dominance at some point this year.”
See an abstract of their paper, “Dominance, Intimidation, and ‘Choking’ on the PGA Tour”, in the Journal of Quantitative Analysis in Sports, 2009.
Submitted by Margaret Cibes
Three happiness books
“Everybody Have Fun”
by Elizabeth Kolbert, The New Yorker, March 22, 2010
The author describes some 1978 research results indicating that lottery winners were not happier than paraplegic accident victims. The paper, “Lottery winners and accident victims: is happiness relative?”, Journal of Personality and Social Psychology, August 1978, is said to be “one of the founding texts of happiness studies, a field that has yielded some surprisingly morose results.”
Then she reviews two 2010 books and one 2007 book about happiness:
(a) By former Harvard president, now Harvard professor Derek Bok: The Politics of Happiness: What Government Can Learn from the New Research on Well-Being, Princeton University Press, 2010.
(b) By University of Maryland public policy professor Carol Graham, Happiness Around the World: The Paradox of Happy Peasants and Miserable Millionaires, Oxford University Press, 2010.
(c) By Harvard psychology professor Daniel Gilbert, Stumbling on Happiness, Vintage, 2007.
Submitted by Margaret Cibes
Flummoxed about flu
“The Flu Season That Fizzled”
by Betsy McKay, The Wall Street Journal, March 2, 2010
Experts cannot explain the unusual “lull” in flu cases at this time of year, compared to the wider incidence of H1N1 swine flu in the summer and fall of 2009.
[C]ases of the new H1N1 swine flu virus have dwindled to a trickle, and run-of-the-mill seasonal flu has barely made an appearance.
The University of Virginia’s student health director stated:
[The] student health center usually sees as many as 130 students a week complaining of flu symptoms this time of year. Recently, no more than three to five students a week have been coming in with fever, cough or other signs of flu ….
It is not clear whether – or how much – vaccination or hand-washing has played a role in the decrease in flu cases. There remains a danger that the H1N1 virus may rear up again, in the same or a mutated form. However, its appearance is also waning in most places around the world at this time.
See “Tracking the Flu” for a time-series chart of the “percentage of all doctors’ visits made by patients with influenza-like symptoms” for seasons 2005-06 through 2008-09.
Submitted by Margaret Cibes
U.S. women prefer macho men
“Why Women Don’t Want Macho Men”
by Jena Pincott, The Wall Street Journal, March 27, 2010
The University of Aberdeen’s online psychology lab conducted an experiment in which 4800 women from 30 countries were presented with pairs of men’s faces and asked to “select the face they considered more attractive and indicate how much they preferred it to the other one.” Interested readers can read more about the ongoing study, and participate themselves, at “Faceresearch.org”.
After crunching the data … the Face Lab researchers proved something remarkable. They could predict how masculine a woman likes her men based on her nation's World Health Organization statistics for mortality rates, life expectancy and the impact of communicable disease. In countries where poor health is particularly a threat to survival, women leaned toward "manlier" men. That is, they preferred their males to have shorter, broader faces and stronger eyebrows, cheekbones and jaw lines. The researchers went on to publish the study in this month's issue of the scientific journal Proceedings of the Royal Society: Biological Sciences.
The Scottish researchers found that women’s masculinity preferences were stronger for women in countries with higher disease and mortality rates and poorer scores on the healthcare index. The U.S., with its low (#20) health index rank, ranks high (#5) in strength of masculinity preferences of its women.
A previous study of 29 U.S. women by a University of California psychologist found that “men who rated as the most masculine generally had higher testosterone levels.” And another study of 2100 U.S. Air Force veterans concluded that:
[M]en with testosterone levels one standard deviation above the mean were 43% more likely to get divorced than men with normal levels, 31% more likely to leave home because of marital problems, 38% more likely to cheat on their wives, and 13% more likely to admit that they hit or hurled things at them.
Discussion
1. How does the phrase “the Face Lab researcher proved something” strike you?
2. What other information would you require in order to decide whether to have any confidence in these results?
3. Can you think of any explanation(s) for a possible association between a country's masculinity preferences and its level of healthcare?
4. If lower levels of health care are, indeed, correlated with higher masculinity preferences, do you feel that the relationship could be a causal one?
Submitted by Margaret Cibes
Long-time smokers less susceptible to Parkinson's
“Try Smoking and Parkinson’s”
by Jeremy Singer-Vine, The Wall Street Journal, March 22, 2010
This comes from a regular column in the WSJ, “The Research Report: New Medical Findings.” The column usually contains summaries of a half-dozen recent research findings, along with a “Caveat” and a “Read the Study” link to an abstract of the original report.
One recent study of 305,468 elderly subjects is said to have concluded:
Lengthier smoking habits—but not more intense ones—seem to reduce the odds of developing Parkinson's disease, according to a study in Neurology.
Interested readers can follow a link to an abstract of the report, “Smoking duration, intensity, and risk of Parkinson disease”, Neurology, 2010.
Caveat: It is possible that genetic factors determine both the propensity to smoke and protection from Parkinson's, rather than the smoke protecting against Parkinson's. Smokers may have remembered the duration of their habit more accurately than its intensity, which would skew the findings.
Submitted by Margaret Cibes
Incorrect metrics
U.S. health care is superior by most world measures
Letters, Wall Street Journal, 30 March 2010
As indicated by the well known aphorism, "It is not the heat, it’s the humidity," choosing the right metric is very important. Bayesians like to clobber the incorrect metric known as p-value, as can be seen by the following table due to Freeman (Freeman PR. The role of p-values in analysing trial results. Statistics in Medicine. 1993 Aug; 12(15-16): 1443-52).
| Number of Patients Receiving A and B |
Numbers Preferring A:B |
Percent Preferring A |
two-sided p-value |
| 20 | 15: 5 | 75.00 | 0.04 |
| 200 | 115: 86 | 57.50 | 0.04 |
| 2000 | 1046: 954 | 52.30 | 0.04 |
| 2000000 | 1001445: 998555 | 50.07 | 0.04 |
The same "statistically significant .04" appears in each row yet the practical significance is wildly different as the sample size varies, indicating that p-value as a metric is deficient.
The choice of an appropriate metric in health care is exceedingly important. The first letter to the Wall Street Journal link above shows how misleading the five-year survival rate metric can be. A letter writer defending the U.S. against the evils of socialized medicine replies to someone who was critical of the U.S. health care system compared to other countries:
For prostate cancer specifically, the rather astounding numbers are 92% in the U.S. versus 51% in the U.K. I am sure that the additional four out of 10 men in the U.K. who will die of prostate cancer find that to be significant, even if Dr. Krock does not.
Those "astounding numbers" refer to five-year survival rates. From Gigerenzer we learn of the misinterpretation common to patients and physicians: reliance on survival rates rather than mortality rates. The paper begins with former New York City mayor Rudy Giuliani thanking God for being treated for prostate cancer in the capitalist U.S. where his five-year survival chances were 82% as compared to "only 44% under socialized medicine." Turns out that "Giuliani’s numbers, however, are meaningless" because in the U.S. prostate cancer is being diagnosed earlier, a lead-time bias, and the cancer is being over diagnosed, that is, a pseudodisease is detected,--"screening-detected abnormalities that meet the pathologic definition of cancer but will never progress to cause symptoms in the patient’s lifetime." When it comes to mortality rates, there are "About 26 prostate cancer deaths per 100,000 American men versus 27 per 100,000 in Britain." The data "suggests that many American men have been unnecessarily diagnosed (i.e., overdiagnosed) with prostate cancer during the PSA era and have undergone unnecessary surgery and radiation treatment, which often leads to impotence and/or incontinence." In a nutshell, "The problem is that there is no relationship between 5-year survival and mortality."
Discussion
1. The "lead-time bias" is due to screening, i.e., mass testing, which is much more common in the U.S. than in other countries. Google the recent discussions regarding the efficacy of breast cancer screening in woman below the age of 50.
2. Gigerenzer’s article contains other interesting observations regarding relative risk vs. absolute risk. It also discusses the need to present Bayes theorem in a non-confusing way so that a patient and a doctor can understand the often remarkable numerical difference between Prob(test+|diseased) and Prob(diseased|test+).
Submitted by Paul Alper