Chance News 70

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"The interpretation of statistical significance tests is liable to a misconception known as the fallacy of the transposed conditional. In this fallacy, the probability of the data given a hypothesis (e.g., P(D|H), such as the probability of someone being dead given that they were lynched, a probability that is close to 1) is confused with the probability of the hypothesis given the data (e.g., P(H|D), such as the probability that someone was lynched given that they are dead, a probability that is close to zero)."

Eric–Jan Wagenmakers,, writing in
Why psychologists must change the way they analyze their data: The case of psi

The authors are criticizing naive use of p-value in the recent ESP research controversy.

Submitted by Paul Alper

”If you averaged the highs and lows of a rollercoaster, it wouldn’t be much of a thrill ride; same with the threat of flu.”

Rebecca Goldin in The flu: It’s about variance
STATS, September 3, 2010

The author reports that CDC flu-death counts have ranged from 3,300 to almost 50,000 in various years, making the yearly average unreliable as an exclusive basis of public health decisions.

(My colleague Jim Greenwood found a good online source for more quotations about statistics in general, The Quote Garden.)

Submitted by Margaret Cibes

"The obstetrician standing next to you when you were born had a much greater gravitational impact on you than Mars did."

Parke Kunkle of the Minnesota Planetarium Society, quoted in the Washington Post,
Astrologers struggle with slippage between constellations, horoscope signs, 26 January 2011

Submitted by Paul Alper

“People never say ‘don’t take your baby on a car journey,’ even though the risk of a car accident is far greater than not breastfeeding.”

Helen Rumbelow, in Significance, December 2010

Submitted by Margaret Cibes

“I have learnt to be a statistician but it didn’t come naturally. …. My Caltech teacher had told Stanford that I was too smart to do statistics, so I spent the first year at Stanford in the Maths [sic] Department; but after my return, I started taking stats courses, which I thought would be easy. In fact I found them harder.”

Bradley Efron
interviewed in Significance, December 2010

Submitted by Margaret Cibes


From a novel, The Kills, by Linda Fairstein, Scribner, 2004:

“Hey, how many people do you need to have in a room to guarantee the chance that at least two of them would have the same birthday?”

“I don’t know. Three hundred sixty-four.”

“Hah! Twenty-three. At least two out of every twenty-three people will have exactly the same birthday. Statistical odds. A lot of life is coincidence.”

Submitted by Margaret Cibes

New ESP study raises ruckus

Read about a new study in which a Cornell psychologist claims to have verified "ESP":
“ESP Study Gets Published in Scientific Journal, by Ned Potter, ABC World News, January 6, 2011 (including 2-min video interview).
“Journal’s paper on ESP Expected to Prompt Outrage”, by Benedict Carey, The New York Times, January 5, 2011. (See also the continuing online debate When science goes psychic in the Opinion section.)

Read the study:
“Feeling the Future: Experimental Evidence for Anomalous Retroactive Influences on Cognition and Affect”, by Daryl J. Bem, Cornell University, Journal of Personality and Social Psychology, 2010.

Read a rebuttal:
“Why Psychologists Must Change the Way They Analyze Their Data”, by Eric-Jan Wagenmakers et al., University of Amsterdam.

We reanalyze Bem’s data using a default Bayesian t-test and show that the evidence for psi ["ESP"] is weak to nonexistent. …. We conclude that Bem’s p-values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

Submitted by Margaret Cibes based on an ISOSTAT posting by Randall Pruim

Additional discussion

For more discussion, see Andrew Gelman's blog post That silly ESP paper and some silliness in a rebuttal as well (6 January), and reader comments there. Also the followup One more time on that ESP study (11 January), which addresses additional coverage of the story by Ben Carey at the New York Times (You Might Already Know This ..., 10 January 2011).

Placebos without deception

Patients in study who knew they were taking placebo still felt better
by Deborah Kotz, Boston Globe, 23 December 2010

Although somewhat of an exaggeration, before the invention of aspirin, MDs had nothing to offer except placebos. Today, no study in the medical field can be taken seriously without a control for the so-called placebo effect. In an unusual twist whereby the placebo is the treatment, Kaptchuk, et al openly beforehand informed 37 patients suffering from irritable bowl syndrome (IBS) that they were receiving a placebo “without any medication in it.” The other 43 patients were a control, i.e., no treatment, in that they received no medication whatsoever.

The Globe article put it this way:

The researchers got some astounding results when they gave placebos — gelatin capsules filled with nondigestible cellulose — to patients suffering from irritable bowel syndrome for three weeks. Nearly 60 percent reported an improvement in their symptoms compared with 35 percent of the patients who took nothing beyond their usual treatments. But here is the kicker: The placebo takers knew they were popping the equivalent of sugar pills, yet they still said they experienced less abdominal pain, constipation, or loose stools during the study.


1. Here is the table of treatment outcomes from the Kaptchuk paper and an associated graphic (the phrase “Open Placebo” means no deception). Use a statistics package to verify the p-values given there.

2. Just to confuse things now that the power of the placebo has been firmly established for IBS, consider this which also was recently published:

In two studies involving more than 1,200 subjects with diarrhea-predominant IBS, researchers found that a two-week course of the antibiotic rifaximin helped relieve symptoms not only during treatment, but also for weeks after the medication was stopped.

Participants who were randomly assigned to receive the drug reported less bloating and abdominal pain, and improved stool consistency for up to 10 weeks, say the authors, whose paper is published in this week's New England Journal of Medicine.

About 40 per cent or more of subjects given the thrice-daily rifaximin pill had significantly diminished IBS symptoms compared to those given placebo, or dummy pills, the study found.

Dr. Lawrence Cohen who was not involved with the study

said rifaximin could have potential, although how much is difficult to determine because the difference in the proportion of those reporting symptom relief in the study's treated group versus the placebo group wasn't that dramatic.

"It's statistically significant, yes. But is it clinically significant?"

While the findings shouldn't be dismissed, Cohen said he is cautious about the study because it was designed and funded by rifaximin's maker, Salix Pharmaceuticals Inc., a fact disclosed by the researchers. Pimentel [director of the Gastrointestinal Motility Program at Cedars-Sinai Medical Center] discovered the use of rifaximin for IBS, and Cedars-Sinai holds patent rights to this discovery and has licensed those rights to Salix.

Submitted by Paul Alper

Go figure, go finger

What your fingers say about you
by Tim Dowling, Guardian, 1 December 2010

Times are hard and academics need to publish in an environment in which not a great deal of money is available for gathering data. A popular way to do things inexpensively and create a stir in the lay press is to look at finger lengths. Previous Chance News wikis on the subject of finger lengths may be found here and here.

In the present article, Tim Dowling comments on the more unusual past claims put forward in academic journals regarding finger length as destiny:

Did you know the length of your ring finger could indicate whether or not you are fertile, prone to prostate cancer or, if you are a women, likely to be a lesbian?

…men with longer ring fingers tended to be more fertile. It's the other way round for women.

…[financial] traders with longer ring fingers made more money than their short ring-fingered colleagues. They're also thought to be more aggressive, and more likely to take risks.

…lesbian women tended to have the more masculine (long ring, short index) finger arrangement.

…women with longer ring fingers did better [on spatial skills such as driving] than those whose ring fingers were equal to, or shorter than, their index fingers.

He sums up the previous results with this picture:

However, the latest connection with fingers seems to indicate that men whose ring fingers are longer than their index fingers are more likely to develop prostate cancer. Its conclusion is “Pattern of finger lengths may be a simple marker of prostate cancer risk, with length of 2D greater than 4D suggestive of lower risk.” However, from we learn that

the report in the British Journal of Cancer [104 (2011), 175–177. doi:10.1038/sj.bjc.6605986] is so hedged about with “mays” and “maybes” that it is unlikely to be considered definitive by too many people. We quote as follows (with bold italic type added for emphasis):

“The ratio of digit lengths is fixed in utero, and may be a proxy indicator for prenatal testosterone levels.”

“Compared with index finger shorter than ring finger …, men with index finger longer than ring finger … showed a negative association, suggesting a protective effect with a 33% risk reduction.”

“Pattern of finger lengths may be a simple marker of prostate cancer risk.”

The finger length/cancer association was also featured in a recent story at (29 December 2010) The weirdest indicators of serious medical risks .


1. The Mermaid’s Tale points out a possible useful aspect of this study:

Of course, on the positive side, a glance at the hand is less embarrassing than a real DRE (digital rectal exam), or a PSA [prostate specific antigen] test to look for prostate cancer. It may be as useful, at least in terms of risk. It's a lot cheaper. Of course the PSA testing companies are likely to resist this current interpretation.

Determine the typical cost of a PSA test. The PSA test is a very common screening test in the United States and much less employed in other countries such as England. What does the following graph

suggest about the efficacy of screening? Although the five-year survival rates are not shown, what does the graph suggest about five-year survival rates in the various countries? What does it suggest about finger length?

2. The three-page British Journal of Cancer study relating prostate cancer and finger length cites 19 authors plus two institutions, The UK Genetic Prostate Cancer Study Collaborators and British Association of Urological Surgeons' Section of Oncology, whose “Lists [are] available on request.” There were 1524 subjects who had prostate cancer and 3044 subjects in the control arm. Information is given for the right hand only.

Table 2. Right-hand pattern and prostate cancer risk

Finger pattern Advanced cases (%) Controls (%) OR † 95% CI P-value
Index shorter than ring 872 (57.2) 1570 (51.6) 1.00
Index equal to ring 305 (20.0) 538 (17.7) 1.05 0.88–1.25 0.580
Index longer than ring 347 (22.8) 936 (30.8) 0.67 0.57–0.80 <0.001
Total 1524 (100.0) 3044 (100.0)

Abbreviations: CI=confidence interval; OR=odds ratio.
† Adjusted for age and social class.

Unlike previous studies of finger length, finger length in this study was self-reported. Why might this be an issue?

Submitted by Paul Alper

More time in school would help?

“The Case Against Summer Vacation”
by David Von Drehle, TIME, Thursday, July 22, 2010

This article suggests that the U.S. should lengthen the amount of time that children spend in school in order for its students to compete internationally in math.

[W]hen American students are competing with children around the world, who are in many cases spending four weeks longer in school each year, larking through summer is a luxury we can't afford.

Here’s the data from a printed chart that’s no longer available online. (I was not able to locate the days/hrs data online, nor any details about the nature of the statistics or the students being measured. I did find that the math scores provided match those in an OCED table[1] for 2006.)

Desk days. Although U.S. students have longer summer breaks, they spend more total hours in the classroom. Yet U.S. math scores still fall below those in many other industrialized countries

Country Median school days (yr) Total instructional hrs Math scores (15-year-olds)
South Korea 204 545 547
Denmark 200 648 513
Japan 200 600 523
Mexico 200 1,047 406
Brazil 200 800 370
Australia 197 815 520
New Zealand 194 968 522
Germany 193 758 504
Norway 190 654 490
U.S. 180 1,080 474
Luxembourg 176 642 490
Spain 176 713 480
Russia 169 845 476
Italy 167 601 462


1. For the countries shown, (a) the correlation between median days and total instructional hours is very slightly negative (about - 0.0068), (b) the correlation between median days and math scores is slightly positive (about + 0.1083), and (c) the correlation between total instructional hours and math scores is moderately negative (about - 0.3969). Are any, or all, of these correlations surprising?
2. From this data alone, could you conclude that extending the U.S. school year or school day would improve math scores?
3. The table shows results after each country's data has been aggregated. What additional raw data and/or statistics about the data might help you to understand these relationships better?
4. What additional information, beyond data, might help you to understand these relationships better?
5. Which large industrialized countries are conspicuously missing from this chart?

Submitted by Margaret Cibes

Firearms and fatalities

Obama’s gun play
by Charles M. Blow, New York Times, 21 January 2011

Recent events in Tucson have focused discussion on the relationship between gun ownership and violence. In the present article, Blow writes, "Obama the gun-control supporter surely knows how anomalous we are among comparable nations. We are a violent society whose intense fealty to firearms has deadly consequences."

To make the international comparison, the article presents the following graphic which plots the percentage of a country's homicides committed with firearms against gun ownership rates, measured in firearms per 100 people. This scatterplot is enhanced by plotting data points as spheres whose relative size reflects firearm homicides per capita, so there are effectively three variables represented on the plot (actually a fourth, categorical variable is included since the spheres are color-coded by continent).

Discussion Questions

1. Just looking at North America, how do the US, Canada and Mexico compare on the three variables?

2. Comment on the construction of the graphic. Does the aspect ratio of the display enhance or detract from the presentation? What is the effect of using spheres as opposed to circles in the representation?

Submitted by Bill Peterson, based on a suggestion from Paul Alper

The height of inequality

The rise and rise of the cognitive elite: Brains bring ever larger rewards
The Economist, 20 January 2011

This is an essay on sources and implications of income inequality in modern societies. The article includes the following graphic, which uses the Gini coefficient to demonstrate the growing inequality in industrialized countries

As described in technical terms by Wikipedia here, calculation of Gini coefficient is based on a plot of cumulative income share against cumulative population percentage, ordered from the lowest to highest earners. The Economist describes an interesting way to visualize the income distribution:

Jan Pen, a Dutch economist who died last year, came up with a striking way to picture inequality. Imagine people’s height being proportional to their income, so that someone with an average [mean, not median] income is of average height. Now imagine that the entire adult population of America is walking past you in a single hour, in ascending order of income. The first passers-by, the owners of loss-making businesses, are invisible: their heads are below ground. Then come the jobless and the working poor, who are midgets. After half an hour the strollers are still only waist-high, since America’s median income is only half the mean. It takes nearly 45 minutes before normal-sized people appear. But then, in the final minutes, giants thunder by. With six minutes to go they are 12 feet tall. When the 400 highest earners walk by, right at the end, each is more than two miles tall.

A more colorful version of Pen's insight appears in a 2006 article from The Atlantic, entitled The Height of Inequality, which includes the following rendering (scroll right to get the full effect!):

Notice the Simpson's-type paradox in the Economist graph, which shows the Gini coefficient rising for (selected) countries but dropping worldwide. The article explains that "This is because poorer countries, such as China, have grown faster than richer countries." Does this make sense?

Submitted by Paul Alper

WHO knows?

“Funny Figures from WHO on Caesareans”
by Nigel Hawkes, Straight Statistics, January 26, 2010
“The Lancet, WHO and Caesareans: over to the Ombudsman”
by Nigel Hawkes, Straight Statistics, April 8, 2010

This article alleges that there are problems with a widely promulgated World Health Organization study, published in The Lancet[2], of more than 122 hospitals and almost 108,000 birth records in nine Asian countries for three-month period in 2007-08. The study concluded that elected Caesarean deliveries were almost 3 times riskier than vaginal deliveries – a conclusion that appears to contradict the evidence shown in the raw data below. Hawkes alleges that there are other problematic issues with this study, such as possible miscalculations and inappropriate "transformations" of data.

Of the 1515 pregnant women who opted for Caesarean deliveries, 0.3% went to ICU, 0.2% needed a blood transfusion, none required a hysterectomy, and none died. Of the rest of the women, who had vaginal deliveries, 0.6% went to ICU, 1.0% needed a blood transfusion, 0.05% required a hysterectomy , and 0.1% died.

Hawkes calls the results “completely implausible,” and asks, “Did no referee raise the alarm?” He filed a formal complaint to The Lancet’s ombudsman, who hasn “refused to consider the evidence presented on the grounds that it had not been peer-reviewed.” (Straight Statistics is not a peer-reviewed journal.)

Reference to this study appeared in “Untimely ripped?”, Significance, December 2010.

Submitted by Margaret Cibes

Vaccines and autism: Case closed?

Autism fraud
New York Times, Editorial, 12 January 2011

A 1998 paper in the Lancet, which reported a link between the MMR (measles, mumps, rubella) vaccine and autism, led concerned parents to forego vaccinations for their children. As reported in earlier Chance News (see CN 60 and CN 45) that study was subsequently discredited because of questionable data analysis. In a sustained effort, the British journalist Brian Deer has worked to systematically chronicle the fallout from study and document the evidence against its findings.

As explained in the NYT editorial cited above, the British Medical Journal has now concluded that the "flaws in the [Lancet] paper were not honest mistakes but rather an 'elaborate fraud'" by the author, Dr. Andrew Wakefield. The BMJ has published the full record of Mr. Deer's investigative work, How the case against the MMR vaccine was fixed.

Do you think this will end the controversy about the MMR vaccine? You might look at a recent NYT story, Why parents fear the needle (by Michael Willrich, 20 January 2011), which traces public concerns about vaccines all the way back to Edward Jenner's work on smallpox in the 19th century.

Submitted by Bill Peterson