Chance News 44

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While writing my book [Stochastic Processes] I had an argument with Feller. He asserted that everyone said `random variable' and I asserted that everyone said `chance variable'. We obviously had to use the same name in our books, so we decided the issue by a stochastic procedure. That is, we tossed for it and he won.

A Conversation with Joe Doob

Statistical Science, Vol. 12, No. 4 (Nov., 1997), pp. 301-311

Anecdotes do not make a science. Ten anecdotes are no better than one, and a hundred anecdotes are no better than ten.

Frank Sulloway quoted on page 93 of Science Friction:
Where the Known Meets the Unknown by Michael Shermer.


Game Theory Explains Why You Can't Hurry Love.

"From a female's point of view, males are not all equal" and "there remains some risk that she will mate with the wrong type of male. She cannot eliminate this risk completely unless she decides never to mate."

Dr Peter Sozou
Warwick Medical School and
LSE Centre for Philosophy of Natural and Social Science.
Quoted in Science Daily
Commenting upon here
And the math is here

Submitted by Paul Alper

Anyone who has ever been skeptical about meta-analysis will enjoy this photograph or this cartoon.

Submitted by Steve Simon

Statistics with heart-pounding excitement

The Manga Guide to Statistics, Shin Takahashi and Trend-pro Co., November 2008, 224 pp.

I suppose it was only a matter of time - now you can be entertained by a manga cartoon and learn about statistics at the same time:

Our heroine, Rui, is determined to learn about statistics to impress the dreamy Mr. Igarashi and begs her father for a tutor. Soon she's spending her Saturdays with geeky, bespectacled Mr. Yamamoto, who patiently teaches her all about the fundamentals of statistics: topics like data categorization, averages, graphing, and standard deviation.

This comic uses real-world examples like teen magazine quizzes, bowling games, test scores, and ramen noodle prices to enliven the subject matter. Not surprisingly, the intended readers are people interested in learning more about statistics.

After all her studying, Rui is confident in her knowledge of statistics, including complex concepts like probability, coefficients of correlation, hypothesis tests, and tests of independence. But is it enough to impress her dream guy? Or maybe there's someone better, right in front of her?

Examples, exercises, and answer keys help you follow along and check your work. An appendix showing how to perform statistics calculations in Microsoft Excel makes it easy to put Rui's lessons into practice.

Further Reading

No Starch Press publishes the finest in geek entertainment -- distinctive books on computing, such as bestsellers Steal This Computer Book, How Linux Works, Hacking: The Art of Exploitation, The Cult of Mac, and The Unofficial LEGO Builder's Guide, with a focus on open source/Linux, security, hacking, programming, and alternative operating systems.

Submitted by John Gavin.

A suggestion for stats classes

Annette Georgey wrote to the Isolated Statisticans

An article came out in today's Wall St. Journal that would be fun to use for introductory stats classes. It touches on several concepts--the limits of observational studies, confounding, spurious correlations, type I errors.

The author, Melinda Beck, uses as example an article"You are what your mother eats" in the Proceedings of the Royal Society B and on a criticism of this article: "Cereal-Induced gender selection? Most likely a multiple testing false positive" in the same journal.

The original article was discussed in Chance News 36 here by Paul Alper so we would advise you to look at this also.

Beck writes

Some statisticians argue for a tougher standard of proof when researchers are fishing in large data sets. One method, a Bonferroni adjustment, requires dividing the usual mathematical formula by the number of variables; if 100 foods are studied, the link must be 100 times as strong as usual to be considered significant. Otherwise, statisticians say only strict clinical trials with a control group and a test group and one variable can truly prove a cause-and-effect association.
Epidemiologists argue that a Bonferroni adjustment throws out many legitimate findings, and that it's irrelevant how many other factors are studied simultaneously. They also note that controlled clinical trials are costly, time-consuming and sometimes unethical. The link between smoking and cancer, for example, was seen in many observational studies, but forcing subjects to smoke for years to prove it would be untenable.

Submitted by Laurie Snell


(0) Do you think that your students will understand Beck's comments on the Bonferroni adjustment? Do you?

Have your students answer the following questions asked by Paul Alper in his discussion of the Royal Society article.

1. Here is a wiki which looks at a different study, on mice, which also claims that nutrition affects the percentages of males and females. Which of the two is an experimental study and which is an observational study?

2. The current study was done in England and of the 740 mothers-to-be, 301 (approximately 40%) said they currently were smokers. Why would this fact cast doubt on the conclusions being applied to the United States?

3. Eating cereal for breakfast is a very American habit, duplicated in few countries; even those other countries, such as England where cereal is eaten for breakfast, have nowhere near the selection possibilities obtainable in the United States. Many industrialized countries eat little or no breakfast at all. What then should the male/female ratio be for these countries?

4. It is often said that many cereals are really candies in disguise. If so, should the mother-to-be "cut to the chase" and just have a candy bar for breakfast? If not, why not?

5. Instead of the customary .05 level, the researchers chose a p-value < .01 for determining statistical significance. Why did they lower the p-value?

6. The researchers keep referring to a "bowl of cereal." Why is this an exceedingly inexact measure?

Submitted by Laurie Snell

Two media frenzies not supported by the data

The Epidemic That Wasn’t, Susan Okie, The New York Times, January 26, 2009.

The Myth of Rampant Teenage Promiscuity, Tara Parker-Pope, The New York Times, January 26, 2009.

Two articles in the New York Times use statistics to debunk media reports of pending social disasters.

"When the use of crack cocaine became a nationwide epidemic in the 1980s and ’90s, there were widespread fears that prenatal exposure to the drug would produce a generation of severely damaged children. Newspapers carried headlines like 'Cocaine: A Vicious Assault on a Child,' 'Crack’s Toll Among Babies: A Joyless View' and 'Studies: Future Bleak for Crack Babies.'

It turns out that while cocaine is not exactly beneficial, the pessimistic prognosis in the media did not pan out.

So far, these scientists say, the long-term effects of [cocaine] exposure on children’s brain development and behavior appear relatively small. 'Are there differences? Yes,' said Barry M. Lester, a professor of psychiatry at Brown University who directs the Maternal Lifestyle Study, a large federally financed study of children exposed to cocaine in the womb. 'Are they reliable and persistent? Yes. Are they big? No.'

Research in this area is difficult, of course, because the data is observational and there are a whole host of confounders.

"Teasing out the effects of cocaine exposure is complicated by the fact that ... almost all of the women in the studies who used cocaine while pregnant were also using other substances. Moreover, most of the children in the studies are poor, and many have other risk factors known to affect cognitive development and behavior — inadequate health care, substandard schools, unstable family situations and exposure to high levels of lead."

The tendency to exaggerate the effects of leads to some serious problems.

"... cocaine-exposed children are often teased or stigmatized if others are aware of their exposure. If they develop physical symptoms or behavioral problems, doctors or teachers are sometimes too quick to blame the drug exposure and miss the real cause, like illness or abuse."

Another area ripe for debunking is the explosion of risky teenage sexual behavior.

"The talk show host Tyra Banks declared a teen sex crisis last fall after her show surveyed girls about sexual behavior. A few years ago, Oprah Winfrey warned parents of a teenage oral-sex epidemic. The news is troubling, but it’s also misleading."

Again, these risks seem to be overstated.

"While some young people are clearly engaging in risky sexual behavior, a vast majority are not. The reality is that in many ways, today’s teenagers are more conservative about sex than previous generations."

This exaggeration of the problem also has bad effects.

"Health researchers say parents who fret about teenage sex often fail to focus on the important lessons they can learn from the kids who aren’t having sex. Teenagers with more parental supervision, who come from two-parent households and who are doing well in school are more likely to delay sex until their late teens or beyond. 'For teens, sex requires time and lack of supervision,' Dr. Kefalas said. 'What’s really important for us to pay attention to, as researchers and as parents, are the characteristics of the kids who become pregnant and those who get sexually transmitted diseases. 'This whole moral panic thing misses the point, because research suggests kids who don’t use contraception tend to be kids who are feeling lost and disconnected and not doing well.'"

One researcher in the area notes the desire of many to hold on to a pessimistic perspective.

"'I give presentations nationwide where I’m showing people that the virginity rate in college is higher than you think and the number of partners is lower than you think and hooking up more often than not does not mean intercourse,' Dr. Bogle said. 'But so many people think we’re morally in trouble, in a downward spiral and teens are out of control. It’s very difficult to convince people otherwise.'"

In response to the Parker-Pope article, Judith Warner wrote a blog entry, The Myth of Lost Innocence, at the New York Times website that speculates about the motivations to exaggerate dangerous teenage sexual practices.


1. What can the media do to minimize the exaggeration of health risks?

2. Why do you think that some people want to hold on to a pessimistic perspective, even when confronted with data showing a different perspective?

Lotteries in the news

George Seymore called our attention to a lottery story widely reported in the news. For example it was on NPR's Morning Edition January 23, 2009. Here we read:

The winning numbers for Nebraska's Pick 3 lottery were 1, 9 and 6 on Monday. The next night, the winning numbers were 1, 9 and 6 — in the same order drawn the previous night. A lottery spokesman said two separate computers randomly generated the same numbers. There were different winners each night. The odds of such an occurrence? One in a million.

Alexander Kastan contributed the following intelegent remarks on the NPR comments:

Actually, the odds of such an occurrence on a particular day is one in a thousand. But even that understates the likelihood. This particular Nebraska lottery is held over 300 times a year. So we expect such an occurence once every three or four years. And of course, that's only in Nebraska. If any other states have similar pick 3 lotteries, we would expect such occurrences even more often.

George writes: P.S. Would appreciate more actual applications and explanations of counter-intuitive probability events.

Fortunately we can do this thanks to Dan Rockmore who suggested another Lottery story reported here on the Fox News on January 7, 2009. The article is titled "Colorado Lottery Investigates 21-Time Jackpot Winner." Here we read

Tadeusz Krupa and his family have won 1,000 dollars or more in Colorado's Cash 5 Jackpot on 21 different occasions, raking in a total of about 158,000 dollars before taxes since December 2007, reported.

Krupa has been so successful that other players complained, prompting the state's lottery to look into his winnings — which include seven 20,000 dollar jackpots, the station said.

What they found is that Krupa and his relatives struck gold fair and square.

"We know that this gentlemen didn't scam the system," Colorado Lottery Deputy Director Tom Kitts told 9 News.

Investigators interviewed Krupa and his family and talked to employees at stores where the lucky tickets were purchased. They've found no evidence of cheating or other illegal activity, according to Kitts.


Here are some of the dates that the Krupa family hit the jackpot.

11/29/08 Janina Krupa Brighton 20,000 dollars
11/29/08 Janina Krupa Brighton 20,000 dollars
11/26/08 Aneta Krupa Brighton 20,000 dollars
11/8/08 Tadeusz Krupa Brighton 20,000 dollars
11/8/08 Aneta Krupa Brighton 20,000 dollars
2/16/08 Tadeusz Krupa Brighton 20,000 dollars
12/14/07 Tadeusz Krupa Brighton 20,000 dollars
4/6/07 Tadeusz Krupa Maspeth 20,000 dollars

What additional information would you need to know to estimate the chance that the Krupa family would win this many jackkpots?

Recession and Churchgoing

Bad Times Draw Bigger Crowds to Churches
New York Times, 13 December 2008
Paul Vitello

This article presents anecdotal evidence to suggest that the economic downturn has produced at least one boom: church attendance. In recent weeks, one small Long Island church has been regularly filling 100 seats in an overflow room where churchgoers view the service on closed-circuit television. In another apparent sign of the times, a New Jersey church reports that prayer requests have doubled, with most devoted to anxiety about job situations.

Moreover, the article states that recent increases in attendances at such evangelical churches are in excess of general growth trends seen for this group over the last decade. Other " spot check " data indicate that Roman Catholic and traditional Protestant groups are also experiencing gains, but not of the magnitude seen by their evangelical counterparts.

For historical perspective on this, the article cites research by David Beckworth, a Texas State University economist, who reportedly found that

During each recession cycle between 1968 and 2004, the rate of growth in evangelical churches jumped by 50 percent. By comparison, mainline Protestant churches continued their decline during recessions, though a bit more slowly.

The recent trend, however, was disputed in a December 20 Letter to the Editor, No Change in Churchgoing from Frank Newport of the Gallup organization. According to Newport,

Gallup has asked 1,000 adults a day since mid-February of this year to assess how often they go to church. The results show that about 42 percent of the adult population has reported attending at least once a week or almost every week each month since February, with no increase in September, October, November or the first half of December.

Similarly, there has been no increase in the percentage who report attending monthly, seldom or never.

You can read more on Gallup's methodology here, or watch a video discussing the findings.

Discussion Question

The polling data initially seem more trustworthy, at least to the statistically inclined. But consider this post on Counting Churchgoers from Andrew Gelman’s statistics blog. There we read evidence that church attendance is often over-reported. So it may be that the anecdotal reports reflect a real phenomenon: people who used to just say they attended church are now actually going. How would you propose to investigate this?

Submitted by Bill Peterson, based on a suggestion from Priscilla Bremser.


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 bell. From 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 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.”

One of the latest extensions of the importance of the 2D:4D phenomenon is to financial trading and may be unearthed 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.”


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.

2. Compare high-frequency trading with outright gambling.

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.

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.



Trading experience


Aproximation Annual Income (1£ = 2$)
19 to 38
1 to 12
£-2,000 to £4,200,000

That is, a very small number of the 44 traders made a great deal more money than the others. The graph above 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 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.

However, what is the physical meaning of the units of this y variable?

8. The 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.

9. Bearing in mind that statistical research can be costly and time consuming, what is the special appeal of 2D:4D?

Submitted by Paul Alper

Lie Detection

From London Times online. we find a discussion of how to tell truth from lies in email messages. One of the main giveaways is the length of a message. E-mails that mask a lie have, on average, 28% more words than truthful messages. "When you're lying, you are trying to give a credible story so you provide more detail, you are in persuasive mode," said Jeff Hancock, director of the Computer-Mediated Communication Research Laboratory at Cornell University. "People also tend to use negative emotional terms because they feel uncomfortable when they are lying," said Hancock. "So they tend to use terms like 'sad', 'angry', 'unhappy' and 'stressed out'." Another telltale sign of a fib is the overuse of "sense terms", such as "see", "feel" and "touch", which Hancock believes are employed to build up an elaborate and evocative account of a scenario that may never have happened. Finally, liars tend to use fewer "causal phrases" to minimise the chances of being caught out. Previous research by the University of Central Lancashire has shown that up to one-third of communications at work involve some degree of deception. The most common work-place lie is faking a "sickie." Hancock has claimed people lie in a quarter of all social interactions, but he concedes they are far more likely not to tell the truth over the phone than on e-mail - because there is no written record of the exchange. Hancock claims accuracy ratings of his software of up to 70%; he has been awarded a grant of £346,000.


1. If you were lying about being late for class, what would be your “causal phrase”?

2. Regarding the phone vs. e-mail, which form of communication would you think would be more likely to be truthful?

3. In the article it is alleged, “One of the main giveaways is the length of a message. E-mails that mask a lie have, on average, 28% more words than truthful messages. ‘When you’re lying, you are trying to give a credible story so you provide more detail, you are in persuasive mode,’ said Hancock.” Assume the 28% cited is correct, why is this fact not very useful?

4. Why is the term “accuracy rating” ambiguous? That is, using Bayes theorem, what are the various candidates for the conditional probability which might be labeled “accuracy”?

5. If we assume the tell-tale signs mentioned in the article are indeed true, how should a liar change his strategy?

Submitted by Paul Alper