Chance News 49

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Probability arises from an opposition of contrary chances or causes, by which the mind is not allowed to fix on either side, but is incessantly tost [sic] from one to another, and at one moment is determined to consider an object as existent, and at another moment as the contrary.
David Hume

Submitted by Margaret Cibes

After reading the above, I coincidentally came across this David Hume quotation on page 72 of Gould's The Mismeasure of Man, second edition:

I am apt to suspect the negroes and in general all the other species of be naturally inferior to the whites. There never was a civilized nation of any other complexion than white, nor an individual eminent either in action or speculation. No ingenious manufacturers amongst them, no arts, no sciences.

The quotation continues on in the same vein and makes one's head spin at the attitudes and prejudices of the famous philosophers.

Submitted by Paul Alper


Steven J. Dubner of the New York Times writes about Bernice Geiger, a person who "never took vacations" for fear of her embezzlement being discovered by a fill-in employee; she "was arrested in 1961 for embezzling more than $2 million over the course of many years." Eventually, "after prison Geiger went to work for a banking oversight agency to help stop embezzlement."

Geiger's "biggest contribution: looking for employees who failed to take vacation. This simple metric turned out to have strong predictive power in stopping embezzlement."

Submitted by Paul Alper

Infuse and Kuklo II

This web site provides a wonderful pun regarding Benford’s Law, “Looking out for number one.” The authors write: “Go and look up some numbers. A whole variety of naturally-occurring numbers will do. Try the lengths of some of the world's rivers, or the cost of gas bills in Moldova; try the population sizes in Peruvian provinces, or even the figures in Bill Clinton's tax return. Then, when you have a sample of numbers, look at their first digits (ignoring any leading zeroes). Count how many numbers begin with 1, how many begin with 2, how many begin with 3, and so on - what do you find? You might expect that there would be roughly the same number of numbers beginning with each different digit: that the proportion of numbers beginning with any given digit would be roughly 1/9. However, in very many cases, you'd be wrong!”

Instead, we get
Figure 1: The proportional frequency of each leading digit predicted by Benford's Law.

Should somebody try “to falsify, say, their tax return then invariably they will have to invent some data. When trying to do this, the tendency is for people to use too many numbers starting with digits in the mid range, 5,6,7 and not enough numbers starting with 1. This violation of Benford's Law sets the alarm bells ringing.”

It is a pity that unlike for accounting data, there is no forensic counterpart to Benford’s Law for determining when a journal article is entirely fraudulent. As stated in Infuse and Kuklo you won’t be able to read [on the JBJS website] the fraudulent article, “Recombinant human morphogenetic protein-2 for type grade III open segmental tibial fractures from combat injuries in Iraq” by Timothy Kuklo, et al, which appeared in the JBJS in August, 2008 because it has been retracted. However, it is available here. The immediate impression is that as far as statistics is concerned, it looks like any other article in the health field.

The important statistics appear in Tables 1 and III

Note that there is no claim that everyone in Group 2 (the group using Infuse) did well or that everyone in Group 1 fared poorly. Further, as in legitimate studies, there are patients who were not included because of an additional problem (head injury) or were lost to follow up. The data is there for reviewers and others to do the calculations which in this paper are the difference in proportions, a standard statistical technique. Small but not immodest p-values indicate that statistical significance is obtained; detailed discussion about the fractures indicates that practical significance is also realized. The bibliography has 39 entries, only one of which has Kuklo as the author; the same entry includes one of the ghost co-authors in the retracted paper. Nothing statistically or otherwise suspicious whatsoever.

Freudian psychology is currently out of favor but Freud's notion of a death wish still seems plausible. How else to explain the pushing of the envelope past falsification of data, denial of connection to the manufacturers of Infuse, and forging of not one, not two but four ghost authors? The aptly titled 1995 book by Feinberg and Tarrant, Why Smart People Do Dumb Things, attributes such behavior to what they deem “the four pillars of stupidity”: hubris, arrogance, narcissism and unconscious need to fail. The first three are overwhelmingly obvious, but the last named cause sounds deeply Freudian.

A New York Times update appears on June 5, 2009 and shows how Kuklo forged the signatures; “He used a distinctively different handwriting style for each of them, a form he submitted to the British journal shows.”

Dr. Timothy R. Kuklo and copies of the signatures of other Army doctors on his study that authorities say he forged.

A putative co-author “suspected that Dr. Kuklo had fabricated the comparison groups, because many soldiers had received both Infuse and a bone graft — not one or the other.” This person said, “It was like he was comparing apples and oranges. But there weren’t any apples or oranges to compare.”

Returning to the statistical aspect of the paper, Table III says 19 of 67 (28%) in Group 1 were patients who had further surgery while 5 of 62 (8%) in Group 2 (Infuse group) had further surgery. Presumably, via a chi-square test, the p-value is listed as .003. Minitab produces the same numerical result of .003 via the Fisher exact test:

Sample X N Sample p
1 5 62 0.080645
2 19 67 0.283582

Difference = p (1) - p (2)
Estimate for difference: -0.202937
95% CI for difference: (-0.330382, -0.0754923)
Test for difference = 0 (vs not = 0): Z = -3.12 P-Value = 0.002

Fisher's exact test: P-Value = 0.003

Some numerical discrepancies arise, however, for Table I. Table I says 51 of 67 (76%) in Group 1 had a successful “union” while 57 of 62 (92%) in Group 2 (Infuse group) had a successful union. Presumably, via a chi-square test, the p-value is listed as .015. Minitab produces the following indicating that because of the small sample sizes, the Fisher exact test yields .017 instead:

Sample X N Sample p
1 57 62 0.919355
2 51 67 0.761194

Difference = p (1) - p (2)
Estimate for difference: 0.158161
95% CI for difference: (0.0356210, 0.280701)
Test for difference = 0 (vs not = 0): Z = 2.53 P-Value = 0.011

Fisher's exact test: P-Value = 0.017

Table I also says 10 of 67 (14%) in Group 1 had post-operative infections while 2 of 62 (3.2%) in Group 2 (Infuse group) had post-operative infections. Presumably, via a chi-square test, the p-value is listed as .001. Minitab produces the following quite different p-value of .032:

Sample X N Sample p
1 10 67 0.149254
2 2 62 0.032258

Difference = p (1) - p (2)
Estimate for difference: 0.116996
95% CI for difference: (0.0210037, 0.212988)
Test for difference = 0 (vs not = 0): Z = 2.39 P-Value = 0.017

Fisher's exact test: P-Value = 0.032

However, these discrepancies are hardly in the Benford class. They may merely indicate what happens when a non-statistician medical doctor acts alone.

Submitted by Paul Alper

Emotional biases in financial decisions

"Control Yourself", by Veronica Dagher, The Wall Street Journal, June 8, 2009

This article describes 5 "biases", or emotional issues, that affect investment decisions and that are studied in the field of "behavioral finance."

(1) "Anchoring" bias refers to being "overly attached to a particular investment."
(2) "Recency" bias refers to assuming that "events or patterns in the past will continue into the future."
(3) "Loss aversion" bias refers to "hoping inaction [will] eventually make the losses go away."
(4) "Endowment effect" bias refers to assigning a "greater value to what [one] own[s] than to what [one doesn't] own, whether that value is warranted or not."
(5) "Overconfidence" bias refers to excessive trading in an attempt to "beat the market."

“One could try to explain all the events of the last several months with models and ratios, but it’s become more and more difficult to do so,” says Richard Thaler, professor of behavioral science and economics at the Booth School of Business at the University of Chicago.

Submitted by Margaret Cibes


The biggest of puzzles brought down to size.
New York Times, 30 March 2009
Natalie Angier

The article opens by reminding us that with bank bailouts running hundreds of billions of dollars the national debt passing ten trillion, the public need help comparing the magnitudes of really large numbers. For practice, the author recommends so-called "Fermi problems,". Named for Enrico Fermi, these are estimation problems that physicists and engineers like to use to sharpen their intuition. Two examples cited in the article are:

What is the total volume of human blood in the world? or, If you put all the miles that Americans drive every year end to end, how far into space could you travel?

Readers may recall that a number of such problems were described by John Allen Paulos in his classic, Innumeracy, where he lamented the fact that estimation skills were not being taught in the schools. A more recent source, featured in the present article, is Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin (Princeton University Press, 2008). A companion article on 31 March gives an online quiz based on the book.

The book serves as the text for course at Princeton in Spring, 2009, "Physics 309: Physics on the Back of an Envelope", which was offered by one of the book's co-authors, Professor Lawrence Weinstein. His course website links to sample midterms and to similar courses at MIT and CalTech.

Submitted by Bill Peterson

Measuring drivers' drunken-ness

"Drunk Driver Data Don't Walk Straight Line Either", by Carl Bialik (The Numbers Guy), The Wall Street Journal, June 10, 2009

This article describes a disagreement between Mothers Against Drunk Driving and a liquor-industry-funded group, Century Council, about the blood alcohol level that would trigger a proposed penalty requiring convicted drunk drivers to install an ignition interlock to prevent them driving when their breath alcohol level is "too high."

Century Council has stated that it wants to limit the level to a minimum of 0.15 grams per deciliter of blood, based on 2007 government studies that show that 3 out of 5 drivers involved in alcohol-related fatal crashes had a BACof at least 0.15, in contrast to about 1 out of 5 with BACs of 0.01 to 0.08 and 1 out of 5 with BACs of 0.09 to 0.14.

According the article's author, a Weststat statistician believes that "the same personality traits that lead to driving while highly intoxicated are probably tied to other risky behavior behind the wheel" and that

these heavy drinkers are far more dangerous than other drunken drivers on the road. [He] compared the blood-alcohol levels of drivers killed in crashes with levels of drivers stopped for random roadside testing during peak drunken-driving hours. .... Compared with sober drivers, drivers at 0.15 or higher were about 400 times more likely to die in a crash. Drivers with levels between 0.10 and 0.14 were 50 times more likely than sober drivers to die in a crash.

MADD prefers a minimum "high" that is the legal limit of 0.08. A 2002 study at Johns Hopkins University, based on interviews with surviving family members of over 800 victims of fatal crashes, found that 55% of dead drivers with BAC levels of 0.15 or higher, and 35% of those with BAC levels between 0.10 and 0.14, drank at least monthly, leading a study co-author to state, "We shouldn't simply be focusing on 'hard-core' drivers."

According to the article's author, "some researchers would prefer to see a lower limit, with penalties tied to the blood-alcohol level, like with speeding penalties. .... Complicating matters, people's alcohol-metabolism varies, as does the relationship between their breath alcohol ... and their blood alcohol."
A blogger wrote, "I recall several years ago, a drunk was let go free because he was able to prove the variability in the gage [sic]."
See "The Numbers All Drivers Should Know" for more information on this topic from The Numbers Guy.
Submitted by Margaret Cibes

Variables lurk in Wal-Mart study?

"Wal-Mart's Weight Effect", by Art Carden, Forbes Magazine, June 8, 2009

This story reports preliminary findings from a University of NC-Greensboro study of big retail stores and obesity. The author of the article is a co-author of the study.

In [the] first round of statistical analysis we found that greater consumer access to a Wal-Mart ... store was associated with lower body-mass indexes and a lower probability of being obese. ... [T]he correlation holds up under a variety of different circumstances, with a clear relationship between warehouse clubs and better eating habits emerging over time. Further, ... Wal-Mart's effect on weight is largest for women, the poor, African-Americans and people who live in urban areas. .... [W]hile we found a statistically significant effect on body mass index, the effect is very, very small.

Bloggers comment.

One blogger suggests that the observed effect of big retail stores on obesity may be a result of the fact that shoppers who purchase fresh fruits and vegetables at stores like Costco have to eat lots of these healthy foods in shorter periods of time because the packages are very large and the contents are perishable.

A second blogger writes, "I notice that people who live within a 2-3 mile radius of my local Wal-Mart are better educated, have better access to health care (... a hospital), have more parks in close proximity, join more adult softball teams, and probably go to the dentist more often. .... This is a correlation [that] has to do with where Wal-Mart locates stores."

A third blogger suggests an "exercise effect" due to long walks through large parking lots for large retail stores.

Submitted by Margaret Cibes

=A New Math War?

The Chronicle of Higher Education June 12, 2009 Jeffrey R. Young

This article suggests that Wolfram's new WolframAlphat will create a war over whether their calculus students should be allowed to have WolframAlpha solve their homework. Of course their is nothing special about calculus because Alpha can also solve problems in other math courses, for example statistics. In addition to giving the answer to a problem but Alpha also tells how it found the solution. There is disagreement about whether they should allow the students to use Alpha, but it does not seem that it will lead to war as suggested by the title.

Those who do not want to change their way of teaching will probably say that students cannot use Alpha while those who are willing to change their ways will figure out a way to take advantage of their students use Alpha. Or they can follow the advice of David Bressoud, president of the Mathematical Association of America who says:

Most math instructors now realize that the end-all and be-all of math instruction is not to give students algorithmic facility, but it really is to understand the mathematical ideas and understand how to use them.

Submitted by Laurie Snell

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