Chance News 73

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From The Flaw of Averages, by Sam L. Savage, Wiley, 2009

“Our culture encodes a strong bias either to neglect or ignore variation. We tend to focus instead on measures of central tendency, and as a result we make some terrible mistakes, often with considerable practical import.” (Stephen Jay Gould, cited p. 11)

“Plans based on average assumptions are wrong on average.” (Savage, p. 11)

“Far better an approximate answer to the right question, which is often vague, than the exact answer to the wrong question, which can always be made precise.” (John W. Tukey, cited p. 38)

“I have found that teaching probability and statistics is easy. The hard part is getting people to learn the stuff.” (Savage, p. 49)

“Statisticians often describe a numerical uncertainty using the Red Words, RANDOM VARIABLE, but I will stick with ‘uncertain number.’ …. [S]top thinking of uncertainties as single numbers and begin thinking of them as shapes, or distributions. …. If you think of an uncertain number as a bar graph, you will not be seriously misled.” (Savage, p. 59ff)

“Joe Berkson, a statistician at the Mayo Clinic, developed his own criterion, which he termed the IOT Test, or Inter Ocular Trauma Test, requiring a graph that hit you between the eyes.” (Savage, p. 325)

See Chance News 52 for a review of The Flaw of Averages by Laurie Snell.

Submitted by Margaret Cibes

From Picturing the Uncertain World, by Howard Wainer, Princeton, 2009:

“[O]n average Bill Gates and I can afford a new Rolls and a winter home in Provence.” (Wainer, p. 36)

Submitted by Margaret Cibes

"Using a model of no greater sophistication than that employed by Benjamin Franklin (weather generally moves from west to east), I was able to predict that the are of precipitation currently over Ohio would be hitting New Jersey by tomorrow and would stay over us until the weekend. Any fool could see it. The improvement in forecasting has not been entirely due to improvements in the mathematical models of the weather. The enormous wealth of radar and satellite data summarized into a multicolored and dynamic graph can turn anyone into an expert."

Wainer, in Graphic Discovery A Trout in the Milk and Other Visual Adventures, p. 15

Submitted by Paul Alper


“It is Friday 13th today and though it is still only ten in the morning some awfully unlucky things have happened. I stubbed my toe; the cat caught a shrew and left it in the middle of the kitchen floor, which was unlucky for me because I almost stepped on it, and was even more unlucky for the shrew. It is a black cat too. Clear evidence that superstition works, even for small rodents. Or perhaps not. Yesterday I broke my fingernail, but it wasn’t Friday 13th then, so that wasn’t the fates being lined up against me, it was just an accident.”

Julian Champkin, in “Friday 13th and black cats”, Significance online, May 2011

Submitted by Margaret Cibes

What's in a name?

Peter, Deborah popular names for CEOs
VPR News Morning Edition, 29 April 2011

"If your name is Peter or Deborah, you're more likely to be a CEO. That's what the social networking site LinkedIn found." You can listen to the rest of this Vermont Public Radio broadcast here.

The story was featured in a variety of news outlets:

Discussion Question
A tweeted comment on this site says: "Great analysis, although this can be explained mostly by the age group ..." What are the implications of this? How might you explore them?

Submitted by Jeanne Albert

Scaling the normal curve

Picturing the Uncertain World
by Howard Wainer, Princeton, 2009, p. 171.

This book is a collection of articles that Wainer had authored/co-authored in Chance (2000-2007), American Scientist (2007), and American Statistician (1996).

In Chapter 16, "Galton's Normal," Wainter gives an example of the relative heights of the points on a standard normal curve and of why our sketches of normal curves do not, and cannot, come close to accurate scale drawings.

He calculates that, even if the height at z = 13 were only 1 mm, then the height of the normal curve at the center, z = 0, would be about 5 x 10^30 km, or 5.3 x 10^17 light years. This is equivalent to a height that would be 3.4 million times larger than the universe. (His figures check out.)

Even if the height were 1 mm at z = 6, the height at z = 0 would be 66 km. Thus it still could not be drawn to scale.

Submitted by Margaret Cibes

Defined by rankings

In a data-heavy society, being defined by the numbers
by Alina Tugend , New York Times, 22 April 2011

On a humorous note, the author confesses that since joining Twitter she can't help regularly checking her number of followers. But the more serious question is this: Are we as a society too dependent on numerical rankings? The article quotes MIT professor Sherry Turkle: "One of the fantasies of numerical ranking is that you know how you got there. But the problem is if the numbers are arrived at in an irrational way, or black-boxed, so we don’t understand how we got there, then what use are they? "

The article gives several examples, two of which happen to correspond to stories that were recently discussed in Chance News 71, namely college rankings and New York City's formula for rating teachers.

Submitted by Bill Peterson

Identifying Osama bin Laden

“Matching Science of DNA With Art of Identification”
by Carl Bialik, The Wall Street Journal, May 7, 2011
“DNA and Bin Laden’s Positive ID”
by Carl Bialik, The Numbers Guy Blog, The Wall Street Journal, May 6, 2011

Bialik discusses the prosecutor’s fallacy in the context of reporting about the identification of Osama bin Laden’s body. He does not dispute the identification made by government officials, said to have been based on a number of factors, including DNA. However, he reminds readers that “claimed match probabilities, such as 99% or 99.99%, can be misstated or misleading” and that further details about a DNA test, as well as evidence related to other factors, must be taken into account before having confidence in an identification.

The problem boils down to this: A very small chance of a false positive in a genetic test isn't the same thing as a very large chance of a positive identification.

And he adds:

One complicating factor with interpreting genetic-identity tests … is that the probability of a positive match depends on what other information is available to confirm or reject it — despite the so-called prosecutor’s fallacy that confuses the two. These other factors, collected in what is called “prior odds” of a positive match, can be difficult to measure. “Many factors (e.g., age, sex, appearance, clothes, etc.) are relevant to prior odds, and there are no standard rule[s] for quantify[ing] them, [according to a University of South Texas scientist].”

Submitted by Margaret Cibes

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