William P. Peterson
Journal of Statistics Education Volume 10, Number 2 (2002), www.amstat.org/publications/jse/v10n2/peterson.html
Copyright © 2002 by the American Statistical Association, all rights reserved. This text may be freely shared among individuals, but it may not be republished in any medium without express written consent.
by Tamar Lewin, New York Times, February 27, 2002, p. 19.
Columbia University's National Center on Addiction and Substance Abuse (CASA) recently released a study entitled "Teen Tipplers: America's Underage Drinking Epidemic." The report is based on data from the yearly Household Survey on Drug Abuse conducted by the Substance Abuse Mental Health Services Administration. The most recent survey from which information is available included 25,500 people, nearly 10,000 of whom were between the ages of 12 and 20. Underage drinkers accounted for about 25% of all drinking by people in the sample. The 25% figure was highlighted in a press release by CASA's Chairman and President, Joseph A. Califano, Jr., which stated in its opening paragraph that "Children under the age of 21 drink 25% of the alcohol consumed in the United States." This was quickly picked up by news agencies and widely reported.
Although teenagers represent 40% of the sample, they make up less than 20% of the US population. Thus the corrected figure for their overall share of alcohol consumption - confirmed by the government agency that collected the data - is 11.4%. In a subsequent press release, a CASA spokesperson stated that, "By an oversight, CASA did not make the adjustment for over sampling in the Household Survey. Nevertheless, CASA believes that the 11.4% is way too low for several reasons," including unreliability of self-reporting, and that data on "binge" drinkers and children under 12 did not contribute to the figures. Curiously, these concerns were not mentioned in the original press release.
You can read Califano's comments in the online news release for the study.
by Andrea Stone, USA Today, February 28, 2002, p. A4.
The USA Today article presents results from a Gallup poll conducted in December and January, which included 9924 people in nine countries with large Muslim populations: Pakistan, Iran, Indonesia, Turkey, Lebanon, Morocco, Kuwait, Jordan, and Saudi Arabia. Some of the more alarming findings include: 53% of those surveyed had an unfavorable opinion of the US. In six of the nine countries less than 18% believed Arabs carried out the 9/11 attacks The article also includes a breakdown of the sample size by country and country-specific figures for answers to two questions: "Do Western societies show concern for the Islamic/Arabic worlds?" and "Were the attacks on the World Trade Center and the Pentagon morally justifiable?"
The Washington Post article reports that this poll has been criticized by, among others, The National Council on Public Polls, a watchdog group. You can find the Council's position in an online document, Media Coverage of the Gallup Poll of The Islamic World). Citing the 53% and 18% figures given able, the Post colorfully states: "One big problem: those numbers were the product of Enron-like arithmetic - sensational but meaningless amalgamations of results from nine separate surveys."
It is interesting to compare this with the error in the teenage drinking poll we presented earlier. The 53% figure represents an unweighted average of the individual, country-specific percentages. Of course, the size of the Muslim populations in the nine countries varies considerably; for example, Kuwait has fewer than 2 million Muslims, while Indonesia has more than 200 million. The initial faxes from Gallup that went out to USA Today and CNN included the aggregate average along with the country-by-country results. But Post quotes Andrea Stone (the author of the USA Today article) as saying simply, "I didn't do the arithmetic."
To explain the problem with simple (unweighted) averaging, the Post presents the following example.
36 percent of those interviewed in Kuwait said the Sept. 11 terrorist attacks were morally justifiable, compared to only 4 percent in Indonesia. If the results of the two countries were averaged, the result suggests that about 20 percent of these Muslims seemed to view the attack as justified. But that figure falls to about 5 percent if the results were properly adjusted to account for population.
Other problems were cited as well. For example, fewer than half the world's Muslims live in the countries included in Gallup's survey, so it is misleading to interpret the results as applying to the "Muslim world." Moreover, even within the countries considered, non-citizens - even non-Muslims - were included in the sample.
by William Safire, New York Times, February 7, 2002, A29.
by Dan Seligman, Forbes, January 21, 2002
Safire describes how has been chided by readers for confusing odds with probabilities. He writes:
In a column last month I offered my "morning line" on the potential Democratic presidential candidates (Tom Daschle, 4 to 1; Joe Biden, 5 to 1; Al Gore, 2 to 1; and seven others at various odds).
"What Safire doesn't seem to realize," wrote Dan Seligman in Forbes magazine, "is that odds translate into percentage probabilities (e.g., 4-1 means the guy has a 20% chance) and that his probabilities add up to 168%. Alas, mutually exclusive contingencies cannot have probabilities adding up to more than 100%."
That's bad news for Gore, whose chances I have just dropped to 3 to 1, and for Joe Lieberman, now a 12 to 1 long shot. Scratch Biden.
It seems that the column in question appeared last year ("Odds-on Favorites to Run Against Bush," Atlanta Journal and Constitution, June 26 2001, p. 11A). Mathematician John Allen Paulos picked up the error and responded in his online column "Who's Counting."
In his Forbes article, Dan Seligman pointedly observes that "liberal arts graduates control the media, which doubtless helps the prose - but generates endless screwups in numbers." In addition to Safire's trouble with odds, Seligman presents a number of problematic examples from recent media reports. Here are a few of them. A recent Fortune article reported that some ill-fated stocks were selling at more than 100% below their conversion price. The Wall Street Journal reported that Ford's fourth quarter dividend was $270 billion; it seems that no one at the paper noticed this should have been $270 million. Even Forbes itself was guilty of innumeracy: the magazine reported that Federal Express conveyors move packages at 540 feet per second (almost 370 mph!), when the units should have been per minute.
by Paul Recer, Ottawa Citizen, March 8, 2002, p. D15.
Imagine a big survey - really big. Astronomers Karl Glazebrook and Ivan Baldry of Johns Hopkins University announced in January that they had computed the average color of the universe, and it was turquoise. This finding was based on data from a more serious research project called the 2dF Galaxy Redshift Survey. You can read more about it online on the astronomers' Cosmic Spectrum web page.
The project involved a survey of more than 200,000 galaxies, at distances up to several billion light years away. The result was a profile of the energy emitted in the universe at different wavelengths. Glazebrook and Baldry then computed an average color assuming that an human observer was able to see all the light at one time. They included this last calculation "on a lark" in a footnote to their paper, and were quite surprised by the popular media coverage that followed.
This coverage also drew the attention of color experts, who sensed that something was not right. Subsequent examination of the astronomers' computer program turned up a glitch. The galaxy data themselves were alright, but they had been combined with a "nonstandard white index." Alas, when this was corrected, the romantic turquoise was gone, replaced by an unremarkable shade of beige.
The Economist, April 27, 2002, p. 80.
Previous research has found that being tall confers an earnings advantage in the workplace. Three University of Pennsylvania economists recently investigated this phenomenon using two large datasets, Britain's National Child Development Study and America's National Longitudinal Study for Youth. You can download the full 38 page pdf version of their research report. As expected, height and earnings were found to be positively associated. Overall, for white British males, an additional inch of height was associated with a 1.7% increase in wages; the corresponding advantage for white American males was 1.8%. In both countries, the shortest quarter of workers averaged 10% lower earnings than the tallest quarter.
The intriguing twist in the new study is suggested by the article's subtitle: "Why it pays to be a lanky teenager," The researchers discovered that most of the earnings advantage can be attributed to height at age 16. Differences in height later in life or in childhood do not add much additional explanatory power. The researchers proposed social adjustment as a possible explanation. Taller teens may have an easier time participating in athletics and other activities, where they develop positive self-esteem and social skills that contribute to later success.
The Economist reproduces a series plot from the original research report showing heights of US presidents along with the average heights of white males at the corresponding points in history. The data suggest that the electorate does favor tall leaders.
You can listen to a telephone interview from ABC Perth (Australia), with Andrew Postlewaite, one of study's three authors. Postlewaite explains that the study focused on white males to prevent confounding with gender and race effects. He reports that a height effect was also found for women, but that the teenage height differences do not completely explain adult earnings differences. For black males, the height effect was also observed, but the sample was not large enough to give statistical significance.
by Scott McLemee, Chronicle of Higher Education, 19 April 2002, p. A20.
When University of Chicago economist David Galenson tried to bring statistics into discussions of art history, he found out that a quantitative perspective isn't always appreciated. His new book Painting Outside the Lines: Patterns of Creativity in Modern Art (Harvard University Press) is a statistical analysis of creativity in avant-garde painting. He tried to publish his research in art journals, but he reports that editors rejected his papers without even sending them out for review.
Using regression analysis, Galenson identified two kinds of innovation: "experimental" and "conceptual." The innovations of experimentalists, such as Paul Cezanne, evolve gradually over time, as new techniques are developed and refined. By contrast, artists like Pablo Picasso seem to innovate in quantum leaps. In the language of market economics, Galenson views artistic creativity and skill as goods, for which artists are compensated with recognition in their community. Many years later, such recognition is reflected in the value placed on the paintings (though the artists themselves presumably may never see this). Galenson found that the highest valuations for experimentalist paintings tended to be for work produced towards the end of the artist's career, whereas conceptualists tended to produce highly valued work earlier.
It is not hard to believe that critically acclaimed works will ultimately fetch higher prices. The real shock comes from Galenson's claim that by looking at price data he is able to use his model to "predict what the artist said about his work and how me made preparatory drawings." This type of inference may involve too radical a conceptual shift for the art community. As art historian Robert Jensen of the University of Kentucky explains, scholars in his field see their work as "the study of incommensurable art objects, these unique things in space and time. ... We've lost the capacity to generalize about the whole history of art."
by Richard Morin, Washington Post, May 26, 2002, p. B5.
Research by L. Rowell Huesmann, a social psychologist at the University of Michigan, appears to confirm longstanding concerns about the link between watching violent television shows and engaging in violent behavior in real life. Moreover, Huesmann found that girls, as well as boys, are susceptible to the negative effects.
Huesmann's study began in 1977 with a group of 329 boys and girls, who were then in elementary school. Investigators interviewed the children, and developed a measurement scale for television viewing that combined both time spent watching and level of violence. Children in the top 20% on this scale were designated "heavy watchers" of TV violence. In 1992, the investigators followed up with new interviews of the subjects, who were now in their twenties. They also checked for possible criminal records.
After controlling for such variables as socioeconomic status and intelligence, the investigators found that the "heavy watchers" had tended to become more aggressive adults. As described in the article, women who had been heavy watchers as children were twice as likely as the other women in the group to have hit or choked another adult in the last year. Men who had been heavy watchers were three times as likely to have been convicted of a crime. Among the women who had married, the heavy watchers were twice as likely to have thrown an object at their spouse in the last year. Among the men who had married, heavy watchers were almost twice as likely to have grabbed or pushed their spouse in the last year.
Huesmann is an acknowledged expert in this field of research. In 1999, he presented his case before a US Senate Committee on Commerce, Science and Transportation. You can download a pdf transcript of his testimony, "Violent Video Games: Why Do They Cause Violence and Why Do They Sell?" There Huesmann draws intriguing parallels between violent TV programming and tobacco. For example, he observes that both are widely distributed and attractive to children; both have been linked to undesirable effects in numerous longitudinal studies; and for both a dose-response relationship has been observed. Nevertheless, in both cases the absence of controlled experiments has allowed industry advocates to perpetuate doubts about whether the observed relationship is causal.
William P. Peterson
Department of Mathematics and Computer Science
Middlebury, VT 05753-6145
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