Some Notes and Highlights from Journals


Sue Kruse pointed out yet another letter to the editor about the chances of TWA flight 800 being destroyed by a bomb. The article mentions the tale of a business executive who commissioned a study to determine the odds of a plane having a bomb. The odds of him being on such a plane were 1 in 13 million. The probability of being on a plane with two bombs was 1 in 42 billion. Upon learning that fact, he decided to start carrying a bomb with him whenever he flew!

Sue goes on to ask, "can statistics be used to prevent potential outcomes?" For example, suppose the rate of murder is related to body piercings. And suppose people without piercings get murdered more often. Does that mean we can prevent a murder by piercing our bodies?

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Jo Deffner described a conversation he had with a friend about playing powerball. His friend "made the observation that if you want to hit the really big payoff and not have to share the jackpot, then you should be sure to at least include some numbers over 31. The reason is simple. Most people who play the lottery will play the birthdays of family members. Consequently, since there are no birthdays falling above the number 31, fewer people have the higher numbers. As a result, your odds of hitting the big payoff without having to share it are higher."


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Christopher Ayer included an article from the Wall Street Journal comparing public and Catholic Schools (see "Testing Catholic Schools", October 1, 1996, pg A22) New York City's mayor Giuliani wants to shift 1,000 low performing students from over-crowded public schools to empty seats in Catholic schools. The statistics in support of his case are pretty compelling:

Enrollment in courses.
In Catholic schools, 76% of all students are enrolled in a college-preparatory curriculum, compared to only 45% of public school students.

Drop-out rate.
According to a major federal report, public school students had a 7.6% dropout rate between the eighth and 10th grades as compared to a Catholic school dropout rate of 1.3%

Academic Achievement
Both among students who parents did not graduate high school, as well as those whose parents did graduate from high school, Catholic school students get significantly higher test scores than their peers in public schools.

Expectations
Of those students who attended a public school, 34% expected to earn a graduate degree, compared to 59% of those who had been enrolled in a Catholic school.

What are some confounding factors that could account for these dramatic differences? Do you think public schools should try to emulate the model set by Catholic schools?

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Colleen Robitzer

A Dennis the Menace cartoon had Dennis with his brother on his shoulders standing on the scale asking his mother "what is 85/2".

Colleen gave an article explaining that Nynex is taking out some public phones that do not have enough business. A pay phone in a good location brings in $200 a day. Before taking out a pay phone, the neighboring property owner is offered the chance to keep the phone by paying $36 dollars a month and keeping the money it takes in. About 200 of those targeted as unprofitable have been converted to such use. How do you think the neighbors decided if it would be worthwhile?

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Regina Ritschen

Regina was interested in using the surveys to consider differences between the MALS class and the Undergraduate class. She found some interesting differences and raised the question whether these differences were significant or just due to chance. We are beginning to get to the point that we can try to answer some of these kind of questions. Lets look at how we might do this for a couple of her questions:

Regina observes that the undergraduate class has just over 50% women (54 women and 47 men), while the MALS class is nearly 3/4 women (17 women and 6 men). Could this just be chance variation? As she observed, these are samples from two quite different populations: the MALS students and Dartmouth undergraduates. Thus we should look at the proportion of women who registered in each group. The Dartmouth undergraduate student body had 2867 men and 2382 women registered in the Fall term. The MALS program had 11 men and 49 women registered in the fall term. Thus 81% of the MALS students who registered were women and 45% of the Dartmouth undergraduates who registered were women. Thus we can ask individually if the MALS class has a smaller number of women than could be accounted for by chance or if the undergraduate class had too large a larger number of women than could be accounted for by chance. Both of these can be checked using our simple binomial distribution.

Undergraduates exercises an average of 9.4 hours per week compared to 5.8 hours for the MALS students. Their average pulse rate was 64.5 while that of the MALS students was 69. How do we see if these differences are significant? To judge whether these differences could reasonable occur by chance we have to look at the standard error in each case. Recall that this is the standard deviation of the population divided by the square root of the sample size. Here it is not clear what the population is, much less what the population standard deviation is. In such a case we would have to use the standard deviation of the sample itself as an estimate of the population standard deviation. It might be more realistic to find the distribution of the number of families with 1 child, 2 children, 3 children etc. and from this calculate the chance that a random child is a first born child.

Regina noticed also that close to 1/2 the members of each class were first born children. As Claudia noted this could happen in the following simple way. Suppose that 1/2 of all people are first born, 1/4 are 2nd born, 1/8 th are 3rd born etc. Then 1/2 the members of the class would be expected to be first born children. In other words we would have to look of the distribution of these possibilities.

Regina asked a more abstract question that is interesting: Should you trust your intuition or your math? For example, an Eskimo intuitively thinks he should stay where he is and let the animals come to him rather than wander around randomly looking for animals. This would be a great project! You can make a simple mathematical model for this and try it out.

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Yoo Rey Yom

Now we can find the probability that you get the win the lottery. There are choose(45,5) = 45*44*43*42*41/5*4*3*2*1 = 1221759 ways to choose the first five numbers. For each of these there are 45 ways to choose the bonus number. Hence there are 1221759*45 = 54979155 ways to choose the first five numbers and the bonus number so your probability of winning the grand jackpot is 1/54979155 = .000000018189. The number of ways that you can get the first five right and the bonus number wrong is 44. Hence the probability that you win the next largest prize (get the first five right but the bonus number wrong) is 44/choose(45,5)*45 = 0000008003033149564 or a 1 in 1249526 chance as advertised.

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Susan Mielriczuk

Susan found a good example of a common problem with newspaper reports. The Valley News had a story on a recent study claiming to show a link between abortions and breast cancer. The article appeared originally in the Washington Post. Perhaps, for reasons of space, the Valley News only included the first two paragraphs of the article. The first two paragraphs usually try to give the most eye catching aspects of a study. This was a particularly controversial study due to the fact that the lead author is a frequent contributor to anti-abortion publications and admitted that the study was done for political reasons. In addition there were a number of questions about the methodology of the study that were discussed in the Washington Post further along in the article (these things are usually left to the end on the grounds that the public is not interested in such technicalities). The possible bias of the lead author were not discussed in the Washington Post article but was in the New York Times and Boston Globe articles about the study

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Jon Wasluk

Jon discussed an article in the Valley News about the possibility of the price of oil going up this year. Among other reasons it mentioned the harsh winter last year. Jon thought that there were a series of mild winters followed by a brutal one but then the next year is not apt to be brutal. It would be interesting to look at historical records and see if this could be verified.

Jon as well as several other have remarked that they are becoming more aware of statistics in their lives. He mentioned that as he sat watching some people stay on the sidewalk and other cut across the grass he wondered if there were differences in these two classes of people that could be detected by a study. It is interesting to think about how you would design a study to see if there are differences.

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Beth Young

A question by Beth led to an article in the Los Angeles Times documenting the history of the Tobacco Companies attempts to influence public opinion described their early success in the 1950's to influence the news reports:

Advance knowledge was obtained of a story on smoking by Bob Considine for Cosmopolitan Magazine. Information was supplied resulting in seven revisions to the story which was already in type. One negatively aimed program (WNBT) was postponed after discussion (with us). Another TV program (ABC-TV, Martin Agronsky) ended on a favorable note after conferences (with us) . Assistance was provided to the New York Times for a Sunday magazine piece . Special conferences are held with AP, UP and INS science writers." (Hill & Knowlton secret memo, July 17, 1954.)

Hill & Knowlton documents describe sit-down sessions with the New York Times, AP, UP, INS, Coronet magazine, the New Yorker, New York Post, Time, Newsweek, U.S. News & World Report, Business Week, Cosmopolitan, the New York Daily News, the New York World Telegram & Sun, Real magazine, Redbook, Bluebook, Harper's, Look Magazine, Life and Reader's Digest.

According to an Oct. 7, 1954, memo, TIRC researchers pitched tobacco's case in private meetings with Arthur Hays Sulzberger, president and publisher, New York Times; William Randolph Hearst Jr., president and publisher, Hearst Consolidated Publications; Mrs. Helen Rogers Reid, chairman of the board, New York Herald Tribune; Jack Howard, president, Scripps-Howard Newspapers, and Roy E. Larsen, president, Luce Publications. Hill & Knowlton reported that the publishers felt that "the sessions had been most helpful in clarifying the Tobacco Industry Research Committee program."

Tobacco's strategy was reflected in newspaper headlines: "Lung Cancers Found in Non-Smoking Nuns," "Air Pollution Blamed for Lung Cancer," "New Survey Disputes Tobacco-Cancer Link," "Finnish Doctor Challenges Cigarette-Heart Ill Link," "Lung Cancer Linked To Auto Exhaust," "Japanese Research Finds No Link Between Lung Cancer, Cigarettes," "Heavy Smokers With Low Mortality," "Cigarette Theory of Cancer Hit," "Three Scientists Raise Questions About Cigarette-Cancer Theory."

Research committee publicists nurtured such pro-smoking articles as "Go Ahead and Smoke Moderately" in Pageant magazine; "Phony Lung Cancer Scare," in People Today; "Who Says Smoking Gives Men Lung Cancer?" and "Smoke Without Fear," published by True magazine.

Beth noted that when you get an article off of the "Interactive Wall Street Journal'' on the web you not only get the article but you also get the background information on which the article was based. For example, she provided an article reporting that government reports show an increase in consumer spending and personal income and in new home sales. You can find the reports themselves on which these article are based. In general these reports are also available from the relevant government web site but the "Wall Street Journal" provides the relevant information which site to go and often provides even the results of doing so.

In her second article Beth provides an article in U.S.A. Today that discusses the increase in cost of in-state tuition by states. The article provides the average cost of in-state tuition for each state along with the median income and the percent of the median income that this average tuition comes to. This is an interesting mixture of mean and median. An obvious question is: does this mean anything without knowing anything about financial aid in these schools?

She wants to know what if anything we finally decided was the definition of bias in the context of PSAT exams? Since these exams are being used to determine who gets scholarships they are clearly being used to assess merit. If merit is equated with how well they will do in college the PSAT are biased because they women perform better in college even though they perform lower in PSAT.

In general a measurement tool is biased if there is a systematic difference in one direction between what it is attempting to measure and the actual measurement.


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Gail Wolek-Osterhout

Gail read an article in the Valley New that reported on a new book listing the good doctors in New Hampshire and Vermont. How do you decide who are good doctors?

She also reported an interesting article in the Chronicle of Higher education that uses a class survey to find students ideas about families and then compares these with national surveys and national trends. The instructor uses this to get students to start to think about their own ideas of how families should work these days.

A report in the New York Times comparing costs of private colleges and public colleges remarks that "even with the higher tuition increases, however, public colleges and universities are still a bargain compared to private ones." How is this determined?

The article remarks that since 1992 the rate of increase of tuition in public universities has either equaled or exceeded the private college, although the dollar amounts remain smaller. The article only gives a graph showing the rise of college costs from 1986 to 1996. She asks if the pictorial presentation is misleading? Well, if you think of rate of increase as the slope of the curve as you learned in calculus it would be since the slope of the public graph between 1992 and 1996 is clearly less than that of the private schools I assume by rate of increase the author means (tuition at 1996 - tuition at 1992)/(tuition at 1992) which is bigger for the private schools than the public schools so, yes, I think the graph

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Christen O'Connor

Christen, as did some others, "had a lot of trouble letting go of the notion that evolution is progressive". Cheer up, you have another book that you can read that say's it is. Here is a brief review of this book.

The Evening Post (Wellington)

October 4, 1996

HEADLINE: The wild heights of evolution

BYLINE: YOUNG Vanessa

BODY:
CLIMBING MOUNT IMPROBABLE

by Richard Dawkins

(Viking, hb $ 49.95)

Reviewed by Vanessa Young

METAPHORS are often overplayed in science writing. That's because they work. Reading the latest book by Richard Dawkins, Britain's best-known science writer, I'd sometimes wonder if I could handle yet another one. But each metaphor effortlessly took me to a new level of understanding of natural selection and the wonders of the plant and animal kingdoms.

Dawkins' metaphor for natural selection is Mount Improbable, a many-peaked mountain range up which living creatures "climb" as they evolve. On one side it has vertical face, at which creationists gaze and conclude (to their peril, with Dawkins around) that natural selection couldn't have been responsible for the wonderful creatures at the top. Taking us around the other side, Dawkins shows the plains sloping gently upwards in a slow but plausible route up the mountain.

This is the crux of this thesis: Darwin was right. The mountain is scalable. Natural selection happens incredibly naturally, without any conscious thought and definitely not by chance. The wild and enjoyable journey Dawkins takes us on (where we do computer simulations of natural selection, watch spiders build webs and wonder at how wings, trunks, eyes and shells might have developed), is all to convince us of this point. He'll use any metaphor to make sure his reader has understood his argument. This book arose out of a series of lectures and retains the chatty feel: animals use "tricks" and "exploit" their environment.

There are various rules on the mountain; one is that if you are on one peak and decide you like the look of life on another peak, you can't scoot across the valley. You have to evolve upwards. Another rule is that living creatures are in it for themselves. Even bees are not primarily spreading pollen for the plants. Dawkins will not let us think the kingdom an altruistic place.

Dawkins is very much the scientist. The potter wasp is distinguished from the human potter whose designs are "planned by a creative process of imagination in the head of the potter". He doesn't allow human creativity to be subconscious to any extent or to be at all similar to that of the wasp.

But the area he is getting into (the wonder of DNA, the "knowing" it contains) is pushing the borders of conventional science. As he says at the end, DNA codes and patterns "weave a massive database of ancestral wisdom, a digitally coded description of ancestral worlds and what it took to survive in them". This could be another way of describing the collective unconscious.
Dawkins meet Jung?


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Christen started her exploration of the class data by making a series of hypotheses that she wanted to check. For example, Men own more CD's than women. This is an excellent way to proceed. Certainly if you do a survey you need to do this. It is easy, after the fact, to find things that appear to be significant. This goes back to our discussion of the difference between looking at a specific plane crash as compared to any old plane crash and coincidences. Finding at least one unusual aspect of your data is usually easy but if you find something unusual this way you will have to do another experiment and see if this occurs when you predict it ahead of time.

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Susanna Rhodes

In trying to predict number of children as a function of age Susanna wondered why her "best fit line" had value -.05 at 0. How could people age 0 have - .05 children? The best fit line is just an approximation for the dependent variable given the independent variable. It may or may not make sense when you extend it beyond the range of the independent variable. We will talk more about this when we get to correlation which is the next topic.