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CHANCE News 4.05
(4 March 1995 to 21 March 1995)
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Prepared by J. Laurie Snell, with help from
William Peterson, Fuxing Hou and Ma.Katrina
Munoz Dy, as part of the CHANCE Course Project
supported by the National Science Foundation.
Please send comments and suggestions for articles to
jlsnell@dartmouth.edu
Back issues of Chance News and other materials for
teaching a CHANCE course are available from the
Chance Web Data Base
http://www.geom.umn.edu/docs/snell/chance/welcome.html
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The average salary of most of the members
of the Sierra Club is $70,000.
Representative Don Young, R-Alaska
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FROM OUR READERS
We failed to find any studies relating to Roger
Pinkham's question about physicians being less likely
to be called in when girls are born than when boys are
born. However, Steven Wells gave us several references
relating to the original question about full moons
including:
Kelly, I. W., J. Rotton, and R. Culver. 1985. The moon
was full and nothing happened. Skeptical Inquirer,
10(2) pp.129-143.
Martens, R., I. W. Kelly, and D. H. Saklofske. 1988.
Lunar phase and birthrate: A 50 year critical review.
Psychological Reports, 63 pp. 923-934
Martens and Kelly provided an update: Psychological
reports, 1994 Aug; 75(1 Pt 2):507-11.
Here is an abstract of this update from Medline.
Martens, Kelly, and Saklofske in 1988 examined 21
studies considering the possible relationship between
lunar periodicities and birthrate. They reported that
the majority of studies uncovered no relationship and
that the positive studies were inconsistent in their
findings. The present update reports on six additional
studies on birthrate and lunar periodicities from five
different countries. None of these studies produced
evidence of lunar periodicities consistent with
folklore or some previous studies.
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Norton Starr sent the following remark:
Regarding CHANCE News 4.05, last item, the one about
Marilyn vos Savant discussing one vs. two engine plane
failures. This is a variation on a classic example
discussed by Mosteller, Rourke, & Thomas in their
"Probability with Statistical Applications", 2nd. ed.,
Addison-Wesley, 1970. See example 3, pages 140-142,
where the safety of two-vs. four-engine planes is
compared, under varying probabilities q of failure
for a single engine. A plane succeeds in its flight if
at least half its engines continue to function. The
four engine plane is safer if q < 1/3 and the two-
engine is safer if q > 1/3. (Of course, for q=0 or 1,
the probabilities are the same)
ON THE INTERNET
"Resampling Stats" is a software package
developed by Julian Simon that allows the user to
simulate a wide variety of chance experiments using a
simple BASIC like programming language.
The value of computer simulations in the understanding
of probability and statistical concepts is generally
recognized today. The way it is used by Simon and co-
author Peter C. Bruce has been the subject of lively
discussions in Chance Magazine and elsewhere. Articles
by Simon and Bruce on the use of Resampling Stats are
available from the Resampling Stats home-page.
For the other side of the coin see "Review of the
Resampling Method of Teaching Statistics" by Jim Albert
and Mark Berliner, American Statistician, May 1994,
Vol. 48, No. 2.
From Resampling Stats homepage you will find examples
of the use of the resampling software including the
resampling approach to solving the problems in Fred
Mosteller's well-know problem book: "Fifty challenging
problems in probability with solutions", Addison-
Wesley, 1965.
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ARTICLES ABSTRACTED
>>>>>==========>> Despite reductions in exposure, lead remains danger to children. The New York Times, 21 March, 1995, C3 Jane E. Brody
This is an excellent review article on current knowledge about the incidence of lead poisoning in children and the effect it has on I.Q. and other learning abilities. In recent years there has been a dramatic decrease in the exposure to lead in the environment. At the same time, studies have led to changes in the level of lead in blood considered dangerous. In 1969 this was 60 micrograms per deciliter of blood and is now 10 micrograms. An estimated three million pre-school-age American children currently have more than 10 micrograms of lead. Silent lead poisoning refers to low levels that are believed to have hidden effects on brain development. Dr. John Rosen, a specialist in the pediatric effects of lead, states that the highest prevalence of silent lead poisoning occurs in African-American children aged 1 to 5 who live in large cities and whose families have marginal incomes. Among children living under these conditions, it is estimated that 33 percent of the African-American children have hazardous amounts of lead in their blood while this is the case for only 17 percent of Hispanic-American children, and 6 percent of White children. One study indicated that every 10-microgram blood level above the 10 danger level at age 2 years led to a 5.8 point decline in overall I.Q. and an 8.9 point decline in achievement test scores by age 10. While there are conflicting studies on the dangers of lead poisoning, recent articles reviewing the existing studies suggest that the dangers are real. However, there are researchers who believe that other explanations should be sought for observed lead-related deficits in I.Q. DISCUSSION QUESTIONS (1) What other explanations might be given for the cause of the observed lead-related deficits in I.Q? (2) What is the relations of studies on lead poisoning and I.Q. to the issue of heritability of I.Q.? <<<========<<
>>>>>==========>> Dirty air can shorten your life. The Washington Post, 10 March 1995 Curt Suplee
An article in the March issue of the "American Journal of Respiratory and Critical Care Medicine" reports on the largest study ever conducted on the health effects of airborne particles from traffic and smokestacks. The study tracked the health histories of 552,138 adults in 151 metropolitan from 1982 to 1989 and compared mortality rates with the amount of fine particle matter such as soot, smoke, and sulfate particles as measured by the EPA. After controlling for age, smoking, etc., researchers found that high sulfate and fine particle levels raised the risk of premature death from all causes by about 15 percent. Death rates from heart disease, lung disease, and respiratory diseases averaged 30 percent higher in the most polluted cities as compared to the cites the least polluted. On the East Coast the preponderance of fine particles are sulfates produced primarily by power plants and industrial sources while on the West Coasts, most are nitrates from automobile pollution. DISCUSSION QUESTION The article comments that "those exposed to the highest concentrations of particles run a risk of premature death about one-sixth as great as if they had been smoking for 25 years". Is that a reasonable way to describe a risk? <<<========<<
>>>>>==========>> Experiment with success. The New York Times, 9 March 1995, A1 Celia W. Dugger
A youth program that worked. The New York Times, 20 March, 1995, A16 Editorial
A million dollar program called the Quantum Opportunity Program financed by the Ford Foundation is reported to have had remarkable success in encouraging under- privileged children to continue their education. In the experiment 25 participants at each of four sites, Philadelphia, Oklahoma City, San Antonio, and Saginaw Michigan, were randomly chosen from a group of students entering ninth grade and whose families were on welfare. These students were given special guidance for a period of four years. The students had adult supervisors who worked with them on a daily basis to give help both in their academic and personal problems. They were paid $1.33 for each hour spent on extra academic study, volunteer work or cultural and educational events and an additional $100 for each 100 hours completed. Their earnings were matched in an account that could be used for college or trade school. The average four year cost per students was $10,600. By the end of the program, 63 percent of the participants graduated from high-school, 42 percent were enrolled in a post-secondary program, 23 percent dropped out of school, 24 percent had children and 2 percent had arrest records. Of a control group, 42 percent finished high school, 16 percent went on to post-secondary schools, 50 percent dropped out, 36% had children and 13% had arrest records. Starting in September, the Labor Department and the Ford Foundation will make a larger test of the program involving 700 participants in five areas. The Times editorial states that "The success of the program shows that careful investments in disadvantaged youths can work". DISCUSSION QUESTIONS. How would you determine if the results of this experiment are statistically significant? The article by Duggar described the Philadelphia program that was considered the most successful. It was clear from the article that they a particularly effective supervisor had been picked. How could you assess the importance of this to the success of such a program? Given the success of this trial, is it ethical to have another trial in which participants are randomly chosen? <<<========<<
>>>>>==========>> Word & Image; Innumeracy<2>. The New York Times, 5 March 1995, Magazine p. 24, Max Frankel
Max Frankel is former executive editor of "The New York Times" and now writes a column on communication for the "Times Magazine". On this occasion, Frankel discusses the poor job newspapers do in communicating information involving numbers. His examples are all taken from the "New York Times", though he assures us that the "Times" is better at dealing with numbers than most newspapers. Frankel starts with a series of examples with missing denominators; for example: "Clinton has reduced the Federal payroll by 98,000". The reader is not told the total number on the Federal payroll, making it difficult to assess the significance of the cut. Frankel comments that: "America needs baseball back, if only because that is the only way it learns to handle rates, probabilities, and context." Frankel next gives examples in which he feels the newspapers handle numbers in a sloppy way or give a false impression of the precision of the numbers provided. His basic example is a report in the "Times" of a study that estimated the economic costs of depression in America to be 14.7 billion dollars. One aspect of this total cost was the loss of earnings of the 18,400 suicides in a year which Frankel describes as "magically rendered as 7.5 billion ($407,608.69 each?)". The original article, in the "Journal of American Psychiatry", provided a detailed justification for this figure. It seems to us that the problem here is just that of having to summarize a lot of information in a short space. Frankel's simpler examples, such as the report that Russian miners were demanding a 150% pay increase (in one paragraph) and wanting their salaries increased by two-and-a-half times (in the next), are more convincing. Frankel discusses several examples from the forthcoming book by John Paulos, "A Mathematician Reads the Newspaper". He admires a conditional probability problem where a positive test gives only a 1 chance in 11 for a patient actually being sick in a situation where a test can be "rightly called 99 percent accurate". He asks "how many newspapers reporting such a study could correctly instruct their readers in the meaning of 99 percent accurate?". The next example shows Frankel's own difficulty in being clear about numbers. He writes: "How many of us had the wit to question, as Paulos does, the judgment that proportionately more blacks (95 percent) voted for David Dinkins because he is black then whites (75 percent) voted for Mayer Guiliani because he is white?" Noting that 80 percent of New York's blacks normally vote Democratic while only 50 percent of whites normally vote Republican, Paulos says it could also be argued that only 15 percent of blacks voted racially as against 25 percent of whites. Frankel should have first just said that 95% of the blacks voted for Dinkins and 75% of the whites voted for Guilianni and then gone on to give Paulos' argument that it is still possible that fewer blacks voted racially than whites. DISCUSSION QUESTION. If you were a science writer, how would you explain what "99% accurate" means for AIDS tests for example. <<<========<<
>>>>>==========>> The lottery paradox and the preface paradox. Pyrrhonian reflections on knowledge and justification. Appendix A, Oxford University Press, 1994 Robert J. Fogelin
Fogelin writes "Since most of our empirical knowledge claims are inductively based, their probabilities typically fall short of 1. It seems, then, that we are willing to say that something counts as empirical knowledge provided the level of probability is suitably high. But however high we set the probability, it is possible to show that fixing the probability at that level leads to paradoxical results". The lottery paradox and the preface paradox discussed in this appendix are meant to illustrate this claim. The Lottery Parodox: In a lottery the probability that any one person wins is very high. Assume that it is above our chosen level. Then we believe that any individual will not win and yet we also believe that someone will win. The Preface Parodox: An author of the history book states in the preface that he believes everything he has written but he has undoubtedly made some mistakes. DISCUSSION QUESTIONS. (1) Do you regard either or both of these situations as paradoxes? (2) If they are paradoxes, are they the same paradox? (3) Assume that all the inmates on death row have been proven guilty beyond a reasonable doubt. Is it true, beyond a reasonable doubt, that all those on death row are guilty? <<<========<<
>>>>>==========>> More evidence shows estrogen therapy cuts risk of heart disease. The Boston Globe, 10 March 1995, A15 Dolores King
Estrogen is taken by millions of American women to treat symptoms of menopause or prevent osteoporosis. Previous studies have indicated that it can cut the risk of heart disease but increase the risk of breast cancer. A study of nearly 100,000 women, reported at the American Heart Association meeting in San Antonio, found that the women who had estrogen therapy had a 30 percent lower risk of dying from all causes then those who had never used estrogen. This result was statistically significant. They also had a 48 percent lower risk of dying from heart disease which was nearly statistically significant. The corresponding results for women under 75 who had estrogen therapy for at least ten years were both highly significant. Jane A. Cauley who presented the results cautioned that the findings may be influenced by factors such as: women who choose estrogen replacement may be more health conscious or more willing to comply with doctor's advice. The article remarks that this is a case where the entire set of risk factors has to be taken into account. The fact that heart disease kills about five times as many women as breast cancer suggests the advantage of estrogen therapy would outweigh the disadvantages. On the other hand , a women with a history of breast cancer who exercises regularly and eats a low-fat diet might not choose estrogen therapy because of being at a lower risk for heart disease than for breast cancer. <<<========<<
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How Shall we Measure our Nation's Diversity?
Chance Magazine, Winter 1995, pp. 7-14.
Suzann Evinger
Black, White, and Shades of Gray (and Brown
and Yellow)
Chance Magazine, Winter 1995, 15-18.
Margo Anderson and Stephen E. Fienberg
The Office of Management and Budget (OMB) provides the
racial and ethnic categories used by federal agencies.
These categories are used, for example, in the census,
in civil rights enforcement, and in demographic
studies. The current categories, established in 1977,
are American Indian or Alaskan Native, Asian or Pacific
Islander, Black, White, Hispanic. The OMB is reviewing
these categories and a wide range of changes have been
recommended to them including:
Change "Black" to "African American" and
"American Indian or Alaskan Native" to
"Native American".
Include "Native Hawaiians" as a separate
category or as part of "Native American"
rather than as part of the "Asian or
Pacific Islander" category.
Add a "Multiracial" category to the list
of racial designations.
In addition to these specific suggestions, more general
suggestions have been made including eliminating racial
and ethnic categories altogether since they appear to
have no real genetic significance.
These two articles discuss the many issues facing the
OMB. Needless to say a revision of racial categories
raises a number of interesting statistical issues such
as: "Should race be self reported?" and "Would
important information be lost by introducing a
multiracial category?".
Anderson and Fienberg make a number of recommendations
which include:
Do away with the labels 'race' and 'ethnicity'
and substitute something like "identified
population groups".
Allow people to identify with more than
one group.
Regarding this last recommendation they remark: "We can
always construct statistical rules for taking multiple
responses and producing aggregate information on the
categories".
DISCUSSION QUESTIONS.
The article continually refers to both racial and
ethnic categories. Is there a difference? If so, what
is it?
What advice would you give to OMB relating to the
questions we have listed that they are considering?
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"How statisticians can help the news media
do a btter job?"
"How the news media can help statisticians
do a better job?"
Chance Magazine, Winter 1995, pp. 24-29.
John C. Bailar III
These two companion articles are based on Bailar's
extensive experience assisting the media reporting
science, particularly in the field of medicine.
In the first article, Bailar stresses that science
writers are professionals just as scientists are and
"have their own interests, professional standards,
technical language, time schedule and so forth".
Bailar gives his own advice, as well as that of an
experienced science writer, as to how to provide
scientific information to a reporter and, through the
reporter, to the public. Much of this advice is very
relevant to our own attempts in the classroom to convey
current scientific knowledge.
Bailar makes six suggestions for ways the news media
can help statisticians do a better job:
Reporters should stress that the outcome
of one study is usually only one part of
a general research program and rarely
should be interpreted in isolation.
The media should not give dead controversies
the impression of still being alive -- for
example, they should not allow tobacco
companies to suggest that the issue of the
danger to health of smoking is still being
debated.
When a controversy is not settled, such as
the possible dangers of magnetic fields, the
media should bring out arguments on both
sides. A recent article ("Explaining EMF:
science writers did it better" by
Sharon M. Friedman, "ScienceWriters",
Winter 1994-95, pp. 7-8) reviewed a large
number of news articles on EMF and found
that the media, as a whole, did not follow
Bailar's advice-but also found three excellent
in depth articles by science writers who did.
News media should be more skeptical when the
pronouncements of individuals or organizations,
including the government, tend to serve some
ulterior purpose. An example would be the
National Cancer Institute announcing dramatic
new progress in curing cancer.
News media should be skeptical about claims that
are not backed by extensive data. Here he
mentions the flurry of news suggesting a
connection between cellular telephones
use and brain cancer.
The News media should continue to educate
the public in the ways that science progresses
-- i.e., the big picture.
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Placing Trials in Context Using Bayesian Analysis.
JAMA, March 15, 1995, pp. 871-875
James M. Brophy and Lawrence Joseph
The authors point out that the standard use of p-values
and confidence intervals to judge the outcome of a
medical trial often lead a doctor to use a drug that
does not take into account information from previous
studies. They argue that a Bayesian analysis can be
used to take into account previous information and can
lead to a different decision about the effectiveness
of a drug.
The authors illustrate this in terms of a recent study
called the GUSTO study that compared two different
treatments, tissue-type plasminogen activator (t-PA)
and streptokinase (SK) for heart attacks. The study
involved 41,021 patients and t-PA had a statistically
significant lower mortality rate (6.3% vs 7.3%,
respectively; p = .001). Since t-PA costs about $2000
and SK only $200, and two similar previous studies
indicated no significant difference, some doctors have
been hesitant to use the more expensive treatment
despite the latest significant result.
A Bayesian analysis is carried out by choosing a prior
distribution for difference in mortality rates for the
two drugs. The authors suggest that people might differ
in how they weight the previous studies. They give three
prior distributions for the mortality difference
corresponding to weighting the previous studies by 10%,
50%, or 100%. For each of these three prior distrib-
utions they obtain the posterior distribution for the
difference in the two drugs given the results of the
GUSTO trial.
From the posterior distribution for the mortality
difference, it is possible to calculate the probability
that t-PA has a lower mortality rate than SK. In
addition, it is possible to calculate the probability
that one drug is "clinically superior". In this
example the authors say that a drug is clinically
superior if the mortality rate is at least 1% lower.
The 50% weighting of the previous studies leads to a
44% probability that t-PA has a lower mortality rate
and a negligible probability that the difference is
clinically significant. Ignoring previous results
altogether, t-PA has a very high probability (99.95%)
of having a lower mortality rate but still only a 48%
chance of being clinically significant.
Thus, a wide range of weightings of the previous
results all provide some justification for not
immediately switching to the more expensive drug.
DISCUSSION QUESTION.
You have a coin that you initially assume is a fair
coin. Jones tosses the coin ten times and gets nine
heads. You then toss the coin ten times and get five
heads. You want to find the posterior probability that
the coin is a fair coin weighting Jones' tosses fifty
percent. How would you do this?
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Statistics as Principled Argument.
Publisher: Lawrence Erlbaum Associations, Hillsdale,
NJ, 1995
Robert P. Abelson
In the preface of this new book, Abelson suggests
students learn to do the statistical analysis for a
study but do not learn what he calls the "narrative"
part for the study. "Ask a student the question, 'If
your study were reported in the newspaper, what would
the headline be?' and you are likely to receive in
response a rare exhibition of incoherent mumblings."
Pursuing the headline question he arrived at the
thesis of his book: "The purpose of statistics is to
organize a useful argument from quantitative evidence,
using a form of principled rhetoric".
The book discusses the many issues involved in making
valid arguments. The author assumes the reader is
familiar with elementary probability, standard tests
such as the t tests, analysis of variance, and simple
issues of research design that might be presented in a
first statistics course. The first 5 chapters review
basic statistical concepts in an informal manner with
no formulas and always from the point of view of using
them to make proper arguments. Chapters 6 through 10
discuss more general topics, such as meta-analyses,
again from the point of view of making valid
statistical arguments.
In all cases the ideas are illustrated in terms of
studies, mostly taken from Abelson's own field of
research, experimental social psychology. One of
Abelson's theses is that problems chosen for study
should be interesting. Consistent with this, he
chooses interesting examples. Here are three of them.
A study found that the average life expectancy
of famous orchestral conductors was 73.4 years,
significantly higher than the life expectancy for
males, 68.5, at the time of the study. Jane
Brody in her "New York Times" health column
reported that this was thought to be due to arm
exercise. J. D Caroll gave an alternative
suggestion, remarking that it was reasonable to
assume that a famous orchestra conductor was
at least 32 years old. The life expectancy for
a 32 year old male was 72 years making the 73.4
average not at all surprising.
A curious reporter found there were an unexpected
number of births on Monday and Tuesday exactly 9
months after the famous New England blackout of
1965. He wrote an article suggesting the obvious
causal effect. The detective work of a curious
statistician found that on Mondays and Tuesdays
more children born by about the same number that
the reporter found. Further, he found that doctors
prefer to schedule induced labor or Cesarean
operations at the beginning of the week, which
provided an explanation for the excess births on
Mondays and Tuesdays.
In 1968 Rosenthal and Jacobson designed a study
for what they called the "Pygmalion effect in the
classroom". They told elementary school teachers
that certain students in their class, called
"bloomers", had been identified by a special test
as being likely to display future excellence.
These students were, in fact, randomly chosen
from the class. The researchers hypothesized
that the bloomers would receive extra attention
and do better in future tests. This was verified.
. One observation was that the mean I.Q. scores of
the bloomers were 4 to 6 points higher than those
of the control group, which caused a great deal
of controversy. The meta analysis of 18 further
studies did not, initially, support this I.Q.
finding; but further analysis did in the studies
where the teachers had not had previous contact
with the students.
This last example, used to illustrate meta-analyses,
has been discussed recently in connection with the book
"The Bell Curve".
In his preface Abelson remarks: "I have always wanted to
write a statistics book, full of tips, wisdom and wit."
He has certainly succeeded! On the back cover Abelson
remarks he is not also the Robert P. Abelson who sings
in the Yiddish theater in New York.
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CHANCE News 4.05
(4 March 1995 to 21 March 1995)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu
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