"The lottery: A tax on people who flunked math."
-- Monique Lloyd=====================================================
The lottery quote appearing on the header was sent to us by
Meredith Warshaw, who commented:
"Thought your readers might appreciate [this] definition from someone on the TAGFAM (families of gifted/talented kids) email list. I imagine that could stir up a fair classroom discussion :-)"
Statisticians take calculated risk trying to shed nerd image.
The Chicago Tribune, 3 August 1996, p1.
Sabrina L. Miller
This article describes how the ASA put on a stat theme day for
Chicago school kids, which apparently turned out to be a bust.
A talk on "Sex, Drugs and Statistics" had no sex, discussed
drugs through the job description of a pharmaceutical worker at Merck,
and presented a statistics lecture via overhead projector. A
talk on "Statistics in Sports" discussed confidence
intervals in the context of an estimate that Chicago Bulls basketball star
Scottie Pippen would shoot 80% for the season--a percentage that
the audience obviously recognized as unrealistic. Bored students
repeatedly interrupted the presentations with wisecracks and
laughter.
Organizers of the event were aware that their first-time attempt at high school outreach would be risky. A teacher at the school noted that, while the idea of making statistics accessible was good, the delivery needed work: "You have to know how to get these kids interested. You can't just stand up there and lecture like a college teacher with an overhead projector for 40 minutes."
DISCUSSION QUESTION:
How do you think this activity could have
been made more successful?
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Web addresses from Chicago talks.
We've just returned from the Joint Statistical Meetings in Chicago, where we heard a number of excellent presentations on statistical education--none of which recommended lecturing for 40 minutes with an overhead!
When we noticed people scrambling to write down URLs, we promised to collect web sites that were referenced at the (non random) sample of talks we attended. Links to these will be included on the Chance Database. Please let us know of any that we missed!
54 STATISTICAL GRAPHICS AND MULTIMEDIA EDUCATION
Stochastic Visualization and the Internet. R.W. West
http://www.stats.sc.edu/~west/asa.html
Interactive Instruction on the Web. B Narasimhan
http://playfair.Stanford.EDU:80/~naras/
110 USING THE INTERNET AND MULTIMEDIA FOR TEACHING
Integrating Computer Oriented Assigments... .E. Mansfield
emansfie@alston.cba.ua.edu [e-mail for Kentucky Derby data]
Datasurfing on the World Wide Web. R. Lock
http://it.stlawu.edu/~rlock/datasurf.html
Fishing for Data Using the Net. S. Turner
http://www.babson.edu:80/faculty/turner/fish/
The Statistical Instruction Internet Pallette. J. Behrens
http://seamonkey.ed.asu.edu/~behrens/siip
A Prototype Multimedi Module. R. Heckerd, et al.
http://milkyway.stats.gla.ac.uk/steps/
A New Approach to Resource Sampling. K Portier et al
http://www.sfrc.ufl.edu/classes/classes.html
130 PUSHING THE FRONTIERS OF ASSESSMENT
Experiences with Alternative Assessment Techniques.
Beth Chance
http://www.uop.edu/cop/math/chance.html
155 THE EFFECT OF COMPUTER AND THE INTERNET ON STATISTICS
The Internet and Reproducible Research. J. Buckheit
http://www.playfair.stanford.edu/~wavelab
201 ALTERNATIVE LEARNING METHODS AND COURSES
Workshop Statistics. A. Rossman
http://stats.dickinson.edu/math/rossman/wshome.html
NOTE: Not all of the addresses worked as we wrote them down at the conference. When we got stuck, we found the AltaVista search engine very helpful. (Name AND Institution AND keyword from talk was often successful). The above have all now checked out.
Armed with the abstract from the conference, readers can probably
find talks we've missed by the same strategy!
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Here are three items from Marilyn vos Savant's column.
Ask Marilyn.
Parade Magazine, 21 July 1996, p6.
Marilyn vos Savant
A reader asks: "Say someone offers you the following bet:
He will toss three coins all at once, if they all turn up heads,
he'll give you $10. And if they all turn up tails, he'll give
you $10. But if they land with either 1) two heads and a tail
or 2) two tails and a head, you have to give him $5. Now--without
stopping to think about it--should you take his bet?"
Marilyn answers, that because this someone probably did stop to
think about it, it's a bad idea to take his bet. She adds that
in this case he will make about $5 for every four tosses of the
three coins, so in the long run you'll lose.
DISCUSSION QUESTION:
Can you verify Marilyn's calculation?
Ask Marilyn.
Parade Magazine, 4 August 1996, p7.
Marilyn vos Savant
A reader asks: "Can you come up with a ballpark figure for
the cost of government regulation and taxes that are included in the
purchase price of a product?"
Marilyn replies that "our research" indicates that about
9% of consumer prices is attributable to federal regulations, 18% to
federal taxes, for a total of 27%. Noting that state and local
regulation and taxes vary widely, she suggests they add about
half again as much, bringing the total to about 40%. Finally,
some experts add "indirect costs" which bring the figure
to 50%.
DISCUSSION QUESTION:
Who do you suppose is the "we"
responsible for what Marilyn calls "our research"? How might you
check on these figures?
In this same week's column, a second reader asks: "Say that
Tom studied a lot of mathematics in college and was campus chess
champion, too. If that's the case, which of the following
statements is more likely to be true? 1) Tom is now a
mathematician. 2) Tom is now a mathematician and plays chess
as a hobby."
Marilyn answers that, although it seems counterintuitive, the
first statement is more likely because it "includes"
the second:
it is true of a mathematician whether he plays chess or not.
The counterintuitive aspect is what Kahneman and Tversky call the
"conjunction fallacy," and the example here is reminiscent
of their famous "Linda problem." But to have the full
punch of that problem, the present example needs to include a characteristic
for which Tom's profile is not "representative"--e.g.,
1) Tom is a waiter. 2) Tom is a waiter and plays chess as a hobby.
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Polling: Box populi.
The Economist, 27 July 1996, p73.
This is a review of the book "The Voice of the People"
by James
Fishkin (Yale University Press). Fishkin, a professor of
government at the University of Texas at Austin, argues that
governments have lost touch with the voice of the people and that
debates on complex issues are increasingly dominated by instant
opinion polls, media sound bites and advertising campaigns by
special interest lobbies.
To determine what the people would believe if they had access
to deeper information on the issues, Fishkin proposes a technique
called "deliberative polling," which he recently implemented
to explore British views on the future of the monarchy. Early in
July, he brought together a randomly selected group of 300
British voters. They were initially polled to get a baseline,
after which they were presented with 3 days of presentations by
politicians, constitutional experts and journalists, before being
polled again.
[Partial results can be found in the AP wire report "The
world in brief: Monarchy a good deal?", The Atlanta Journal and
Constitution, 29 July 1996, p5. At the beginning of the
discussions 26% believed that the monarch should no longer be
head of the Church of England. In the final poll, that figure
was up to 56%--a dramatic change!].
There is a charming reference here to a 1940s film called "Magic
Town", which depicts a Midwestern town named Grandview whose
citizens' opinions always statistically match those of the
country. Jimmy Stewart plays a pollster who uses the town as
a shortcut for measuring national public opinion. But when the
citizens learn what is happening, they feel obligated to make
the most informed choices possible. They arrange for their own
surveys, providing library reference materials at every polling
booth. The reviewer opines that the citizens of Grandview would
have been enthusiastic about Fishkin's approach!
DISCUSSION QUESTIONS:
1. In the deliberative poll on the monarchy, how do you think
the organizers selected the politicians, constitutional experts
and journalists who made presentations?
2. Beyond the usual difficulties in polling, what problems do
you see in justifying an inference of the form "Here is our
estimate of what the population would think if it had time to
fully educate itself on the issue"? Is there a parallel
here with treatments in a medical experiment?
3. Do you see any potential for deliberative polling in
reforming the political process in this country?
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Here is a Web site for those interested in the most up-to-date
information from traditional polls:
http://www.politicsnow.com
PoliticsNow advertises itself as the place "to find the latest political news from ABC News, The Washington Post, National Journal, Newsweek, and The Los Angeles Times on the race for the White House to the battle for control of Congress and beyond."
The website includes a feature called "Poll Track",
which is regularly updated with results from national and state polls.
Some brief selections follow:
STATE POLLS Conducted in Late July
State Clinton Dole Date SourceMichigan 49 39 July 28-30 Mason-Dixon
Michigan 58 35 July 24-29 EPIC/MRA
Missouri 49 37 July 28-30 Mason-Dixon
New Jersey 47 35 July 28-30 Mason-Dixon
New York 57 35 July 27-29 Mason-Dixon
North Dakota 39 47 July 25-27 Mason-Dixon
South Dakota 41 45 July 25-27 Mason-Dixon
Virginia 44 46 July 26-28 Mason-Dixon
RECENT NATIONAL POLLS
Source Date Sample Clinton DoleCBS/NY Times Aug 3-5 N=NA 59 36
NBC/Wall St J Aug 2-6 N=NA 55 35
ABC Aug 1-5 N=1514 55 39
The full Web site also provides extensive charts and graphical
displays of the results. This is a potential source of data for
student projects.
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Business Bulletin
The Wall Street Journal, 25 July 1996 p1.
Decisions go sour...
Paul Nutt, professor at Ohio State University's Fisher
College of Business, has done research indicating that business
managers fail about 50% of the time on decisions ranging from
deciding what products to sell to office renovations.
DISCUSSION QUESTION: Does this mean that businesses should be tossing coins rather than paying MBAs to make their decisions?
Beating the competition...
A study by professors at the Wharton School at the University of Pennsylvania shows that marketing managers may sometimes put their competitive urge ahead of profits. When asked in a product pricing exercise to choose between a low-price, high-profit strategy and a high-price, low-profit strategy, most subjects chose the high-profit route. But when a second group was told that, while the lower price would let them double their profits, it would let their competitors do even better, 60% of the subjects sacrificed profit in order to beat the competition.
One explanation for the results: since market share correlates
with profit, managers may assume that it causes profits. Says
Wharton professor J. Scott Armstrong, "Psychologists call
this social comparison theory. Parents call it sibling rivalry.
Managers call it warfare."
DISCUSSION QUESTION:
What is the analogy with sibling rivalry?
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Study blames cot deaths on smoking parents.
Reuters, 25 July 1996, p8.
Researchers reporting in the British Medical Journal estimate
that crib deaths would be reduced by 61% if smoking were
eliminated from babies' environments. The two year study
included every case of crib death in three regions of England.
Mothers of the 195 babies who died were questioned, and
comparisons were made with mothers of 780 babies whose babies
lived. It was found that 62% of the mothers of babies who died>
smoked, compared with 25% of the mothers of babies who lived.
Researchers added that risks were greater if a mother smoked
before birth of her baby as well as after, and that risk
increased with the level of exposure to smoke after birth.
Having a smoker as a father was also a problem.
DISCUSSION QUESTION:
All of the data appearing in the article
are given above. How do you think the 61% figure (for the
potential reduction in crib deaths) was arrived at?
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Unconventional Wisdom: New facts and hot stats from the social
sciences.
The Washington Post, 28 July 1996, C5.
Richard Morin
White bigotry, black self-hate.
In national opinion polls, nearly one in six whites will agree
with the statement that "blacks have less inborn ability
to learn than whites". This is disturbing, but perhaps not surprising.
What is surprising is that one in eight blacks also say that
blacks are less intelligent. These results come from General
Survey Data collected since the early 1970s by the National
Opinion Research Center at the University of Chicago. Some other
surprises: Morin reports that one in six blacks say that white
homeowners should be "legally allowed to discriminate against
blacks" when selling their homes.
The director of the survey says such results are reminiscent of
the famous survey 50 years ago when white and black children were
shown black and white dolls and asked which they preferred. Many
black children chose the white dolls as being "prettier."
One explanation for such trends is that blacks may have on some level
internalized the prejudices of a predominantly white society.
The researchers also suggested that the recent results may be
due in part to respondents misunderstanding the questions.
DISCUSSION QUESTION:
The actual question on housing (reported
at the end of the article) asked whether respondents would favor
a law allowing a "homeowner to decide for himself whom to sell
his house to, even if he prefers not to sell to blacks." If
Morin's phrasing had been used, do you think the responses would have
been different?
Gold Medal Smiles
Spanish psychologists analyzed the facial expressions of 22
Olympic gold-medal winners from the Barcelona games. During the
moment when they were handed their medals, they smiled about 70%
of the time; they smiled less than 10% of the time immediately
before the presentation and afterwards during the playing of
their national anthems. This despite the fact that the athletes
reported feeling intensely happy throughout the ceremony. These
findings are consistent with other research indicating that
smiling is a social function rather than a spontaneous reaction
to feelings of happiness.
Go, NBC
Writing in the Journal of Sport and Social Issues, Catrioni Higgs
and Karen Weiller report that during the 1992 games, NBC devoted
56% of its coverage to men, 44% to women. (This is billed as
an unofficial Olympic record in its approach to equal coverage.)
In gymnastics, tennis, rowing and cycling, women were featured the
majority of the time; men were more prominently featured in
track and field. Here are some of the data (air times in
hr:min).
Sport Total Air Time % Male % Female
Basketball 18:23 74% 26%
Track/Field 9:10 63 37
Gymnastics 5:48 16 84
Swimming 3:35 48 52
Volleyball 3:05 75 25
Diving 2:11 44 56
Cycling 0:52 40 60
Kayaking 0:27 81 19
Tennis 0:18 33 67
Rowing 0:12 33 67
DISCUSSION QUESTION:
1. If you take away basketball (where, as the article mentions,
intensive coverage was lavished on the men's "Dream Team"),
how do the sexes compare overall for the remaining sports?
2. What reasons can you suggest for different sexes being
favored in coverage of particular sports?
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Time for a Reality Check on the Deficit.
The Wall Street Journal, 1 August 1996, p1.
Roger Lowenstein
Last year, President Clinton had a standoff with Republicans
Congressional leaders over their respective plans to balance the
budget. At one point, Congress shut down the government and then
threatened to not raise the debt ceiling, which would have forced
the country to default. Yet, despite the fact that no agreement
was reached on how the budget should be balanced, the deficit
has gone down dramatically. A year ago, the deficit for 1996 was
projected at $160 billion, about the same as in 1995 but down
from $290 billion in 1992. But most recent estimates put this
year's deficit at only $117 billion. The article cites a
stronger than expected economy and stock market for the drop.
We discussed the difficulty of projecting deficits in an earlier
Chance News (5.02, Item 11). The present article is even more severe in
its criticism. An unnamed economist, who publishes long-term,
macro-economic forecasts for a living, is quoted as saying that
such forecasts are a "joke." Lowenstein asserts that:
"If General Motors doesn't know how many cars it will sell next year,
neither does the Congressional Budget Office. Nor, then, does
it know the sum total of cars, trucks, terrorist-prevention devices
and other goods and services of GM and other companies combined.
If one-year projections can miss by a third, seven-year estimates
are virtually meaningless." He recommends that planners
focus instead on obvious long-term problems such as Social Security
and Medicare, rather than arguing over detailed projections about
exactly when the budget will balance.
DISCUSSION QUESTION:
Is Lowenstein arguing that we should
completely abandon long-range forecasts? Would you agree?
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Making the grade? Disasters have US weighing airline safety rankings.
Chicago Tribune, 4 August 1996, p3.
Andy Pasztor and Bruce Ingersoll
An article reviewed in Chance News 5.07 looked at airline safety
in the wake of the ValuJet disaster. Now, with the recent crash
of TWA flight 800 off Long Island, even more attention is being
paid to this issue. The Federal Aviation Administration (FAA)
and Transportation Department are reportedly considering plans
to publish periodic safety rankings of US airlines. Preliminary
proposals range from a single strict numerical safety ranking,
to a sorting of carriers into categories based on safety systems,
security measures and maintenance records.
Not surprisingly, the airlines vigorously oppose any such system.
Indeed, there is general agreement that the data now collected
by the FAA can be confusing. Says David Hinson of the FAA: "If
you fall because of turbulence during a flight and break your arm,
that's considered and accident, the same as fatalities in
a crash." Furthermore, because crashes really are infrequent, an
airline that looks bad during one review period could look
sterling during the next.
DISCUSSION QUESTIONS:
1. Would you prefer to fly on an airline that had one crash, but no other accidents during the last year or on one that had no crashes, but a dozen instances of passenger injuries from turbulence and other in-flight disturbances? Does a crash in the air "count" the same as one on take-off or landing?
2. A previous discussion question (Chance News 5.07, Item 21) noted that
some observers feel air travel is so safe that crashes can be
viewed as chance events. Would ranking airlines then ignore W.
Edwards Deming's advice that we should not declare winners and
losers on the basis of the variability inherent in a process?
or does that logic not carry over from the manufacturing context
to human safety issues?
3. Speaking about counterterrorism, aviation-security consultant
Frank McGuire says here: "On a scale of 1 to 100, the FAA
rates a 30. I think the public should forget about total security on
an airplane." Do you think McGuire is sure the rating should
not be 28 or 32? What do you suppose his rating system means?
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Warfare 2020: Ones and zeroes, not bombs and bullets, may win tomorrow's battles.
US News & World Report, 5 August 1996, p34.
Richard J. Newman
This piece is part of a Special Report on how technology is
shaping the future of war. One theme here is that electronic
linking of military hardware will dramatically reduce the number
of soldiers needed to wage a war. The opening two-page spread
features a graphic showing historical data transfer rates (in
words per minute) and the number of soldiers needed to cover 10
square kilometers.
War Year Rate (wpm) Technology Soldiers----------------------------------------------------
Civil War 1865 30 telegraph 38,830
WWI 1915 30 telegraph 4040
WWII 1945 66 teletype 360
Gulf War 1991 192000 computer 23.4
Future 2010 1.5 trillion computer 2.4
DISCUSSION QUESTIONS:
1. Does it make sense that data transmission rates were the same
in WWI as in the Civil War? How do you explain the 10-fold
reduction in number of soldiers required per unit area?
2. Make some plots of the data for 1865-1991. How would you
describe the trends?
3. We tried a log transform on the transfer rates and computed
10/(#soldiers) to find the area a single soldier could cover.
Then a plot of area vs. log(rate) looks roughly linear. Would
you be comfortable extrapolating this to log(1.5 trillion) to
predict the number of soldiers required?
4. How do you think the data transfer rate for 2020 was
estimated? The associated number of soldiers?
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School choice data rescued from bad science.
The Wall Street Journal, 14 August 1996.
Letter to the Editor, by Jay P. Greene and Paul E. Peterson
Greene is an assistant professor of political science at the
University of Houston, Peterson is the director of the program
in education policy and government at Harvard. The two have
reanalyzed data from Milwaukee's six-year-old school choice
experiment, where low income families were given the opportunity
to use publicly funded vouchers to pay for private schools of
their choice. Green and Peterson conclude that the program has
been successful in raising student performance. They dispute
the findings of John Witte of the University of Wisconsin, whose
claim that there are no educational benefits has been widely
quoted by teachers unions.
Greene and Peterson explain that the design of the Milwaukee
experiment provided an excellent opportunity for statistical
analysis. The Wisconsin legislature had ruled that, if choice
schools were over-enrolled (it turned out that they were), then
applicants would be admitted at random. The result was to create
randomized treatment and control groups. Comparisons between
these two groups show reading scores of the voucher group were
an average of 3 and 5 percentile points higher than the control
group during the third and fourth years of the study. Math
scores for the corresponding periods were 5 and 12 points higher.
During the first two years, the choice group actually averaged
a fraction of a point lower. The authors say these early
differences were not significant, adding that it takes time for
the educational benefits to accumulate.
Witte's results are criticized because he compared the choice
students with a cross-section of public school students, who on
the whole were much less disadvantaged.
DISCUSSION QUESTIONS:
1. Greene and Peterson call the third- and fourth-year results
"substantively significant." Do you think this phrase
refers to
statistical significance or practical significance?
2. The letter compares Witte's methodology to the infamous 1936
presidential poll in the Literary Digest, which published a
prediction based on 2.2 million responses to a 10 million letter
mailing. Is this analogy apt?
3. Playing devil's advocate, the authors write: "But could
it be that students who weren't doing well in choice schools left
after two years, leaving behind third- and fourth-year students
who would have scored better no matter where they went to school?
To answer this question, we checked to see whether the third-
and fourth-year students' scores had differed significantly from
those of the group as a whole during the first two years. They
had not, confirming that the substantial effects of choice
schools were due to accumulated learning over three to four
years." Do you agree with this argument? After all, there
was no difference between the choice group and the control group
during the first two years, either.
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Omaha hands I-Cubs fifth loss in six games, 6-2.
The Des Moines Register, 16 August 1996, Sports p1.
Randy Peterson
The the manager of the Iowa Cubs (the AAA, American Association
farm club of the Chicago Cubs) is upset about the team giving
up too many runs to the opposition with 2 outs. The paper supports
the complaint by noting that they had given up 224 runs (39.8%
of the total runs they've given up) with two outs. As of Friday
they had played 126 games.
DISCUSSION QUESTIONS:
1. Runs can be scored when there are 0, 1, or 2 outs. If
we naively assume that over the long run 33.3% of the total can be
expected in each situation, would the data reported above really
seem out of line?
2. Does the 33.3% each assumption seem reasonable? How might
you go about checking it?
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Please send comments and suggestions for articles to
jlsnell@dartmouth.edu.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!