!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
CHANCE News 3.12
(11 Aug to 1 Sep 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Prepared by J. Laurie Snell, with help from Jeanne
Albert, William Peterson and Fuxing Hou, 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 in the Multimedia Online
Document Library at the Geometry Center Mosaic
(http:\\geom.umn.edu\) or from their
Gopher (geom.umn.edu) in Geometry Center Resources.
=======================================
What used to be called prejudice is now
called a null hypothesis.
A. W. F. Edwards
========================================
<<<========<<
>>>>>==========>>
OTHER INTERNET SOURCES
Dow Jones historical data
We mentioned the M.I.T. experimental stock market data
last time, that gives the prices of a large number of
stocks, but could not find the historical data for the
Dow Jones averages. Shunhui Zhu informed us that you can
obtain such data by ftp to dg-rtp.dg.com. The directory
is pub/misc.invest/historical-data/index/stocks/
We will put the Dow Jones closing values from 1930 to
1992 and the daily Standard and Poor closing values from
1928 to 1987 in the "Teaching Aids" in the Chance Data
Base.
FROM OUR READERS
James Hilton suggested the following article:
Breakthroughs: Cranberry Therapy.
Discover Magazine, August 1994, p13
Issue: August, 1994
A study carried out at the Women's Hospital in Boston
suggests that women who have a daily cranberry drink are
less likely to harbor bacteria that cause urinary tract
infections.
Since this is a problem mostly for elderly women,
researchers studied 153 women whose average age was 78.
Each day for six months, half the women drank a ten-
ounce glass of cranberry juice while the other half was
given a placebo drink with the taste and color of the
real thing. At the trial's end, 28 percent of the women
taking the placebo had bacteria in their urine. Only 15
percent of those who had the cranberry drink were
similarly infected.
DISCUSSION QUESTIONS:
Is the difference found in this study statistically
significant?
<<<========<<
>>>>>==========>> Milt Eisner suggested the following DNA article: DNA: What the code won't unlock; in the search for evidence, our faith in science can lead us astray.
Washington Post, 14 August 1994, C3
Naftali Bendavid
This is a well-written account of DNA fingerprinting,
much of which was covered in articles we have previously
abstracted. Here are a couple of points we found
interesting.
James Starrs, a professor of law and forensic science
who has participated in many DNA trials, says that
juries are enthralled by color charts and graphs of DNA.
He comments: "I've never seen a jury so alert -- no
understanding, but alert, following the Yellow Brick
Road. I don't know of any other instance in forensics
where the jury is just overwhelmed with a visual and
pictorial presentation." He remarks that he had a
pretty hard time understanding it himself when he
attended a seminar on DNA testing.
A second interesting observation was: in 1987 Fred Zain,
a former DNA technician at West Virginia's criminal
laboratory, testified that the semen from a crime scene
was that of the defendant. Five years later another DNA
test proved this person innocent. An investigation found
that Zain had been falsifying DNA results for years,
apparently on a misguided one-man crusade against crime.
DISCUSSION QUESTION:
If the F.B.I testifies that there is a one-in-a-billion
chance of a match as good as that found in the evidence,
do you think the possibility of a Zain in their
organization was taken into account?
<<<========<<
>>>>>==========>> DNA Fingerprinting; It's a case of probabilities.
Boston Globe, 22 August, 1994
Richard Saltus
Another DNA article, well-written, but again covering
familiar ground. We found this one interesting because
of the quotes from the well know statistician Herman
Chernoff. For example, Chernoff says that experts "will
quote odds of 1 in 100 billion that a DNA match could
have occurred by chance", only to have a lawyer attack
them on the grounds that "there are only 5 billion
people in the world" - a statistically irrevelant fact.
Eric Lander predicts that Simpson's defense attorneys
will use a population genetics argument. The very small
probabilities are obtained by assuming independence
between the alleles at difference positions in the DNA
and also between those obtained from mother and father.
Both assumptions can be challenged by population
genetics. There are ways to give less convincing
probabilities for match that do not rely so heavily on
these assumptions. The lawyers will argue that the
disagreement between what number to quote will show that
the evidence does not meet legal standards for use in a
trial.
The article has an excellent discussion of what the
population genetics argument is all about.
DISCUSSION QUESTION: Do you agree that the remark that
when odds of 1 in 100 billion for a match are given, the
fact that there are only 5 billion people in the world
is a statistically irrelevant fact? If so why?
<<<========<<
>>>>>==========>>
Ask Marilyn (A hat check problem).
Parade Magazine, 21 August, 1994
Marilyn Vos Savant
Charles Price is baffled by the following problem: Take
an ordinary deck of 52 cards and shuffle it. Then turn
the cards over one at a time, counting as you go: ace,
two, three, and so on, until you reach king; then start
over again. The object is to turn over all 52 cards
without having your spoken number match the card in rank
that you turn over.
Charles mentions that he has tried it hundreds of time
and only once turned over all the cards with no match.
He expected it to happen more often. Obviously, he
wanted to know the chance of getting through the deck
without a rank match, but he has to settle for Marilyn
telling him only that the expected number of matches is
4 so he should not expect to succeed very often.
The origin of matching problems like this and the
related "hat check problem" can be found in a book
Montmort written in 1708 to help explain some of the
common games of the time that involved probability-- in
particular, the game of Treise played as follows:
One player is chosen as the banker and the others are
players. Each player puts up a stake. The banker
shuffles the cards and starts dealing calling out the
cards in order ace, two, three, ... ,king. The game
continues until there is a rank coincidence or the
banker has dealt thirteen cards without such a
coincidence. If there is no match, the banker pays the
players an amount equal to their stakes and a new dealer
is chosen. If there is a match he wins from the players
an amount equal to their stake and starts a new round
counting again ace, two, three, etc. If runs out of
cards he reshuffles and continues the count where he
left off.
Montmort remarks that the dealer has a very favorable
game and could easily get several matches before losing
the deal. He despairs of finding the actual advantage
but solves some related problems. He first simplified
the game by assuming that the deck of cards had only 13
cards of one suit. He then found that the probability
of getting through the 13 cards without a match was
about 1/e = .368 providing the first solution to what is
now called the "hat check" problem. Later, with the help
of John Bernoulli he showed that in drawing 13 cards
from a 52 card deck the chance of not getting a rank
match was .357 making it clear that the dealer has a
considerable advantage.
In the problem that Charles suggested you are to go
through the entire deck of 52 cards and this makes the
problem harder because you can have different match
patterns. Your matches might be with distinct ranks or
with the same ranks or both.
We called Charles to see where he found the problem and
he said that it was a solitaire game that a friend had
suggested. Evidently, if you get your letter in
Marilyn's column you become an instant celebrity and get
lots of phone calls. One of his more interesting calls
was from a Steven Landfedler. We called Steven and he
told us a story about a lifelong obsession with this
problem.
He learned this game of solitaire from his grandmother
Enrestine Landfelder who was a gypsy from Eastern Europe
who played a lot of cards. She called it "frustration
solitaire" . Steven was 15 at the time (1956) and tried
to find the chance of winning but it was too hard for
him.
He became obsessed with finding the solution. As
he grew older he was better able to read math
books but this was certainly not his specialty.
He found references that solved the problem but
said things like "carrying out "difficult but
routine calculations" or, worse yet, mentioned
ideas that were a complete mystery to him such as
"using Rook Polynomials". (For a solution using
the connection to Rook Problems see Riordan's
"Introduction to Combinatorial Analysis.")
However, Steven persevered and, using what he had
gleamed from his reading, was able to work out the
solution to his satisfaction. He remarked that he
still wanted to find an explanation that he could
give to his daughter who is a math teacher. We
will try to write up such an explanation. If we
succeed we will put on the Chance Data Base in
Teaching Aids. (Now who's obsessed with this
problem!)
DISCUSSION QUESTION:
For the game of Treize estimate the expected
number of matches before the first run of 13
without a rank match and, from this, estimate the
advantage to the banker.
<<<========<<
>>>>>==========>>
The Price is Right.
Talk given at the summer 1994 MAA meetings.
William T. Butterworth, Barat College, Lake Forest, IL
Paul R. Coe, Rosary College, River Forest IL.
The authors remark that two games "Any Number" and
"Spelling Bee" (played on the TV program "The Price is
Right") involve interesting probability problems.
The "Any Number" game involves trying to guess the
numbers in the price of a car before guessing the
numbers in either of the prices of two other (lesser)
prizes. Each digit 0-9 is used only once among the
three prices, and there are initially four unexposed
numbers in the price of the car and three in each of the
prices of the other two prizes. (The leading 1 in the
price of the car is given and does not count as one of
the digits.) The contestant guesses one number at a
time until all of the digits in the price of one of the
prizes have been guessed. The player then wins that
prize.
The "Spelling Bee" game uses a large board of 30 tiles,
on the back of which 11 have a C, 11 have an A, 6 have
an R, and 2 have all three letters, C, A, and R. The
contestant is allowed to choose from 2 to 5 tiles, the
number being based on the contestant's knowledge of the
price of several small items. The contestant will win a
new car if the word CAR can be spelled using exposed
tiles. Additionally, unexposed tiles worth $500 each
are revealed sequentially so that the contestant can
stop at any time and receive the dollar value of any
unexposed tiles.
In their talk they showed video clips of the T.V.
program and discussed a strategy for stopping in the
"Spelling Bee."
<<<========<<
>>>>>==========>> Suburban taxes are higher for Blacks. Analysis shows.
The New York Times, 17 August 1994, pg. A1
Diana Jean Schemo
Professor Andrew A. Beveridge of Queens College, in a
study for The New York Times of 31 suburbs in the U.S.,
has found that, in 18 of the suburban regions, or 58
percent, Blacks are taxed higher than Whites on homes of
comparable value. The taxes differed by only 3.3
percent, or $38 per year, in suburban Dallas-Fort Worth,
but by as much as 47 percent, or $412 per year, near
Philadelphia. White homeowners were found to have
significantly higher taxes in just one suburb, greater
Miami, while in the remaining 12 there was no
statistically significant difference. The findings were
based on 1990 Census data.
The article considers several possible explanations for
the apparent disparity, and significant attention is
given to questions of intentional versus
institutionalized racial discrimination. For the most
part, deliberate racism by the taxing jurisdictions or
local assessors is downplayed as a likely cause. Rather,
it is suggested that recent demographic trends, which
have seen the flight of businesses from suburbs where
Blacks have moved in and Whites have left, have left a
greater tax burden for the newcomers.
In addition, to keep their tax burden low, wealthier and
more politically organized long-term residents in many
traditionally White areas have pressured local
governments to delay tax assessments, so that new
assessments are more likely to be made only when a house
is sold. The article suggests that Blacks have formed a
significant proportion of recent suburban home buyers,
and have thus been disproportionately taxed at higher
rates.
DISCUSSION QUESTIONS:
1. Professor Beveridge also examined the tax rates in 30
urban areas and found that Blacks paid higher taxes than
Whites on comparable homes in nine cities, or 30
percent, while Whites paid higher taxes in seven cities,
or 23 percent. According to the article this analysis
was therefore "inconclusive". Why?
2. The Census data on which the study was based came
from the responses of Black and White homeowners who
were asked: "What is the value of this property; that
is, how much do you think this house and lot or
condominium unit would sell for if it were for sale?
What were the real-estate taxes on this property last
year?" The answers to the first question were given in
price ranges, to the second in exact dollar amounts. An
estimated tax rate for each house was then calculated by
dividing the amount of taxes paid by the midpoint of
home's price range. The responses of Black and White
homeowners in the selected regions were then compared.
What do you think of this method of analysis? The
article states that the findings were "consistent with
those of other researchers who have used sales data..."
instead of "subjective estimates". What do you think
this remark means?
<<<========<<
>>>>>==========>> Study fuels homosexuality debate: results point to gray areas in definitions.
USA Today, 17 August 1994, pg. 8A
Margaret L. Usdansky
A new study, presented at the meeting of the American
Statistical Association in August has found that "almost
10 percent of American men and 6.4 percent of American
women have had sex with someone of the same gender at
least once in their lives." The article states that
these figures are considerably higher than those
obtained from other recent studies.
The current study, based on a 1988 Louis Harris survey
of 1,834 men and women aged 16 to 50, included questions
about sexual attraction as well as sexual experiences.
According to the article, more than 18 percent of the
men and 17 percent of the women had either had sex with
or were attracted to a person of their own gender, or
both, sometime during their life; but only 4.1 percent
of the men and 2.3 percent of the women had exclusively
same-sex partners. About 10 percent of the respondents
in the survey said they had not had sex with anyone
during the past five years.
To determine the size of the lesbian and gay population
in America, Randall Sell, co-author of the study,
points out that: "It all depends on what your definition
of homosexuality is." The article also discusses the
misconception by many that the population is divided
exclusively into two groups, homosexual and
heterosexual. Instead, it suggests that there is a
broad spectrum of sexual attraction and behavior, and
that people may be at different places along the
spectrum at different times during their lifes. The
article includes the following summary of the study:
Sexual experience in the past 5 years (percentages)
Men Women
Same-sex partners only .8 .3
Same-and-opposite-sex partners 5.4 3.3
Opposite-sex partners only 83.9 86.0
No sexual partners 9.9 10.4
Homosexual experience, attraction since age 15
Men Women
Atrractions but no same-sex partners 8.7 11.0
Same-sex partners only rarely 3.6 2.9
Same-sex partners often 1.9 1.2
DISCUSSION QUESTIONS:
1. The study's findings were based on surveys which
asked people to describe their sexual feelings and
experiences. How reliable do you think this information
can be? Would you be completely truthful in responding
to such questions? Do you think different responses
would be obtained if the questions were asked over the
phone as opposed to in writing? How about in person?
2. The opening sentence of the article states that
"almost 10 percent of American men and 6.4 percent of
American women have had sex with someone of the same
gender at least once in their lives." The 10 and 6.4
percent figures are later in the article given as the
percentages of the survey respondents who have had these
experiences. Why is it possible to extend these
percentages to the whole population?
<<<========<<
>>>>>==========>> A minority of one percent: the truth about homosexuals.
British Daily Mail, 20 August, p 12
This article begins: "An American study has confirmed
British findings that only one percent of men are active
homosexuals-- demolishing the long-standing myth of 10
percent." By "active homosexuals", the article is in
fact referring to those participants who said they had
had a sexual relationship with a member of the same sex,
but not with the opposite sex, in the past five years.
Acording to the article, the study reported that 1
percent of men and 1/3 percent of women were in this
category, which "flatly contradict[s] the estimate of 10
percent for men and women by researcher Alfred Kinsey",
who reported his findings forty years ago.
The article also states that "between 8 and 12 percent
of men and women had homosexual fantasies but never
acted them out." These figures agree with those given
in the USA today article, but they are not emphasized
there. Instead, the USA Today states that "More than 18
percent of men and over 17 percent of women said they
had either had sex with someone of the of the same
gender or had felt attracted to someone of the same
gender - or both". These last figures are also stated
in "Men, women in 3 lands polled on homosexual
attraction" from The Buffalo News, 24 August 1994, which
also says that "the study found homosexuality is far
more prevalent than the standard 10 percent attributed
to Alfred Kinsey".
DISCUSSION QUESTION:
The Daily Mail says the study "demolishes" the 10
percent figure, while The Buffalo News says the study
found that homosexuality is "far more prevalent" than 10
percent. Why do you think the two papers disagree? How
would you define "active homosexual"?
The quote from the USA today article "More than 18
percent ...." is correct but does not seem consistent
with their table. Can you explain why this might be the
case?
<<<========<<
>>>>>==========>>
Taking vitamins. Can they prevent disease?
CONSUMER REPORTS, September 1994, 561-569.
This article begins by describing the "Great Vitamin
Scare of 1994" which resulted after the report of a
study from the National Cancer Institute on the effect
of beta-carotene supplements on 29,000 male smokers in
Finland. This study showed that the incidence of lung
cancer was 18% higher in the group of smokers who took
beta-carotene supplements than the group of smokers who
did not take the supplements. This contradicted more
than a dozen population studies showing that people who
ate foods rich in beta-carotene had a relatively low
lung cancer risk. The NCI study also contradicted
previous studies on the benefits of taking vitamin E.
The article goes on to describe the aftermath of the
study and presents a nice summary of the types of
controlled clinical trials used to study the effect of
vitamins. Results of studies on diet, antioxidants, and
disease (cancer and heart disease) are also summarized.
There is a description of current clinical trials which
should yield information in the next five years on
results of taking vitamin supplements. The authors
conclude that it is better to eat more fruits and
vegetables than to rely on vitamin supplements to
prevent disease.
Following the article are tables of data resulting from
the Consumer Guide's test of 86 different supplement
products: Vitamins C and E, beta-carotene, and multi-
vitamin/mineral formulas. The data sets listed include
the cost, number of pills per bottle, and manufacturer
for each product.
DISCUSSION QUESTIONS:
1. What is your opinion of the effect of taking
vitamins? Does this article convince you that it is
better to eat more fruits and vegetables than to take
vitamin supplements?
2. Try to design some other research studies that would
better determine the effect of taking vitamins on
preventing different diseases.
<<<========<<
>>>>>==========>> Beta carotene, vitamin E, and lung cancer. New England Journal of Medicine 1 Sept 1994, p 611 Correspondence
There are several letters about the study reported in
the April 14 issue of this journal which was a
controlled study to see if vitamin E and beta carotene
supplements could help prevent lung cancer in smokers.
See Chance News.
The first writes: "What was not comprehensible, and was
quite disturbing, was the irresponsible manner in which
the findings of the study were interpreted by its
authors and those of the accompanying editorial." The
writer feels that, since the negative effect of beta-
carotene was significant at the 95% level, the authors
should have been more forthright about accepting this as
a real finding and not just sort of dismissing it as
something that probably happened by chance (since
previous observational studies suggested that beta
carotene was effective). The authors of the original
article argue in response that this writer is going too
far in thinking that a single study ever settles
anything.
Other letter-writers express ideas of what might have
gone wrong as well as explanations for the apparent
negative effect. For example, one writer observes that
animal studies have suggested that alcohol interacts
with beta carotene to produce negative effects. The
writer suggests that, since smokers are known to drink
more than others, it may be that this interaction caused
the negative effect, at least in part.
DISCUSSION QUESTIONS
The authors of the editorial that accompanied the
original study say: One reason they did not take the
negative effect too seriously is that they regard the
observation as hypothesis-generating, not hypothesis-
testing. The reason they give for this is, the original
article had as its hypothesis that beta-carotene had a
positive effect. What do they mean by this and do you
agree with them?
<<<========<<
>>>>>==========>> Beer makes for more trouble than wine.
The Herald(Glasgow), 24 August 1994, p4.
A study on crime and alcohol consumption conducted by
Jan van Dyk, professor of criminology at Leyden
University in the Netherlands, found that beer-drinking
nations have higher levels of assaults and domestic
violence than those countries that prefer wine.
The study was based on surveys in more than 40
countries. Countries with high levels of beer drinking
ranking high in violence included the Netherlands,
Britain, Canada and Australia. Countries with high
levels of wine drinking, Italy, Greece, Spain and
France, had the lowest violence levels. Van Dyk
attributes the association to cultural norms, stating
that drinking beer and getting into fights are part of
"normal recreation patterns" in beer drinking countries.
He recommends that the rest of the world follow the lead
of Scandinavian countries, which heavily tax alcohol.
DISCUSSION QUESTIONS:
(1) How does the evidence presented make a case for
taxation? Should beer be taxed but not wine? How about
taxing beer more heavily?
(2) What are some confounding factors for this
observational study?
<<<========<<
>>>>>==========>> The tyranny of the mean: gender and expectations.
Notices of the AMS, Sept. 1994, pp. 766-769.
Marcia C. Linn
The "tyranny of the mean" refers to people's tendency to
rely on expectations about groups rather than about
individual performance when evaluating professionals,
job applicants, or students. Linn's lead-in example
concerns the medical field: since more men are surgeons
people expect male surgeons to be better than female
surgeons, and will choose a male over a female without
considering these individuals' records. She argues
that, if anything, the opposite tends to be true:
groups with smaller memberships are likely to be more
selective.
She draws an analogy with the "Gambler's Fallacy,"
whereby people expect that black is more likely after a
run of three reds. Thus expectations for the next spin
are confused with expectations for the population
distribution of red and black.
Linn explains that she was discouraged from studying
statistics by advisers who argued that few women went
into such fields, thereby applying population
expectations to her as an individual.
While men score better than women on college entrance
math exams, women earn higher grades in pre-college math
and science courses. Reasoning from the population
expectation leads people to conclude that the exam
scores must be better predictors of success in math and
science. This is the tyranny of the mean: "test score
data supports expectations about success in mathematics
based on group membership." But, Linn argues more women
would be admitted, and more scholarships awarded to
them, if the grades were used as a measure. Having found
that women do better in college courses than men with
comparable S.A.T. scores, M.I.T. a few years ago relaxed
the requirement that students score 750 or higher on the
SAT-M. More women were admitted and the gap between
women and men's grades decreased and there was a general
increase in the overall talent in the class.
The article includes a bar chart that compares the
performance of men and women in all types of college
mathematics courses. From this chart we find
Course Number Percent Ave Scores Female Males
Females
Calculus (Several Universities) 561 29 2.30 2.77
Honors Calculus 173 26 3.22 3.38
Courses beyond Calculus 503 23 2.72 3.00
Calculus 4647 35 2.36 2.41
Pre-calculus 3530 41 2.17 2.38
Regular Math 900 60 2.19 2.52
Remedial Math 2391 48 2.42 2.36
Algebra and Trigonometry 358 39 2.18 2.59
College Algebra 336 52 1.98 2.24
These were taken from a variety of different studies
listed in the article. The men picked a poor choice for
their single victory over the women.
DISCUSSION QUESTIONS
1. Two of the differences between men and women are
marked by footnotes "difference tested and not found
significant." One is marked "difference tested and
found significant. Which do you think these are? What do
you think about the other six?
2. Would it be reasonable to combine all the data to do
a "meta-analysis" to test the hypothesis that women do
better than men in college mathematics courses?
2. In College algebra--marked "not significant"--the
bar for the average female grade appears to be 50%
longer than that for average male grade, and so visually
appears to be one of the most striking differences.
What is going on here?
3. Is the author's explanation of the gambler's paradox
reasonable?
<<<========<<
>>>>>==========>> Gender gap continues to close on S.A.T.'s.
New York Times, 25 August, 1994, A12
The annual report on S.A.T. scores was released by the
College Board. The president of the board said: "Since
1987, women have narrowed the male-female gaps in S.A.T.
scores by six points for math and verbal, even though
they are the majority of S.A.T. takers and come from
families with less income and education than men --
factors which tend to depress scores." .
The 1994 scores for the A.C.T., or American College
Testing, showed that women's scores improved for the
third consecutive year, while men's scores dropped. The
men's average score on this test is only slightly higher
than the female score. It is suggested that the smaller
difference between men and women on this test is because
it is only about a quarter mathematics, and it is on the
mathematics part of the S.A.T. where the large
difference occurs. The article includes a table of
scores for men and women of different ethnic groups.
DISCUSSION QUESTION:
Do you think that the president of the board put too
positive a spin on his remarks?
<<<========<<
>>>>>==========>> Darts trounce professionals in latest duel.
Wall Street Journal, 18 August, 1994, C1
John R. Dorfman
In the continuing contest between the darts and the
professionals, the professionals' stocks had an average
loss of 10% from Feb. 2 through July 31, while the darts
had an average gain of 16.9% in this period. The Dow
Jones was down 5.3% in this period.
In the series of 50 overlapping six-month contests that
were started in 1990, the investment professionals and
the Dow Jones are even, at 25 wins each, but the
professionals are beating the darts 29-21.
DISCUSSION QUESTION
How would you decide if the professionals are doing
significantly better than the darts? Are they?
<<<========<<
>>>>>==========>> Computerized testing runs into trouble Political and technical questions are raised. Chronicle of Higher Education, 3 Aug, 1994, A16 Robert J. Jacobson
Fifteen years ago New York State passed a "truth in
testing law" that required the Educational Testing
Service to release some of their tests with answers. (We
can't seem to find out exactly what information they
have to release). Now the author of this legislation is
trying to extend it to include computer adaptive tests
(CAT).
In CAT tests, the student answers a randomly chosen
question of medium difficulty and then the computer
produces an easier or harder question depending on how
good the answer to the previous question was. Such tests
are claimed to provide the same information with about
half the number of questions used in a more standard
test. CAT versions of the graduate record exam have
been taken by about 18,000 students, and it is expected
to completely replace the pencil and paper version by
1996-7.
Under the proposed bill, testing agencies would be
required to disclose the item pools that were used in
the previous year, along with the correct answers and
rules used to determine test scores. Also, during four
four-week periods, during each year, examinees would be
allowed, immediately after completing a test, to review
all the questions they were given, along with the
answers. The GRE board wants to release complete copies
only once every three years to prevent the pool of
questions from being compromised.
ETS researchers presented a paper in April, at the
annual meeting of the National Council on Measurement in
Education, saying that there were a number of unresolved
questions: the effect of allowing students to review
their questions during a test, the effect of repeated
administrations of the test on their validity, how
students with little computer expertise will be
affected? etc.
DISCUSSION QUESTION
The article states that ETS has demonstrated in a
limited study that scores for a CAT version of the GRE's
General Test are "adequately comparable" with scores
from a paper-and-pencil form, or can be made so. How do
you think they did this study?
<<<========<<
>>>>>==========>> What is a 5.8 really? Ranking figure skaters
Canada News Wire, 18 August 1994
This article discusses a study on the methods used in
scoring and rating figure skaters that was presented at
the recent American Statistical Association meetings in
Toronto. A "greatly simplified" description of the
process is given: Each skater is first ranked by each
judge, and the winner is the one with the highest median
rank.
Although there is typically an international panel of
judges with widely differing backgrounds, according to
the article "they are amazingly similar in their
scoring." For example, after analyzing two years of
competition data, the standard deviation of
approximately 700 scores given to men skaters on
technical merit was .126.
DISCUSSION QUESTIONS:
(1) Why do you think the median rank is used, and not
the mean?
(2) The only talks at the American Statistical
Association that were reported on in the media were
talks that involved sports or sexuality. Do you find
this surprising?
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CHANCE News 3.12
(11 Aug to 1 Sep 1994)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu
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