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CHANCE News 3.16
(5 Nov  to 10 Dec 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.

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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We've concluded that this is something the
casual user might see once every 27,000 years.

Intel spokesman John Thompson
commenting on the Pentium chip
division error.
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FROM THE INTERNET

David Griffeath's "Primordial Soup Kitchen."

Interacting particle systems is a branch of probability that
uses computer simulation both for understanding the
evolution of the processes and suggesting conjectures for
analytic results. These simulations result in color graphics
that are often also works of art.

of his work and links to others working in this field.
David includes each week a "soup" and "recipe" from his
explorations.  The soup is a color graphics snapshot of a
particle system and the recipe is a description of the
system that produced the "soup". Here is a recipe to give
you a taste of one of his soups.

The Cyclic Particle System.

A prescribed number of colors N are arranged cyclically in a
"color wheel." Each color can only be replaced (eaten) by
its successor (mod N). Cell x chooses a site y at random
from its four nearest neighbors in the two-dimensional array
(with wrap-around at the boundaries). If the color at y can
eat the color at x it does; i.e., site x is painted with the
color from y next time. From a completely random initial
configuration, this probabilistic interaction nucleates wave
activity that self-organizes into a very stable steady state
of spirals.

Check out these soups and also Rick Durrett's movie
for a model for the spread of measles. These and many
more interesting things can be reached from David's
homepage: http://math.wisc.edu/~griffeat/kitchen.html
<<<========<<

>>>>>==========>>

The Journal of Statistical Education is on the Web!

http://www2.ncsu.edu/ncsu/pams/stat/info/jse/homepage.html

Volume 2 No.2 just came out. Read it on the web!
<<<========<<

>>>>>==========>>

Joan Garfield contributed the following article.

Untrue Facts.
Minneapolis Star Tribune,  28 November 1994, p 1E
Sandra Y. Lee

in McCall's Magazine, is "Intimidated by numbers and willing
to believe the worst, people too readily accept distorted or
even false statistics." Citing statistics such as "one in
four college-age women has been the victim of rape or
attempted rape", and "left-handed people die an average of
demonstrates that "many well-known statistics and studies
are distorted, misleading, or just plain false."  Some of
the people quoted in the article are sociologist and survey
expert Judy Tanur, Cynthia Crossen, author of the recently
published "Tainted Truth: The Manipulation of Fact in
America"; and Christina Sommers, who discussed female-
victimization statistics in her book "Who Stole Feminism?"

In addition to statistics on rape and lefthandness, this
increases on Super Bowl Sunday, drug abuse, alcohol abuse
and pregnancy as the biggest problems in public schools,
whether there is a link between drinking milk and diabetes,
whether baldness and birthdays cause heart attacks, and if
our parents had easier lives than we have.

A guide called "How to decipher the 'facts'" is offered,
that helps readers of research presented in the media focus
on the answers to six questions in determining what to
believe: Who was surveyed or studied? How many people were
surveyed and how many responded? How were the questions
worded? How was the problem defined? Who paid for the study?
Was the study published in a peer-review journal such as the
"New England Journal of Medicine?"

Discussion questions:

1. Which of the seven topics discussed have the most
reliable facts? Do you agree with the conclusions of the
author or experts cited regarding each topic?

2. What other questions do you think are important to ask in
determining whether or not to believe the results of a
research study.
<<<========<<

>>>>>==========>>
In the last Chance News we reviewed the book "The Social
Organization of Sexuality" based on a recent large sex
survey. In a discussion question, we asked for possible
explanations for the observation that the median number of
sex partners since age 18 was 6 for men and 2 for women.
Paul Campbell sent two references relating to this issue.

M.Morris, "Telling tales explains the discrepancy in sexual
partner reports", Nature 365:437-440.

Einon, D. (1994) Are Men More Promiscuous than Women?
Ethnology and  Sociobiology 15:131-143.
<<<========<<

>>>>>==========>>
Mike Proctor sent a discussion on the ALLSTAT list about the
UK national lottery.  In this lottery, six numbers are
chosen without replacement from a set of 49 numbers.  You
win the jackpot if your choice of six numbers agrees with
the six chosen.  You win some prize if you have at least
three of the six numbers chosen in your set. The discussion
centered around the following questions:

Discussion questions:

Assume that those who buy tickets choose their numbers at
random.

(1) If the advertisers say that they expect that 250,000
prizes will be given out, how many tickets do they expect
to sell?

(2)  If you buy a single ticket, what is the probability
that you win the jackpot?

(3)  Assume that 14 million tickets are sold.  Estimate the
probability that the jackpot goes unclaimed. How likely is
it to be won by a single person? by exactly k people?

ARTICLES ABSTRACTED

2. Needle program reducing HIV infection rate.
4. Channeling and faith healing.
5. Hackers join hunt for key to a fortune.
6. Birthdays blight hope of lottery jackpots.
7. Slim pickings in National Lottery.
8. Forensic DNA typing dispute.
9. The poor quality of random numbers.
10. No need to fear a lottery shortfall.
11. Cholesterol-lowering drug may save lives.
12. New research supports x-rays screening.
13. Psychic powers: what are the odds?
14. Is a bitter winter on the way?
15. Binge drinking on campuses difficulties.
16. The Bell Curve (Part 2).

<<<========<<

>>>>>==========>>
Marilyn vos Savant

When I play in card games I like to shuffle
the cards several times, but I'm often told
that if I shuffle them too much they'll be
returned to their original order.  What are
the odds of this happening with five to 10
shuffles?
Teri Hitt, Irving, Tex.

In her answer Marilyn considers both the case where Hitt
means a perfect shuffle and an imperfect shuffle. For a
perfect shuffle she correctly states the following relevant
result:

Some magicians are so deft with their hands
that they can shuffle the cards "perfectly,"
meaning a shuffle in which the deck is exactly
halved, and every single card is interwoven
back and forth.  If you do this eight times,
the cards will be returned to their original
position.

A study shows that with ordinary imperfect
shuffles, you need at least seven to make
sure that the cards are randomly mixed.
Six aren't quite enough, but eight aren't
a significant improvement--although the
mixing does improve with each shuffle.

If we interpret Hitt's question in terms of imperfect
shuffles then it is natural to consider the model of a
binomial cut followed by a riffle shuffle introduced and
analyzed by Gilbert, Shannon, Reeds, Bayer, and Diaconis.
can be found in teaching aids on the chance data base.

This analysis provides a simple combinatorial expression for
the probability that the deck will be back to the original
order after k shuffles.  Applying this result to 5 shuffles
gives a probability of 3.21097 x 10^(-56) so this is
probably not what Hitt had in mind.  Marilyn assumes that if
she meant imperfect shuffles she was more interested in
being sure that they are well mixed and suggests that seven
shuffles suffices.

That "seven shuffles do not suffice" is shown by the
following example:

New Age Solitaire

This fascinating game was introduced by Peter Doyle as a way
of bringing home the fact that 7 ordinary riffle shuffles,
followed by a cut, of a 52-card deck are not enough to make
every permutation equally likely. Here is how John Finn
describes the game.

We start with a brand new deck of cards, which in America
are  ordered so that if we put the deck face-down on the
table, we have Ace through King of Hearts, Ace through King
of Clubs, King through Ace of Diamonds, King through Ace of
Spades. Hearts and Clubs are the Yin suits, and Diamonds and

We shuffle the deck of cards 7 times, then cut it, and then
start removing and revealing each card from the top of the
deck, making a new pile of them face-up (so if this were all
we did, we'd just have the deck unchanged after going
through it once, except that the deck would be lying face-up
on the table).

We start the pile for each suit when we discover its ace,
and add cards of the same suit to each of these 4 piles,
according to the rule that we must add the cards of each
suit in order.

Thus a single pass through the deck is not going to
accomplish much in the way of completing the 4 piles, so
having made this pass, we turn the remaining deck back over,
and make another pass.

We continue this until we complete either the two yin piles
(hearts & clubs), or the two yang piles (diamonds & spades).
If the yin piles get completed first, we call the game a
win; it's a loss if the yang piles get completed first.

If the deck has been thoroughly permuted (by having put the
cards through a clothes dryer, say), then the yins and yangs
will be equally likely to be first to get completed.  Thus
our expected  proportion of wins will be 1/2.

But it turns out that after 7 shuffles and a cut, we are
significantly more likely to complete the yins before the
yangs, so our proportion of wins will be greater than 1/2.

John Finn and Jeanne Albert using True BASIC and Charles
Grinstead using Mathematica have written programs to
simulate New Age Solitaire. They can be found in teaching
aids on the chance database. Running these programs shows
that a casino could make about a 50% profit by offering this
apparently fair game and shuffling seven times followed by a
cut.

This raises the question of how many shuffles are necessary
to prevent the casino from making more than they now make on
a game such as craps (about 1.41 percent) by taking
advantage of the cards being imperfectly shuffled. We will
try to answer this next time.
<<<========<<

>>>>>==========>>
Study: needle program reducing HIV infection rate.
The Boston Globe, 27 October 1994, p9.
Associated Press

The New York Times reported results of a two-year study on
needle exchange, conducted by the Beth Israel Medical
Center's Chemical Dependency Institute.  Among the 2500
participants in the exchange program the infection rate was
2%  a year, compared with a 4-7% rate for high-frequency
intravenous drug users in general.

DISCUSSION QUESTION: 1. Very little is said in the article
about how participants were chosen.  Can you think of any
confounding variables, and ways that they might be
controlled for?

2. The article notes that some critics have questioned
whether needle exchange programs that work in smaller cities
would work in New York City.  What issues do you think these
<<<========<<

>>>>>==========>>
Parade Magazine, 27 November, 1994, p.13.
Marilyn vos Savant

"Suppose a person was having two surgeries
performed at the same time.  If the chances
of success for surgery A are 85%, and the
chances of success for surgery B are 90%,
what are the chances that both would fail?"

Marylin gives correct answers assuming independence:  1.5%
that both will fail, 8.5% that A will succeed and B will
fail, 13.5% that B will succeed and A will fail.

DISCUSSION QUESTIONS:

(1) Explain why it is ridiculous to assume independence
in this case.

(2) Try to do your own analysis by making a plausible
guess as to the dependence between these two events.

(3) Do you think that Savant is trying to land a job
with the FBI?

<<<========<<

>>>>>==========>>
Channeling and faith healing--Scam or
miracle?
Parade Magazine, 4 December 1994, p.14.
Carl Sagan

A discussion of scientific arguments against alleged
evidence for supernatural healing and other phenomenon,
which concludes that most faith healing is delusion or scam.
The following interesting calculation in included.  Sagan
notes that roughly 100 million people have visited Lourdes,
France in the last 136 years, many in hopes of being cured
of diseases that are untreatable with modern medicine.  He
states that the spontaneous remission rate for all cancers
taken together is estimated to be one in 10,000 to one in
100,000.  Supposing that no more than 1% of the visitors to
Lourdes are there to treat their cancers, one would expect
to have seen between 10 and 100 "miraculous" cures of cancer
alone.  Yet, Sagan notes, there have been only 64 miraculous
cures of any kind authenticated by the Roman Catholic Church
at Lourdes.

DISCUSSION QUESTION:

What do you think of the statistical analysis above?  Is  1%
a reasonable figure for the percentage of visitors to
Lourdes seeking cancer cures? Seeking medical cures of any
kind?
<<<========<<

>>>>>==========>>
There have been several recent articles in the British press
about Britain's new National Lottery.  Here is a sampling.

Hackers join hunt for key to a fortune.
The Sunday Telegraph, 13 November 1994, Pg. 7
Robert Matthews

"beat the odds" by using computers to choose their six
numbers.  As the article points out, "Mathematicians agree
that if the balls really are chosen at random, no scientific
tricks can beat the system: by definition, randomness cannot
be predicted." However, if there are irregularities in the
balls or in the drum from which they are chosen, players
hope to exploit such defects which could bias the pick
toward certain combinations.

The article describes software called "L25 JustLotto",
marketed by Gemini Consultants, that uses Markov chain
analysis in an attempt to predict future jackpot numbers
from previous ones.  While a correlation may exist between
certain numbers, Dr. David Balding of Queen Mary Westfield
College London comments "the problem is that you could never
benefit from it, because the amount you'd pay out before you
won would exceed your winnings."  The article also mentions
the potential for using neural-network based learning
algorithms to spot patterns in past lottery jackpots. Such
methods are being used to "beat the stock market, and are
rumored to produce substantial returns."

DISCUSSION QUESTIONS:

1.  What do you think Dr. Balding means by his remark?

2.  Do you agree that "by definition, randomness cannot be
predicted."?

3.  According to Professor David Bounds, recognizing
patterns in past jackpot numbers won't help much since "any
deviation from randomness is likely to be so small that it's
going to take forever for it to show up in the data."  What
is the significance of this comment?
<<<========<<

>>>>>==========>>

Birthdays blight hope of big lottery jackpots.
No millionaires as more than a million share the first payout
The Daily Telegraph, 21 November 1994, Pg. 5
Tim Butcher

The first National Lottery drawing produced 1,152,611
winners--those who matched at least three of the six jackpot
numbers ranging from 1 to 49--which was more than five times
the 200,000 winners expected by the lottery's organizers.
especially birthdays and anniversaries, many of which would
be 31 or less, and, in particular, single digits.  The first
draw in fact produced the numbers 3,5,14,22,30, and 44.  The
article also mentions the enormous popularity of the first
lottery--more than 24 million people bought 49 million
pounds worth of tickets.

DISCUSSION QUESTION:

1.  How likely is it that five (or more) of the six numbers
drawn are 31 or less? or that two (or more) of the six are
single digits?
<<<========<<

>>>>>==========>>

Slim pickings in National Lottery.
The Times, 24 November 1994, letter to the editor
George Coggan

No need to fear a lottery shortfall.
The Times, 29 November 1994, letter to the editor
The Director General of the National Lottery

Mr. Coggan is concerned about the possibility that, because
people tend to pick low numbers, (see above article), there
may not be enough money taken in from the sale of tickets to
cover all the prize money.  He points out that while the
first lottery generated two single digit numbers, "sooner or
later" a jackpot combination with three such numbers will
come up.  He estimates that, "if the number 7 had come up
instead of say 44", there would have been a shortage of
around 5 million pounds.

In the reply, the Director General attempts to calm Mr.
Coggan's fears by pointing out that, although in the first
lottery there were many more 10-pound winners (those who
matched three of the six numbers) than predicted, "it is
just as likely that future draws will produce fewer than
expected winners."  The Director also cites "best advice"
and observations of other lotteries in claiming that the
chance is "extremely remote" that insufficient prize funds
will be available in some future lottery.  Finally, in a
remark which almost makes the previous arguments
reassured to know, however, that I have not relied totally
upon statistics or evidence from other lotteries. Camelot's
[the lottery organizer's] license to operate the National
Lottery also requires them to provide substantial additional
funds by way of deposit in trust and by guarantee to protect
the interests of the prize winners in unexpected
circumstances."

DISCUSSION QUESTIONS:

1.  In the reply it is noted that since people generally
don't pick their numbers randomly, "the number of the lower
prizes can vary by up to 30 percent from the theoretical
expectation."  What does this statement mean?

2.  Do you agree with the remark that future lotteries are
just as likely to have a fewer-than-expected number of
winners?  If so, why is it significant?

3.  How might you determine the chance which the Director
General calls "extremely remote"?  What information would
you need?
<<<========<<

>>>>>==========>>
Forensic DNA typing dispute.
Nature, 1 Dec 1994, p 398
Correspondence from R.C. Lewotin and Daniel L. Hartl

These are separate letters from the two well known
biologists who started the current battle over the use of
DNA fingerprinting in the courts by their articles in
Science Magazine (Vol. 254 1745-1750, 1991 and Vol 260 473-
474, 1993. They are responding to the article by Lander and
Budowie in Nature (Vol. 371, 735-738 1995) declaring the end
of the controversy over the forensic application of DNA
technology.  They obviously do not feel that the war is
over.

Lewontin discusses three problems he feels are still to be
dealt with:

The first is laboratory reliability of DNA technology.  He
feels that this problem will not be resolved until the FBI
and other laboratories agree to independent third-party
quality control of their work.

The second problem is calculating probabilities when there
is population heterogeneity and this is the subject of
Hartl's letter.

The third is the jury's ability to understand simple
probability arguments. He does not feel that this can be
resolved by a one-time instruction by a judge. (I guess we
can all agree on that!)

In his letter, Hartl points out that the 'interim' ceiling
principle based on racial databases is a stop-gap measured
intended to be replaced by a more refined method based on
databases from diverse ethnic groups.  He is not convinced
that this will be carried out and fears that the ceiling
principle itself will be dropped.

He points out that differences in allele frequencies in
ethnic groups have been shown to be statistically
significant.  He asserts that Budowie's argument to ignore
substructure is based on the claim that these differences
are not "forensically significant,". He wonders what that
means and who decides if the differences are forensically
significant.

(1) In his letter Lowenten remarks that "it is common for
people to believe that a 1 in 4 chance means that the event
is bound to happen on the fourth trial." Do you think it is
really that bad or did he mean to say that it is bound to
happen in four trials?

(2) In his letter Hartl remarks: "Statistical significance
is an objective, unambiguous, universally accepted standard
of scientific proof. When differences in allele frequencies
among ethnic groups are statistically significant, it means
that they are real."  Do you agree?

(3) Do you think the war is over?
<<<========<<

>>>>>==========>>
The poor quality of random numbers.
Nature, 1 Dec 1994, p 403

Lerrenberg, Landau, and Wong (Phys. Rev. Lett. 69, 3382-
3384; 1992) reported that they had gotten some erroneous
results from simulations related to the Ising model and
suspected problems with the random number generator. Now
Vattulainen, AlaNissila, and Kankaala (Phys. Rev. Lett. 73,
2513-2516; 1994) have shown that their errors can be traced
to the random numbers used. They show that the random number
generators of the type that were used fail to satisfy two
simple tests.  The first is called a "random walker" test.
For an example of this test, carry out a two dimensional
random walk at the origin and let it run for a thousand
steps.  Then record which quadrant it is in. Repeat this a
large number of times and see if the proportions of times
the walk ended up in each of the four quadrants are
reasonably close to 1/4.  For the second test produce 0's
and 1's with probability 1/2 each and average successive
groups of n.  Then see if the proportion of times these
averages are less than 1/2 is sufficiently near 1/2. That
standard random number generators does not give reliable
time ago by David Griffeath and Bob Fisch when they were
developing their award winning "Graphical Aids for
Stochastic Processes"

Discussion question:

What kind of a statistical test would you use to see if the
results of the two tests described are "sufficiently close"
to the expected proportions?
<<<========<<

>>>>>==========>>

Study finds cholesterol-lowering drug may save lives.
New York Times, 17 November, 1994, B11
Gina Kolata

As mentioned in previous issues of Chance News there has
been a lot of controversy about the effect of using drugs to
lower the cholesterol level of persons having a high
cholesterol count.  A number of previous studies appeared to
show that drugs were effective in preventing heart disease
but not in decreasing the overall death rate. To make
matters more mysterious, the excess deaths in those who took
the drugs seemed to be in non-disease related illnesses such
as suicide and homicide or cancer.

It is claimed that these problems have been settled by a
large Scandinavian study involving 4,444 men and women age,
35 to 70, with heart disease and having moderate to high
cholesterol levels.  In this study, half were given the
cholesterol-lowering drug, simvastatin. The others were
given a placebo. The subjects were followed for a median of
5.4 years. Those given the drug had their cholesterol level
decrease by an average of 30 points and had a death rate 30
percent lower than those in the control group.

There were essentially no side effects from the drug and
there was no difference in the deaths in the two groups from
other causes including suicides or cancer.

Experts predict that this study will result in a significant
increase in the use of drugs for lowering cholesterol levels
for those with known heart problems and high cholesterol.
For those with high cholesterol and no heart problems the
situation is more complicated.  Only about 40% of those with
high cholesterol levels die of heart disease, and there is
no good way to predict who these are.  The drug simvastatin
is expensive, costing between \$650 and \$1,000 dollars a
year. It is felt that further studies are needed to
determine the value of the drug for those who do not have a
heart condition.

Discussion questions:

(1) Should we be concerned that the study was sponsored by
Merck, the company that makes simvastatin? (The article
states that it was carried out independently in several
countries)

(2) The investigators said that for every 100 people who
took simvastatin, nine would have been expected to die of
heart disease, but only four did.  Similarly, 21 would have
been expected to have a non-fatal heart attack, but only
seven did.  How do you think they arrived at these
conclusions?
<<<========<<

>>>>>==========>>

Disputing 4 studies, new research supports x-rays as cancer screen.
The New York Times, 30 Nov 1994, B11
Jane E. Brody

There have been four major studies that seemed to show that
annual chest X-rays were not effective in lowering cancer
mortality rates for smokers and former smokers. These four
studies, three in the United States and one in
Czechoslovakia, involved about 38,000 middle-aged men who
smoked.  The studies were judged by the "mortality rate",
which is the number of cancer deaths during the time period
observed divided by the total number in the group followed.
The studies did not show a significant difference in
mortality rates between those screened and those not
screened. This failure to show an overall mortality benefit
led the American Cancer Society to recommend against X-ray
screening for lung cancer.

Now oncologist Dr. Gary Strauss has re-examined the data.
Strauss used a different statistic called the "fatality
rate" to evaluate the result.  The fatality rate is the
number of cancer deaths divided by the number of cancers
detected in the group followed. Using this statistic,
Strauss found a significantly higher fatality rate in the
controls than in those screened.

Discussion questions:

(1) The article remarks that there are 46.3 million current
smokers and 43.5 million former smokers in the United
States.  Do you think that the cost of screening should be
taken into account in considering recommending annual X-ray
screening for all in these two groups?

(2) Survival time can appear to be longer when a cancer is
detected earlier and this is called "lead time bias".  Could
this be a problem with judging the outcomes of a screening
study by mortality rates?  How about by fatality rates?
<<<========<<

>>>>>==========>>
Psychic powers: what are the odds?
New Scientist, 26 November 1994, Pg. 34
John McCrone

This enjoyable article describes the recent psychokinesis
research of Robert Jahn, whose work is "currently the most
respected of PK studies because of its scale and
sophistication...."  Jahn, a professor of engineering at
Princeton, runs the Princeton Engineering Anomalies Research
(PEAR) laboratory but, as the article makes plain, within
mainstream academic circles he is not exactly revered for
this work.

Several experiments are described, but by far his most
extensive study has involved over 100 subjects who together
have logged over 14 million trials of the following
experiment: each subject attempts to psychically persuade an
electronic random number generator to produce more heads or
more tails in a series of 200 "coin flips".  According to
the article, the results are "tiny but highly significant.
The size of the effect is about .1 percent, meaning that for
every thousand electronic tosses, the random event generator
is producing about one more head or tail than it should by
chance alone."

Naturally, the article contains a description of attempts by
skeptics, including members of the Committee for the
Scientific Investigations of Claims of the Paranormal
(CSICOP), to evaluate or even discredit Jahn's work.  In
particular, an experimental subject who is believed to be a
member of the PEAR staff apparently participated in 15
percent of the 14 million trials but was responsible for
half of the total "successes".

Jahn's beliefs about possible explanations for his results
have also come under fire.  The article says that he does
not think that there is a "mental interference with a
physical event but something much more subtle--a distortion
of the laws of statistics themselves....the subjects somehow
distort the 'probability envelope' of an outcome."

DISCUSSION QUESTIONS:
1. The subjects in Jahn's coin flipping experiment sit and
watch "a cumulative line rising or falling on a computer
screen" which charts their progress in producing more heads
or more tails.  As a precaution, the subjects are required
to move the line up for half the time, and down for half the
time.  Why do you think this is necessary?  What kind of
behavior would you expect for the line if the subjects were
causing no effect?

2.  The article says that "there is only a 1 in 5000 chance
that Jahn's results are a statistical fluke."  How do you
think they determined this figure?  What does it mean?
<<<========<<

>>>>>==========>>
Is a bitter winter on the way? Or did the almanac cry wolf?
The New York Times, 11 December 1994, Ideas & Trends
William K. Stevens

In response to The Old Farmer's Almanac's prediction of a
snowier than normal winter for most of the Northeast this
are long-range forecasts?"  The answer varies with the type
of indicator forcasted (temperature, for example, which is
the simplest to predict), and with the time period over which
the prediction extends.  "Two weeks ahead is generally taken
as the limit" for "precision" forcasts, while the Weat her
Service's 6-to-10 day temperature forcast accuracy rates
range from 75 percent in winter, 65  percent in summer,
and lower for spring and fall.  According to the article,
"since forecasters would be right 50 percent of the time just
by chance, 'all the knowledge that's put into the forecast
squeezes out another 10 or 15 percent in the winter and much
less in the summer', said Fred Gadomski, a meteorologist at
the Penn State Univ weather communications  group."

In particular, the article states that "to make accurate daily
forcasts months or a year ahead, as several almanacs try to do,
is impossible", according to many meteorologists.  Instead the
Weather Service tries  to forcast the weather relative to what
is "normal" for a given region.  That is, they give probabilities
that a particular part of the country will experience above-normal,
normal, or below-normal precipitation or temperature for the
upcoming month or season.  Determining these probabilities is
greatly facilitated this season by the return of El Nino, the
marked warming of surface temperatures in the Pacific.

Accompanying the article are two maps of the U.S. with bands
indicating the probability that given regions will experience
warmer-than-normal temperatures and precipitation for the winter
months  December, January, and February.  So, what can the
Northeast expect?  The maps indicate a 55 percent chance for
above normal  temperatures in most of New England (except
norhtern Maine, which shold see below normal temperatures),
and a 50 percent chance for above normal percipitation.

DISCUSSION QUESTION:

1.  Considering the difficulties mentioned in making long-range
predictions, how do you think the Weather Service determines
what is  "normal" weather for a given region?

2.  Do you agree that "forecasters would be right 50 percent of
the time just by chance?"
<<<========<<

>>>>>==========>>
Binge drinking linked to campus difficulties.
The Boston Globe, 7 December 1994, Pg. 1
Richard A. Knox

A survey of nearly 18,000 students at 140 four-year colleges
and universities in the U.S. has found that half the men and
39 percent of the women identify themselves as so-called
"binge" drinkers--at least five drinks in a row during the
last two weeks for men, four in row for women.  Perhaps more
significantly, the Harvard School of Public Health study
found that this drinking appears to have an adverse effect
on the non-binge-drinking students at these institutions.
The study is the first of its kind to examine college and
university alcohol consumption rates on a national scale.

The article reports that almost nine out of ten students at
the institutions that comprise the top 30 percent of alcohol
consumption rates said they had been subjected to a variety
of abuse which they attributed to their alcohol-drinking
classmates.  These abuses included unwanted sexual assaults,
other physical assaults, property damage, and interruption
of study or sleep.

Interestingly, the study concluded that college policies to
and Robert Sherwood, Dean for student development at Boston
College, states that setting the legal drinking age at 21
and not 18 has created or at least exacerbated existing
problems.

DISCUSSION QUESTION:

their survey design?  How reliable do you think the study
is?
<<<========<<

>>>>>==========>>
The Bell Curve - continued.
Part II: Cognitive Classes and Social Behavior

We continue our attempt to describe what is in this  lengthy
book. This has become less necessary with the appearance of
a review by someone who has read the book.  This review is
by Stephen Jay Gould and appeared in the  November 28 issue
of the New Yorker Magazine (Page 139). However, we shall not
give up quite yet.

Part II is almost entirely based upon the National
Longitudinal Survey of Youth (NLSY).  Recall that this study
began in 1979 and follows a representative sample of  about
12,000 youths aged 14 to 22. It provides information about
parental socioeconomic status and subsequent work,
education, and family history.  It also had IQ information
because, in 1980, the Department of defense gave the
participants their battery of enlistment tests to see how
this civilian sample compared with those in the voluntary
army.

In part II the authors seek to see how IQ is related to
social behavior.  They limit themselves to non-Latino whites
to avoid the additional variation of race which they treat
in Part III. Their method is to carry out a multiple
correlation analysis with the independent variables being
cognitive ability and the parents socioeconomic status (SES)
(based on education, income, and occupational prestige) and
a dependent variable which, in the first chapter, is
poverty.  The next seven chapters replace poverty
successively with education, unemployment, illegitimacy,
welfare dependency, parenting, crime, and civil behavior.

IQ scores are standardized with mean 100 and standard
deviation 15 and NLSY youths are divided into 6 groups
corresponding to intervals determined by the 5th, 25th,
75th, and 95th percentiles. Those in these six groups are
labeled very dull, dull, normal, bright, very bright. In
the same way the NLSY youths are also divided into six
groups by the 5th, 25th, 75th and 95th percentiles using the
SES index and labeled very low, low, average, high, very
high.

The authors find that the percentages in poverty for each of
the six socioeconomic groups, going from very low to very
high  are 24, 12, 7, 3, 3.  The percentage in poverty for
each of the six IQ classes,  going from very dull to very
bright, are 30, 16, 6, 3, 2  They observe the similarity of
these percentages and turn to multiple regression to attempt
to see which is more directly related to poverty.

For this they carry out a logistic regression with the
independent variables age, IQ, and SES, and dependent
variable poverty.  Giving IQ and SES, age has little effect
so they concentrate on IQ versus SES.  To do this they plot
two curves on the same set of axes, an IQ curve and an SES curve.
The IQ curve considers a person of average age and SES and plots
the probability of  poverty as IQ goes from low to high. The
SES curve considers a person of average age and IQ and plots the
probability of poverty as SES goes from low to high.  The IQ
curve shows about 26% probability of poverty for very low IQ
decreasing to about 2% probability of poverty for very high IQ.
The SES curve indicates about 11%  probability of poverty for
very low SES score and decreases to about 5% probability of
poverty for very high SES score.  Thus fixing SES and varying
IQ has a significant effect on poverty but fixing IQ and varying
SES  does not have much effect on poverty. It is argued that
this  shows that IQ is more directly related to poverty than is
socioeconomic status.

This same procedure is carried out in the subsequent
chapters to show that being smart is more important than
being privileged in predicting if a person will get a
college degree, be unemployed, be on welfare, have an
illegitimate child etc.  There are some exceptions to this
but the general theme of part II is that it is IQ and not
socioeconomic status that is important in predicting these
social variables.

Little in said about variation while discussing these
examples but in the introduction to part II the authors
remark that "cognitive ability will almost always explain
less than 20 percent of the variation among people, usually
less than 10 percent and often less than 5 percent." (They
give all the regression details in an appendix).  "Which
means that you cannot predict what a given person will do
from his IQ score.  On the other hand, despite the low
association at the individual level, large differences in
social behavior separate groups of people when the groups
differ intellectually on the average."

Discussion questions.

(1)  What is the basis for the author's argument that, "even
though cognitive ability explains only a small percentage of
the variation among people, large differences in social
behavior separate groups of people when the groups differ
intellectually on the average"?

(2) In the introduction to part two the authors state that
"We will argue that intelligence itself, not just its
correlation with socioeconomic status, is responsible for
group differences. ". What statistical evidence would allow
the authors to conclude this?

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CHANCE News 3.16
(5 Nov to 10 Dec 1994)

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