!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

               CHANCE News 4.04
              (16 February to 3 March 1995)


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Prepared by J. Laurie Snell, with help from 
William Peterson, Fuxing Hou and Ma.Katrina 
Munoz Dy, as part of the CHANCE Course Project 
supported by the National Science Foundation.

Please send comments and suggestions for articles to
jlsnell@dartmouth.edu

Back issues of Chance News and other materials for
teaching a CHANCE course are available from the
Chance Web Data Base
http://www.geom.umn.edu/docs/snell/chance/welcome.html

      ===========================================
      Statistics are the heart of democracy.
                                  Simeon Strunksy
      ===========================================

Note: The deadline for applications for the Chance
Workshop at Dartmouth this summer is March 15.  
A description of this workshop appears at the end
of this Chance News.

FROM OUR READERS

Marty Gray sent these comments on the "Bell Curve"

My interest in "The Bell Curve" started from Gould's 
review in "The New Yorker", in which he tore into M&H's 
(Murray and Herrnstein) statistics stating that it (the 
book) contained its own refutation.  Unfortunately, 
Gould echoed M&H's ignorance of R^2 as it applies to 
logistic regression except that M&H correctly dismissed 
it as not useful and Gould assumed they were hiding 
something.  

It appears that none of the three understood that R^2 
is not a useful statistic in logistic regression.  
Gould also excoriated M&H for not including scatter 
plots in their longitudinal study.  Scatter plots of a 
binary variable are of little use since the dots 
cluster and blend on 2 lines providing little insight. 
It would have been more informative if standard error 
bars had been included in their (M&H's) graphs. Let's 
just say I was disappointed with Gould's math knowledge 
and his attack, in ignorance of logistic regression, on 
another's professionalism.

 It's particularly galling as the book needs to be 
critiqued from a perspective that minimizes its use as 
racist propaganda, not one that just accretes reviewer 
error. The purpose of statistics is to condense and 
accurately portray information which can then be 
utilized by various consumers. Policy decisions need to 
be made on facts, not pre-slanted junk designed to 
garner large constituencies.

The areas where I think M&H are most vulnerable from a 
purely technical point of view are in failing to 
discuss more completely cause and effect versus 
correlation.  People tend to confuse these. Also, their 
two main variables, IQ and SES, are somewhat positively 
correlated. This can distort the charts. It would tend 
to understate the importance of SES on most of their 
results. Also, the charts would have been more 
informative if the variables were stripped of their 
correlates before plotting. I am looking forward to see 
what other studies reveal.

DISCUSSION QUESTION
How is R^2 be defined for logistic regression? Since 
JMP gave it to the authors, why shouldn't they use it?
                  <<<========<<


>>>>>==========>>
Roger Pinkham commented on the sex ratio discussion in 
the last Chance News:

Your latest reminded me of something that happened to 
me years ago.  My first wife's grandfather was a 
doctor, and I found his hand written records of some 
1500 births he had "attended".  Sometimes he was not at 
the actual birth but went as soon as called or 
notified. 

I was excited because I had heard from a number of 
nurses that those who work in hospitals "know" that 
more babies are born near the full of the moon, and I 
had always wanted to check the truth of the statement.  
I set about sniffing around in the data and found to my 
complete bewilderment that nearly sixty percent of the 
listed births were boys!  Befuddled I mentioned my 
bewilderment to a doctor friend.  He was not at all 
surprised, and told me that often when girls were born 
a physician was never called.  Thus I never did get to 
answer my question.  

I have been told that such as study has been done, but 
I do not know who, when, or where.  Your readers might 
be interested in the question and/or know where 
acceptable, accessible data might be.  

Editor: If anyone knows about such a study please send 
us a note.
                  <<<========<<


>>>>>==========>>
Note: "Chance Magazine" arrived as we were finishing 
this Chance News.  The following articles would be of 
particular interest to our readers.

    How shall we measure our nation's diversity? 
    by Suzann Evinger

    Black, white, and shades of gray (and brown and
    yellow) by Margo Anderson and Stephen E. Fienberg

    How statisticians can help the news media do a
    better job, by John Bailar III

    How the news media can help statisticians do a
    better job, by John Bailar III.

We will abstract these in the next Chance News.
                  <<<========<<


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

ARTICLES ABSTRACTED


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


>>>>>==========>>
New research denies gene-race connections.
The Post and Courier (Charleston, SC), 21 Feb. 1995, p4.
Donna Alvarado


Luca Cavalli-Sforza is a well known Stanford population 
geneticist who heads the Human Genome Diversity 
Project. At the annual meeting of the American 
Association for the Advancement of Science, he talked 
about this project and about the concept of race.  He 
said "I find the term 'race' pretty useless." Evidence 
from his study and others suggests traits we think of 
as determining "race" such as skin color are not 
necessarily good markers for more important genetic 
variations.

For example sickle cell anemia, which has been viewed 
as primarily a disease of Black people, is also found 
among some Southern Europeans as well as Africans, and 
not found in some South African tribes. In a recent 
book Cavalli-Sforza, synthesized 50 years of research 
in population genetics and found a wide range of 
genetic variation among both African and non-African 
groups. This book contains more than 500 color-coded 
maps showing areas of genetic similarity.  These maps 
show that genetic diversity of populations is better 
explained by geographic origin than by skin color.

DISCUSSION QUESTIONS

(1) Why do we classify people by race?  In light of 
this research should we?
                  <<<========<<


>>>>>==========>>
A hospital sees gain for Blacks on cancer.
The New York times, 22 Feb. 1995, C10.
Warren E. Leary


National figures indicate that Blacks who get cancer 
have a poorer survival rate than whites.  
Investigators, at St. Jude Children's Research Hospital 
in Memphis, made a study of cancer patients treated 
over a 30-year period and found no difference in 
survival rates between Blacks and Whites among their 
patients.

The results of the study were reported in the current 
issue of the "Journal of the American Medical 
Association".  Researchers followed 798 African-
American and 4,507 White children treated at the 
hospital.  In the early part of the study, from 1962 to 
1983, the survival rate for Black children was 37 
percent as against 50 percent for White children. From 
1983 to 1992 the survival rate for Blacks was 67% and 
for Whites 66%.  Most of the improvement came from new 
ways to treat a particular form of cancer from which 
Black children had a very low survival rate.

The St. Jude researchers said that their results did 
not contradict other studies because Black adults with 
cancer generally are diagnosed later, have less access 
to quality health care, etc.  However, their study does 
suggest that the difference can be decreased or 
possibly wiped out if the two groups are treated 
equally. At St Jude, patients are given the most modern 
treatments and are treated at no charge if they have no 
insurance. In addition to treatment, extensive 
supportive care is given for the patient and the 
patient's family which can also affect the outcome.

DISCUSSION QUESTION

(1) Was there a significant difference in outcomes of 
the two groups considered over the entire period of the 
study?  

(2) Was it necessary to restrict the period to the 
second half to be able to say that there was no 
significant difference?  Is this fair?
                  <<<========<<


>>>>>==========>>
The box problem: to switch or not to switch.
Mathematics magazine, Feb. 1995,  p27.
Steven J. Brams, D. Marc Kilgour


This article discusses the paradox usually called the 
"envelope paradox".  You are asked to choose at random 
one of two envelopes, each of which contains a certain 
amount of money.  You are told that one has twice as 
much money as the other. You open the envelope and find 
that it has x dollars.  You reason that the other 
envelope has 2x dollars with probability 1/2 and x/2 
with probability 1/2.  Thus the expected value of the 
amount in the other envelope is 1.25x so you should 
switch which seems absurd. 

The author points out that, to calculate the expected 
value if you switch, you need to know the apriori 
probability that specific amounts of money were put in 
the envelopes.  Given this, he shows that you should 
switch if and only if the probability that you have 
the better envelope is less than 2/3.  He proves that 
this condition must always be satisfied for at least 
one possible value for the amount in your envelope, 
and gives an example of an apriori distribution where 
it is always satisfied.  In this case you should, 
indeed, always switch!

DISCUSSION QUESTION

(John Finn)  Assume that you are told that one envelope 
has $5 and the other has $10 and choose one at random.  
Before looking in the envelope you can still argue that 
the other envelope has x/2 or 2x with equal probabilities 
and so you should switch.  Here however, it is very clear 
why this argument is nonsense. Why? 
                  <<<========<<


>>>>>==========>>
Ask Marilyn.
Parade Magazine, 19 Feb. 1995, p22.
Marilyn vos Savant


A reader asks:  

     "If one couple eats lunch at a cafeteria 
      twice a week (the day of the week varies), 
      and they see another couple about 75% of the 
      time, is there a logical reason for the first
      couple to assume the second couple eats there 
      more often than the first couple does?"

Marilyn answers yes, assuming the couples have lunch at 
the same time, but vary their days at random (she 
implicitly uses independence as well).  Even though she 
describes the venue as the school cafeteria, she 
assumes all seven days of the week are equally likely.  

Her reasoning goes as follows.  If both couples eat 
once a week, they have a one in seven chance of 
meeting.  If couple #2 now goes twice a week, couple 
#1's chances of seeing them double to two in seven.  
Now, if couple #1 also goes twice a week, their chances 
of seeing couple #2 double again, to four in seven.  
But since, reportedly, they see couple #2 more often 
than that (three times in four), they can conclude that 
couple #2 dines there more often.

DISCUSSION QUESTION:

(1) Continuing Marilyn's line of reasoning, if you now 
go three times a week,  your chance of meeting your 
friends going twice a week doubles to 8/7.  Help!  What 
is wrong?

(2) Consider the following model for selecting one 
week's dining dates (two lunches for each couple).  Put 
7 cards, labeled Su, Mo, Tu, We, Th, Fr, Sa in a box.  
Couple #1 draws two at random without replacement 
(which determines their days of dining).  The cards are 
marked and then returned to the box.  Couple #2 then 
draws two cards at random from the box.  Zero, one or 
two of these will be found to have marks;  these 
correspond to meetings.  What are the chances of each?  
At what fraction of lunches will the couples meet in 
the long run?

(3) If each couple goes twice a week, estimate the chance 
that they meet at least 75% of the time over a period 
of a year. 
                  <<<========<<


>>>>>==========>>
Ask Marilyn.
Parade Magazine, 19 Feb. 1995, p22.
Marilyn vos Savant


Another reader writes:  

    It is my contention that speeding
    on the interstate highway is not 
    dangerous. Is there any evidence that 
    those who regularly speed have a higher 
    incidence of accidents?  I believe other 
    behavior really causes accidents--like
    unsafe lane changes, poor use of brakes 
    and tailgating.  If I'm correct, what
    is the purpose of ticketing speeders, 
    other than generating revenue?"

Marilyn says this is a good example of how to use good 
statistics to reach bad conclusions.  She cites the 
following data from the National Highway Traffic Safety 
Administration, which show the relative speed involved 
in U.S. auto accidents in 1993 (speeds appear to be 
rounded to nearest 5 mph):

20 mph or less .......   2.0%
25 or 30 mph .........  29.7%
35 or 40 mph .........  30.4%
45 or 50 mph .........  16.5%
55 mph ...............  19.2%
60 or 65 mph .........   2.2%

Because so few accidents are recorded at high speeds, 
one might erroneously conclude that it is safe to 
travel at high speed.  Marilyn attributes this to the 
fact that drivers are typically observing the speed 
limit when they have an accident.  Thus the data 
"amount to nothing more than a chart of average driving 
speeds, recorded only because an accident occurred."

She also notes that it is also erroneous to assume that 
people who speed don't tailgate or make bad lane change 
and braking decisions.

DISCUSSION QUESTIONS:

(1) Marilyn's statement about "a chart of average 
driving speeds" suggest that speeds recorded at 
accidents constitute a representative sample of all 
driving speeds.  Do you agree that this is so?

(2) I (Bill Peterson) recall a question on my driver's 
license exam about the conditions under which most 
accidents occur.  The answer was daylight conditions, 
fair weather on a straight road.  Does this mean 
driving winding roads at dusk in an ice storm is safer?

(3) Suggest a measure of relative safety at each 
driving speed.  Do you think it is possible to get the 
data to compute such a measure?
                  <<<========<<


>>>>>==========>>
Studies find death penalty tied to race of the victim.
The New York Times Feb. 24, 1995.
Erik Eckholm


This is a survey of the studies designed to see if 
there is bias against Blacks in capital punishment.
The writer discusses this issue in connection with  
New York state preparing to revive the death penalty.

While there has been a long time concern that the race 
of the defendant would affect the chances of being 
given the death penalty, in fact, studies have shown 
that the significant distinction is the race of the 
victim.  

A 1990 review of 28 studies made by the General 
Accounting Office in Washington stated that "In 82% of 
the studies, race of victim was found to influence the 
likelihood of being charged with capital punishment or 
receiving the death penalty". The disparities seem to 
be concentrated in a group of cases in the middle of 
severity and constituting only about 1/4 of the cases.
The review described as "equivocal" the evidence that 
the race of the defendant mattered. 

The Supreme Court has ruled that statistical evidence 
of bias in the sentencing is not sufficient, and that 
it is necessary to prove actual discrimination in the 
handling of the case. 

DISCUSSION QUESTION:  The article states that "Since 
most murders involve killers and victims of the same 
race, eliminating the disparity linked to the race of 
the victim would likely mean that the proportion, and 
perhaps the absolute number, of Blacks on death row 
would rise."  Why is this?
                  <<<========<<


>>>>>==========>>
Title:  New picture of who will get AIDS is crammed 
with addicts.
The New York Times, 28 Feb. 1995, C3 
Gina Kolata


An unpublished analysis by researchers at the Federal 
Centers for Disease Control and Prevention in Atlanta 
has found that last year nearly seventy-five percent of 
the 40,000 new infections with H.I.V. were among 
addicts.  This indicates that the AIDS epidemic is 
becoming more closely tied to the drug epidemic.  The 
biggest surprise in this new phase of AIDS' demographic 
evolution is its rapid spread among crack users.  

Dr. James Yorke, a mathematician who has modeled the 
spread of AIDS and other diseases and who is director 
of the Institute for Physical Sciences and Technology 
at the University of Maryland, noted that the 
transmission of H.I.V. differs from the transmission of 
other sexually transmitted diseases because it is 
riskier to have sex with many partners, only some of 
whom are infected, than to have sex the same number of 
times with one infected person.  Dr. Don C. Des 
Jarlais, a drug-abuse specialist in New York, says that 
the reason for this trend is that H.I.V. is transmitted 
more easily during two periods of the infection:  
(1) when a person first contracts the virus and (2) a 
decade or so later when the immune system is 
collapsing.  He gives the following example:

      If a woman has sex 100 times with a man 
      who is infected with H.I.V. but the man 
      is in the long latent stage when the virus
      is more difficult to transmit, she is much 
      less likely to get infected than if she has 
      sex just once with one man who may be in 
      the infectious stage. So a woman is at 
      much greater risk having sex once with 100
      partners, most of whom are infected, than 
      having sex 100 times with a man who is
      infected but in the latent stage.

DISCUSSION QUESTION

What do you think of the example given by Des Jarlais?
                  <<<========<<


>>>>>==========>>
Ask Marilyn.
Parade Magazine, 26 Feb. 1995, p6.
Marilyn vos Savant


A reader poses the following question:  "I'm flying 
over the China Sea in a single-engine plane.  The same 
route is being flown by my buddy in a twin-engine 
plane.  The engines are made by the different 
companies, but they're the same in all other respects, 
such as age, condition and inherent reliability.  It is 
known that the twin-engine plane cannot maintain flight 
on a single engine.  Our destination is hours away.  
Which plane has a higher probability of going down 
because of engine failure?"

Marilyn says the single engine plane is safer, claiming 
that if all other factors are equal, the twin-engine 
plane is twice as likely to go down.  She offers the 
following analogy.  You have a choice between boarding 
two identical planes for a flight.  One has a happy 
baby on board; the other has two.  If you can't stand 
the sound of crying, which plane would you rather be 
on?

DISCUSSION QUESTION:

(1) You are going to roll a die.  You lose if a six comes 
up.  What is your chance of losing?  Now you are going 
to roll a pair of dice.  You lose if either comes up 
six.  Are you twice as likely to lose?  What is Marilyn 
forgetting?

(2) Show that for small probability  p of failure
her statement is almost correct. Are we justified in 
assuming that p is small?
                  <<<========<<


>>>>>==========>>
CHANCE WORKSHOP
June 21 to June 24
Dartmouth College

CHANCE is an introductory mathematics course whose aim 
is to make students more informed and more critical 
readers of current issues in the news involving concepts 
of probability and statistics. 

The workshop will allow college teachers to experience a 
shortened version of the CHANCE course, complete with 
discussions of current issues in the news, computer labs 
with data analysis software, hands-on-activities, 
videos, journal writing and the use of the Internet. 
Representatives of other NSF projects will present 
results of their projects that are useful in teaching a 
CHANCE course.  

Participants will receive food, housing and course 
materials but will be asked to provide  their own 
transportation. An e-mail network will be established to 
allow participants to share information as they develop 
their own CHANCE courses, and there will be a follow-up 
meeting at an annual meeting of the MAA. This workshop 
is supported by the National Science Foundation.

Presenters:  J. Laurie Snell, Peter Doyle, Joan 
Garfield, William Peterson, and Nagambal Shah.

Application forms are available by e-mail from 
jlsnell@dartmouth.edu or by mail from J. Laurie Snell,  
Dartmouth College, Department of Mathematics, 6188 
Bradley Hall, Hanover NH 03755. Phone 603-646-3507.  
The deadline to apply is March 15, 1995.

 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

               CHANCE News 4.04
              (16 February to 3 March 1995)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please send suggestions to: jlsnell@dartmouth.edu

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