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

Back issues of Chance News and other materials for
teaching a CHANCE course are available from the
Chance Web Data Base

      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.


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 

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.

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 >>>==========>>|<<==========<<<