Chance News 16
It is as useless to debate whether an actual sequence of coin tossing was governed by the laws of probability as "to debate the table manners of children with six arms."
Chances are, Michael Kaplan and Ellen Kaplan
Here's more from Doob on this subject:
Then and later the most embarrassing probability class lecture was the first, in which I tried to give a satisfying account of what happens when one tosses a coin. (A famous statistician told me that he solves the difficulty by never mentioning the context.) One wants to talk about a limit of a frequency, but "limit" has no meaning unless an infinite sequence is involved, and an infinite sequence is not an empirical concept. I made vague and heavily hedged remarks such as that the ratio I would like to have limit l/2 "seems to tend to 1/2", that the coin tosser "would be very much surprised if the ratio is not nearly 1/2 after a large number of tosses", and so on.
The students never seemed to be bothered by my vagueness. For that matter professionals who write about the subject are usually also unbothered, perhaps because they never seem to be tossing real coins in a real world under the influence of Newton's laws, which somehow are not mentioned in the writing.
Statist. Sci. 12, no. 4 (1997), 301–311
Submitted by Laurie Snell
Here is a Forsooth from our local newspaper suggested by Dana Williams.
The All England Club said yesterday the men's champion will receive $1.170 million and the women's winner $1.117 million -- a 4 percent increase for both in British currency.
The Valley News
April 26, 2006
And here is a Forsooth from the Associated Press.
A Malaysian man was speechless when he received a $218 trillion phone bill and was ordered to pay up within 10 days or face prosecution... It wasn't clear whether the bill was a mistake...Associated Press
And here are two Forsooths from the April 2006 RSS News.
HIV patients in low socio-eonomic classes are 89 per cent more likely to die than better-off people with the infection, claims a study of 2684 adults in the Journal of Health Care for the Poor and Underserved (Nov).
8 November 2005
A ten-year study of men in Wales found that those who had sex twice or more a week were 50% less likely to have died than those who had it less than once a month.
1 February 2006
Exponential decay in Biblical ages
WHY did people live longer BEFORE Noah's Flood than they did after it? written by Arnold C. Mendez, Sr. and published at BibleStudy.org.
While looking on the web for good examples of the coefficient of determination, I came across a statistical analysis of the ages of Biblical patriachs. Apparently the author believes in a literal interpretation of the Bible and wants to answer skeptical comments about the unusual ages reported for some of the patriarchs in the Bible.
"One of the most intriguing facts in the Bible is the immense life spans of the patriarchs before and just after the flood. Adam lived 930 years, Methuselah the longest lived of the patriarchs lived 969 years. Noah lived 950 years."
Why is it that no one today lives so long?
"After the flood the earth was completely different than the earth before. There were widespread global differences. These would include changes in the climate, composition of the atmosphere, hydrologic cycle, geologic features, cosmic radiation reaching the earth, ozone concentration, ultra violet light, background radiation, genetics, diet, and a host of other subtle and/or profound chemical and physiological changes. These changes caused a rapid decline of the longevity of post flood humanity."
The statistical model comes in the analysis of the decline in ages after the flood. An exponential decay model produces the following equation y=487.78exp(-0.0907x) where x represents the generation number. After 20 generations, the ages settles down to a more modern figure of 70 years. The coefficient of determination is 0.889.
"This means that the decay rate of the patriarch's death after the flood was only 11% from being a perfect match."
You can view a graph of the data and the fitted line below, taken directly from the article.
The author argues that the ages must be genuine since they fit an exponential curve so well and the writers of the time would not have the mathematical sophistication to fake an exponential decay curve.
1. Does a coefficient of determination of 89% sound impressive to you? What do you think about the author's comment that this is "only 11% from being a perfect match"?
2. An exponential decay models does have some problems. Explain what the limitations would be for an exponential decay in ages.
3. What other models (linear or non-linear) would be worth considering for this data?
4. Is there an alternative explanation for this pattern of ages?
Submitted by Steve Simon
Is Jerry Falwell's debate team really number 1 in the nation?
Adapted from Who's Counting: Distrusting Atheists
The NY Times Magazine, Newsweek, and 60 Minutes are three of the media outlets devoting considerable attention to the "national champion" debate team from conservative fundamentalist Jerry Falwell's Liberty University. But does the team deserve this number one ranking or is it bogus, an artifact of the way the so-called overall category
As bloggers Jim Hanas, Ed Brayton and others have observed (and as is briefly and unobtrusively buried in the Times article itself), the ranking is based on the performance of the team in all tournaments, including novice and junior varsity contests.
The way rankings are determined in the "overall" category, winning at any of these second-tier tournaments adds to the team's point total. Liberty, which has a broad-based program, enters many of them and racks up many of its points by doing so.
The schools with the top individual teams, however, often don't have novice or JV teams and usually don't enter many of the lesser tournaments.
Even with such extensive, but light opposition, and the points resulting from it, the Liberty varsity team seldom reaches the semifinals and has yet to win a single varsity tournament.
In fact, in the varsity rankings Liberty is 20th, not first, and, when the quality of its opponents is taken into account, it ranks even lower than that.
As Hanas remarks, referring to Liberty as the No. 1 team and one of the nation's great collegiate debate programs is a bit "like calling the best Division III basketball team the NCAA champion."
Another analogy is to the brief 1992 presidential campaign of Iowa Sen. Tom Harkin. He was way behind in the primaries, but some of his staffers jokingly suggested that their man was leading. In winning Minnesota, Iowa and Montana, they argued that he had captured the largest land mass of any of the contenders.
Submitted by John A. Paulos
Does a glass of wine a day keep the doctor away?
UCSF points out flaw in studies tying alcohol to heart health.
San Francisco Chronicle, March 30, 2006
Moderate alcohol use and reduced mortality risk: Systematic error in prospective studies, Kaye M. Fillmore et al, Addiction Research and Theory, March 30, 2006.
A large numbers of observational studies have suggested that moderate drinkers have a lower risk for heart attacks than nondrinkers or heavy drinkers. The results of these studies are usually illustrated by a U shaped graphic like this:
This graphic is from the article "Alcohol and Mortality in British Men; Explaining the U-Shaped Curve", The Lancet, December 3, 1988, A. Shaper, et al.
In their summary the authors wrote:
In a prospective study of 7735 middle-aged British men, 504 of whom died in a follow-up period of 7.5 years, there was a U-shaped relationship between alcohol intake and total mortality and an inverse relationship with cardiovascular mortality, even after adjustment for age, cigarette smoking, and social class. These mortality patterns were seen in all smoking categories (with ex-smoking non-drinkers having the highest mortality) and were observed in manual but not in non-manual workers. The alcohol-mortality relationships are produced by pre-existing disease and by the movement of men with such disease into non-drinking or occasional-drinking categories. The concept of a "protective” effect of drinking on mortality, ignoring the dynamic relationship between ill-health and drinking behavior, is likely to be ill founded.</blockquote?>
The authors are concerned that this and other similar studies are seriously flawed because they include subjects who have recently quit drinking and who are typically older people with medical problems who are told by their doctors to quit drinking. They suggest that this could explain why those who don't drink have a higher mortality rate than moderate drinkers. Evidently this concern was not pursued until a recent study of Kaye Fillmore and her colleagues to appear om the next issue of the journal Addiction Research and Theory.
The Chronicle article described the new study as follows:
Fillmore and colleagues from the University of Victoria, British Columbia; and Curtin University, in Perth, Australia, analyzed 54 different studies examining the relationship between light to moderate drinking and health. Of these, only seven did not inappropriately mingle former drinkers and abstainers.
All seven of those studies found no significant differences in the health of those who drank -- or previously drank -- and those who never touched the stuff. The remaining 47 studies represent the body of research that has led to a general scientific consensus that moderate drinking has a health benefit.
The article quotes Dr. Tim Naimi at the Centers for Disease Control as saying "The whole field of 'moderate drinking' studies is deeply flawed" and goes on to say:
In a study published in May 2005 in the American Journal of Preventive Medicine, Naimi and other CDC colleagues found that the comparatively higher risk of heart disease in abstainers could be explained by socioeconomic factors rather than lack of protection from alcohol consumption. Non-drinkers, for example, tended to be poorer than drinkers, had less access to health care, and had less healthy diets.
Note that in the 1988 article, Shaper and his colleagues were also concerned about difference in drinking habits of different groups, in particular manual and non-manual workers.
Naimi says, "Anyone who suggests that people should begin drinking, or drink more frequently, to reduce the risk of heart disease is misguided".
However, the UCSF news release for the study by Fillmore and her colleagues suggests that there might still be hope for us:
The authors caution that their report, published online in advance of the May 2006 issue of Addiction Research and Theory, has not disproved the notion that light drinking is good for health, as too few error-free studies have been performed. They suggest, however, that the extent to which these benefits actually translate into longer life may have been exaggerated.
(1) The chronicle quotes Dr. Arthur Klatsy, a well-known researcher on the benefits of moderate drinking:
There are inherent weaknesses in all the epidemiological studies of alcohol and heart health. What is needed is a randomized trial in which a group is assigned to consume one or two drinks a day and another abstains, and their comparative health is assessed over a period of years.
Do you think it would be possible to carry out such a study?
Submitted by Laurie Snell
Comparison of schizophrenia drugs often favors firm funding study.
Washington Post, April 12, 2006; Page A01
Most statistics textbooks would claim an experiment is superior to an observational study which in turn is better than mere anecdotal evidence. And the best experiment is a double-blind clinical trial. Well, perhaps not according to Shankar Vedantam's article in the Washington Post of April 12, 2006. The deputy editor of JAMA, Drummond Rennie, says "There will be two classes of [clinical] trials--the believable ones and the non-believable ones." The latter are represented by those which are sponsored by the members of the pharmaceutical industry.
As John Davis put it in the American Journal of Psychiatry, "On the basis of these contrasting findings in head-to-head trials, it appears that whichever company sponsors the trial produces the better antipsychotic drug." Vedantam writes, "Other experts note that industry studies invariably seek to boost the image of expensive drugs that are still under patent. Moreover, they say, the trials are relatively brief and test drugs on patients with simpler problems than doctors typically encounter in daily practice." Turns out that "cheaper drugs not under patent" were superior to the expensive drugs when the federal government did the testing,
In addition, industry studies can be "misleading in multiple ways," including testing "too low a dose of a competitor's drug." Although not mentioned in the article, I suspect that another way to mislead is to have too high a dose of the competitor's drug, thus increasing the severity and the number of side effects. Then, of course, there is the tried and true practice of deep-sixing a test which comes out the wrong way (aka as the "file drawer" technique).
Unfortunately, the justified cynicism runs deeper. Davis, "joked in an interview that he no longer gets to fly first class to Tokyo and Monte Carlo since he stopped accepting money from pharmaceutical companies." He "guessed that 90 percent of industry-sponsored studies that boast a prominent academic as the lead author are conducted by a company that later enlists a university researcher as the 'author'." Rennie goes even further concerning so-called author-shopping: "We know that happens all the time. The only reason that the company wants a non-company person as an author is to give credence to an advertisement... .The whole entire paper from start to finish is an advertisement."
While the discussion focused on antipsychotic drugs, it not beyond imagination that similar advertisements posing as research clinical trials take place more generally. Consequently, perhaps the first question to ask of any statistical study is: Who is doing the funding?
1. Why do statistics textbooks claim an experiment is superior to an observational study which in turn is better than anecdotal evidence? And why is the best experiment a double-blind clinical trial?
2. Would author-shopping be more prevalent in pharmaceutical studies than elsewhere?
3. The director of the National Institute of Mental Health, Thomas R. Insel, claims, "The publc is less interested in statistical significance and more interested in clinical significance." If so, why is a statistician needed?
Study: Medical manual's authors often tied to drugmakers.
USA TODAY, April 20, 2006
Submitted by Paul Alper
Use it or lose it?
Ooops! Mental training, crosswords fail to slow decline of aging brain.
Wall Street Journal, April 21, 2006 B1
Mental exercise and mental aging. Evaluating the validity of the "Use it or lose it" hypothesis.
Perspectives on Psychological Science Vol.1 No.1 Page 68 - March 2006
Timothy A. Salthouse
Having suffered through the discovery that the studies claiming that a glass of wine a day will keep the heart attack away are seriously flawed, we now are told that there is no convincing evidence that working crossword puzzles, contributing to chance news, or other mental activities will slow the decline of an aging brain. The many studies making this claim has led to the slogan "use it or lose it".
It has been shown that there is a large variation in the results of cognitive tests for people of the same age, and that cognitive ability generally decreases with age. So, in analogy with the benefits of physical activity, one might hope that mental activity slows cognitive decline.
The Wall Street Journal article discusses the findings of Timothy Salthouse reported in the first issue of the new Journal Perspectives on Psychological Science. Salthouse reviews recent studies that support the slogan and explains why the they do not prove a causal relation between mental activity and the slowing of cognitive decline.
Here is an example. Consider an experiment that observes two groups of similar age one of which plays bridge and the other does not. After a ten-year period you find that the group that plays bridge does better on cognitive tests than the group that does not. It would not be surprising if the bridge group has a higher cognitive ability at the beginning of the study and so does better on cognitive tests because it started at a higher cognitive level.
Of course this simple explanation does not apply to all studies but Salthouse manages to show that most of the recent studies do not demonstrate a causal relationship. He concludes his article with the following comment:
Although my professional opinion is that at the present time the mental-exercise hypothesis is more of an optimistic hope than an empirical reality, my personal recommendation is that people should behave as though it were true. That is, people should continue to engage in mentally stimulating activities because even if there is not yet evidence that it has beneficial effects in slowing the rate of age-related decline in cognitive functioning, there is no evidence that it has any harmful effects, the activities are often enjoyable and thus may contribute to a higher quality of life, and engagement in cognitively demanding activities serves as an existence proof-if you can still do it, then you know that you have not yet lost it.
Submitted by Laurie Snell
Use and Reliability of Internet information
The Internet's Growing Role in Life's Major Moments by John Hoorigan and Lee Rainie, April 19, 2006.
The Pew Internet & American Life Project conducted a survey in March 2005 that showed that
fully 45% of internet users, or about 60 million Americans, say that the internet helped them make big decisions or negotiate their way through major episodes in their lives in the previous two years.
This survey interviewed 2,201 adults 18 and older, but the results shown above are based on the 1,450 self-identified Internet users. The margin of error is +/-2% for all respondents and +/-3% for all Internet users.
The major episodes considered in this survey (and the percentage of Internet users who cited such an episode as "crucial" or "important") are
- pursuing more training their careers (42%).
- deciding about a school or a college for themselves or their children (42%).
- helping another person cope with a major illness (39%).
- making major investment or financial decisions (29%).
- helping themselves cope with a major illness (28%).
- looking for a new place to live (30%).
- buying a car (27%).
- switching jobs (25%).
Since the total percentage who responded "crucial" or "important" on at least one of these eight items was 45%, there is a lot of overlap in these episodes. Apparently once you start using the Internet for one important decision, you apparently use it for a lot of other important decisions as well.
Surprisingly, not that many people complained about information overload.
Information overload was not experienced by the majority of those who relied heavily on the internet in the five key decisions. Just 15% said they felt they sometimes felt overwhelmed by the amount of information they had, 71% said they had all the information they needed and thought it was manageable, and 11% said they were missing information that they wish they had. Few who bought a car in the past two years reported information overload (9%). And even among [those] who said the internet played a crucial or important role in helping someone with an illness, only 22% said they felt overwhelmed by the volume of information. With the stakes high — offering help to another person about a major illness — one might have expected higher levels of anxiety about sorting through such information.
The article cites the increasing use of Broadband connections as an important factor in the growth of the use of the Internet for helping to make big decisions.
Another interesting statistic is that most people who relied on the Internet to help make big decisions felt that the information was reliable. Only 5% reported getting bad information or advice from the Internet. This led one commentator, John Paczkowski, to quip that this is
either an encouraging sign of search effectiveness or a worrisome warning about credulity.
How reliable is information on the Internet? An entry in issue #10 of Chance News discusses a Nature article that made a head to head comparison of the Encyclopaedia Britannica, a print encyclopedia edited by panel of 4,000 experts, to the Wikipedia, an Internet encyclopedia edited by a team of over 27,000 volunteers.
Some additional commentary that appeared after this article was published in the Chance Wiki are a critique of the Nature article by the Encyclopaedia Brittanica and a response by Nature to this critique. Interestingly enough, the Wikipedia itself has coverage of the controversy and tries to present a neutral point of view about itself.
A good summary of the reliability of health information on the Internet, is Health information on the internet: Patient empowerment or patient deceit?, a review article by M Akeerkar Shashank and LS Bichile published in the Indian Journal of Medical Sciences 2004; 58 (8): 321-326.
This article cites research that most Internet users have a high opinion about Internet searches.
Most adults in four countries who participated in a recent Harris Interactive survey find online health care information to be trustworthy, of good quality, easy to understand and easy to find. In some cases, these majorities are very large.
As a result, these users do not critically evaluate their sources.
Only about a quarter of health seekers thoroughly check the source, timeliness of information and verify a site's information every time they search for health information. Half of all health seekers search for medical advice and "only sometimes," "hardly ever," or "never" check the source or date of the information they read online. Studies have pointed out the difficulty faced by Internet surfers in distinguishing credible health information from that which is not trustworthy.
This article, though, does not cite much data that the Internet sources are indeed unreliable, but instead focusses on the percentage of sources that have a commercial interest or which promote alternative medicine.
1. What psychological factors might cause people in the Pew survey to underestimate the proportion of unreliable information available on the Internet?
2. If you were to design a study to evaluate the reliability of information on the Internet, how would you collect a representative sample of web pages?
Submitted by Steve Simon