Chance News 10
The weather man is never wrong. Suppose he says that there's an 80% chance of rain. If it rains, the 80% chance came up; if it doesn't, the 20% chance came up! - Saul Barron .
From: Statistical Quotations
"'Four million ... heard it. Ten percent remember it. One percent of those matter. One percent of those do something about it. That's still' - he does the math - 'four people.'" From: _The Betrayal_, by Sabin Willett, NY: Villard (Random House), 1998.
Submitted by Margaret Cibes
Logarithmetic behavior as metaphor
For many years Ed Barbeau has edited a wonderful column in the College Mathematics Journal called Fallacies, Flaws, and Flimflam. In Barbeau's column in the November 2005 issue of the College Math Journal Norton Starr provides a contribution called "Logarithmic behaviour as metaphor". Norton provides examples from a wide variety of writers who say that something is growing logarithmically when they mean it is growing exponentially.
Norton says that he became interested in this when a convocation speaker at his college (Amherst) said:
As opposed to all other appetites which are stimulated by deprivation and satisfied by food, good education stimulates with plenty so that appetite for knowledge and understanding escalate logarithmically to insatiability.
Norton finds examples among faculty, newspapers, television and of course on the web. He writes:
Here are three examples of metaphorical growth from the New York Times, with the third suggesting an improved understanding on the part of this newspaper:
- from a review of Harlow Shapley's autobiography: "if the autobiographer opts for a method he believes will grant him immortality without industry, his risks rise logarithmically."
- from a story about corruption and drugs:"' The drug situation is a horror story, increasing logarithmically.'"
- from a more recent story: "Street crime, fed by an explosion of drug abuse, has risen exponentially."
RRS Coincidence column
Norton Starr, who provides our RSSNews Forsooth items, told us that the RRSNews now has a Coincidence column. He sent us the coincidence story from the Nov 05 RSSNews and suggested some questions relating to this story.
This month's contribution is from Pam Warner of the University of Edinburgh Medical Statistics Unit who relates a story told to her by a colleague named Wilma during a recent morning coffee-break.
Wilma had been waiting in a queue for a check-out (in Edinburgh) and a little boy, accompanying the lady ahead of her in the queue, struck up a conversation with her. He asked her what her name was, and on being told that it was Wilma exclaimed that was the same name as his granny (the lady he was with).
Wilma then returned the compliment, asking him what his name was, and he said Kieran. She in turn commented that that was funny as she had a young grand-daughter (in London) whose name was Kiera.
By this time Kieran's grand-mother (the other Wilma) was involved in the proceedings, and chipped in 'Next thing you will be telling me is that Kiera's Mum's name is Pamela...', to which our Wilma could only reply astounded, 'It is!'
(1) What's the likelihood of two instances of a grandmother, her daughter (even though in this case it might be daugher-in-law) and her grandson having the same names, say in Britain?
(2) How does the above probability vary with size of population>
(3) How likely is it that such a pair of trios would encounter each other in person?
Pi in the News
“Expressed in digits, pi begins 3.14159…, and it runs on to an infinity of digits that never repeat. Though pi has been known for more than three thousand years, mathematicians have been unable to learn much about it. The digits show no predictable order or pattern. The Chudnovskys were hoping, very faintly, that their supercomputer might see one.” From: “Capturing the Unicorn,” by Richard Preston, in _The New Yorker_, April 11, 2005
Submitted by Margaret Cibes
If you were trying to explain to your Uncle George what it would mean for the digits of pie to be a random sequence, what might you tell him?
Suggested by Laurie Snell.
How stocks share in soccer sorrows
Phillip Coggan, December 01, 2005, Financial Times
Sports Sentiment and Stock Returns by Alex Edmans, Diego Garcia and Oyvind Norli, Social Science Research Network. www.ssrn.com
Motivated by psychological evidence of a strong link between sporting outcomes and mood, a new study claims a statistically significant link between a nation's soccer team's results and the subsequent day's performance of that country's stock market, attributed to sudden changes in investor mood.
The study analysed about 1,200 football matches played across 39 nations, focusing on the FIFA World Cup or on Continental competitions such as the European Championship. Elimination from those competition is, on average, associated with a stock market performance that is 38 basis points (slightly more than a third of a percentage point) worse than normal.
The Financial Times summarises the results by saying that the magnitude of the loss effect and its concentration in Western European countries with developed stock markets, suggests that investors would have obtained large excess returns by trading on these mood events. The effect seems to be strongest in small stocks, where local investor sentiment is most likely to be dominant. It seems to be unrelated to the potential economic effects - such as loss of merchandising revenue - that defeat might have.
The authors even suggest a profitable trading strategy
One such strategy would be to short futures on both countries’ indices before an important match to exploit the asymmetry of the effect.
They also claim that the loss effect is stronger for more important games, robust to changes in estimation methodology and to the removal of outliers in the data. It seems that there is also a statistically significant stock market loss effect using cricket, rugby, ice hockey, and basketball games in countries where these sports are popular.
However, a similar positive effect was not found when teams won. That may be because sports fans have unrealistic expectations of their team's chances of success. For example, 86 per cent of fans thought England would beat Brazil in the 2002 World Cup quarter-final, even though Brazil were the world's top-ranked team and bookmakers assigned only a 42 per cent probability to an England victory. A loss is more crushing to sentiment than a win is helpful. Furthermore, success in one round still leaves the possibility of elimination in the next.
The Financial Times article goes on to say
The study seems to chime with other surveys which found that increases in heart attacks, murders, suicides and riots are associated with sporting defeat. The mood of the population is adversely affected by a loss, particularly for sports in which a large proportion of the population takes an interest.
Other academic work that suggests investors are not entirely rational and so can be affected by factors like the weather, holidays and even the annual switch to daylight-saving time in the US.
Submitted by John Gavin.
Expert political judgment: how good is it?
Everybody's an expert
The New Yorker,Dec. 5,2005
It is the somewhat gratifying lesson of Philip Tetlock's new book, "Expert Political Judgment: How good is it? How can we know?" (Princeton; $35}, that people who make predictions their business--people who appear as experts on television, get quoted in newspaper articles, advise governments and businesses, and participate in punditry roundtables--are no better than the rest of us. When they are wrong, they're rarely held accountable, and they rarely admit it, either. They insist that they were just off on timing, or blindsided by an improbable event, or almost right, or wrong for the right reasons. They have the same repertoire of self-justifications that everyone has, and are no more inclined than anyone else to revise their belief's about the way the world works, or ought to work, just because they made a mistake...People who follow current events by reading the papers and newspmazines regularly can guess what is likely to happen about as accurately as the specialist whom the papers quote.
Teklock's is a Berkeley psychologist and his conclusions are based on a study that he started 20 years ago and ended in 2003. He chose two hundred and eight-four people who mad their living giving advice on political and economics issues. He asked them to estimate the probability that events would come to pass both in areas that they were considered experts as well as areas that they were not experts such as would Gorbachev be ousted in a coup, would the United States go to war in the Persian Gulf? ect. By the end of the study in 2003 the experts had made 82,361 predictions.
For most of the questions the subjects were asked to rate the probability of three options: no change, more of something and less of something. In most cases the experts did less well than the monkey who would choose one of the three at random.
While this might be disappointing, Tklock felt that he did learn why some people make better forecasts than other. He explained this in terms of Isaac Berlin's "The Hedgehog and the Fox summed up by this quotation:
The fox knows many things, but the hedgehog knows one big thing.--Isaiah Berlin
To be continued
The Beginner's Handbook of Dowsing
This book was written by Joseph Baum (NY: Crown Publishers, Inc., c. 1974). “Dowsing” refers to the use of a “divining rod” in search of water, ore, or oil.
Baum’s wife told the contributor that author Joe Baum, a commercial art director, was so successful in dowsing for water on their Massachusetts farm that local drillers often sought his help, with 100 percent success in his locating large underground water sources.
In this book, Baum describes a test once administered to a group of oil dowsers. The test’s creator, a geologist, felt that if a dowser could find oil thousands of feet down he most certainly could spot it three feet away. The experiment involved 10 cigar boxes filled with sand, with 1 of the boxes containing a small bottle of oil buried in its sand. The boxes were shuffled and spread out on the floor. After each contestant dowsed, the boxes were reshuffled, and the dowsing repeated, until a contestant had dowsed 10 times. A dowser who correctly identified the box with oil all 10 times was guaranteed financial backing to sink a well. Some 50 dowsers tried it and the highest score was 3 successful dowsings out of 10 tries.
(1) Suppose that each contestant had experienced a long history of successful dowsing, resulting in a 90% chance of success on each trial. In this case, what would have been the probability of guessing correctly at most 3 times out of 10? Would you have expected these folks to have achieved a higher maximum score than 3 out of 10?
(2) Suppose that each contestant had had no experience with dowsing and had randomly guessed. What would have been the probability of guessing correctly at most 3 times out of 10? Would you have expected them to have done better than experienced dowsers?
(3) Was there anything about the test itself, or the assumption behind the test, which might have adversely affected the contestants’ ability to dowse successfully?
Submitted by Margaret Cibes