Chance News 65

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Contents

Quotations

"All scientific work is incomplete - whether it be observational or experimental. All scientific work is liable to be upset or modified by advancing knowledge. That does not confer upon us a freedom to ignore the knowledge we already have or postpone the action that it appears to demand at a given time."

Sir Austin Bradford Hill, as quoted at Toxipedia. Submitted by Steve Simon.


"His lectures were loud and entertaining. ...He took umbrage when someone interrupted his lecturing by pointing out some glaring mistake. He became red in the face and raised his voice, often to full shouting range. It was reported that on occasion he had asked the objector to leave the classroom. The expression 'proof by intimidation' was coined after Feller's lectures (by Mark Kac)."

Gian-Carlo Rota, Fine Hall in its golden age: Remembrances of Princeton in the early fifties.
Submitted by Paul Alper


“In the dark candlelit room where they swear allegiance to FIFA, coaches and commentators have agreed that if you are a soccer person, you have to say you don’t buy into stats.”

Mark Brunkhart, president of Match Analysis, as quoted in When it comes to stats, soccer seldom counts, New York Times, 8 July 2010.
Submitted by Bill Peterson


“Basically, I’m not interested in doing research and I never have been. I’m interested in understanding, which is quite a different thing. And often to understand something you have to work it out yourself because no one else has done it.”

David Blackwell, as quoted in David Blackwell, scholar of probability, dies at 91, New York Times, 16 July 2010.
Suggested by Priscilla Bremser

Forsooth

The following Forsooths are from the RSS NEWS June 2010

Labour's betrayal of British workers. Nearly every one of 1.67m jobs created since 1997 has gone to a foreigner.

Immigration was at the centre of the election campaign today as it emerged that virtually every extra job created under Labour has gone to a foreign worker.

Figures suggested an extraordinary 98.5 per cent of 1.67 million new posts were taken by immigrants.

The ONS figures show the total number of people in work in both the private and the public sector has risen from around 25.7 million in 1997 to 27.4 million at the end of last year, an increase of 1.67 million.

But the number of workers born abroad has increased dramatically by 1.64 million from 1.9 million to 3.5 million.

Daily Mail, 8 April 2010

The English language currently comprises roughly a million words. Discounting new words that are added every day, and those occasionally lost to posterity, the possibility of forming a three-word combination is therefore a million cubed, or a quadrillion--that's followed by 216 zeros.

The Guardian, 21 August 2009

Submitted by Laurie Snell


Some responses to a Josephson Institute survey of American public and private, “The Ethics of American Youth: 2008”:

30 percent said that they had stolen from a store within the past year.
42 percent said that they sometimes lie to save money.
64 percent said that they had cheated on a test during the past year.
26 percent admitted that they had lied on at least one or two questions on the survey.
93 percent said that they were satisfied with their personal ethics and character.
77 percent said that when it comes to doing what is right, I am better than most people I know.
--

The 2008 survey had 29,760 respondents, although not all respondents replied to all questions. The website has links to the original questions and to demographic background data for every question.

Submitted by Margaret Cibes

Return on investment in college

Union, RPI rank high on education value.
by Caitlin Tremblay, Daily Gazette (Schenectady, NY), 30 June 2010, p. A5

The article reports that that two local colleges (Union College and Rensselaer Polytechnic Institute) “are listed among New York state’s and the nation’s best colleges for making back the money spent on a bachelor degree, according to a study by the website PayScale.com …Payscale, a compensation research website, took the price of the schools’ degree and compared it to the average income of graduates to calculate a ‘return on investment.’ Only those with undergraduate degrees and full-time hourly or salaried jobs were included…Topping Payscale’s list are Massachusetts Institute of Technology (annual ROI of 12.6 percent), California Institute of Technology (12.6 percent) and Harvard University (12.5 percent).”

The website Paycale.com (which also explains the methodology) asserts that “A return on investment (ROI) calculation tells you what you get back for what you spend - and it's a great way to compare college costs…PayScale helps you figure out which school's tuition costs will return the biggest dividends for you after graduation.”

Discussion Questions

With the help of the Payscale.com website methodology description:

  1. Critique, from a statistical perspective, the use of the results of this study in comparing colleges with regard to assessing “what you get back for what you spend.”
  2. How might the validity of such a study be improved and, if implemented, how would this impact any reservations you might have about the conclusions that you might draw?
  3. Comment on any other aspects of the underlying methodology and how it might be improved.

Submitted by Gerry Hahn

Paul the octopus plumps for Spain

ESPN soccernet, 9 July 2010

Spain will defeat Netherlands in Sunday's World Cup final, according to the latest prediction from Paul the psychic octopus.

To intense media interest on Friday morning, Paul, who has an unblemished record in the tournament so far, picked Spain as the victors in the Johannesburg final and also predicted that Germany will defeat Uruguay in Saturday's third-place play-off.

The decision was welcomed in Spain - who were also tipped by Paul to defeat his home country, Germany, in the semi-finals - with Marca's website leading with the story of how el pulpo Paul predicted that Spain would be campeones.

Paul has achieved global fame after correctly predicting the results of all of Germany's games at the tournament in South Africa. In order to harness his powers, his keepers at Sea Life Oberhausen present Paul with the choice of two glass boxes, both containing a mussel but each bearing the flag of a different country.

The odds of Paul correctly predicting Germany's results so far are 1 in 64 and he proved correct once again when tipping Spain to beat Joachim Low's side in the semi-final, which they duly did thanks to a header from Carles Puyol.

Many German fans were unhappy with Paul's decision to plump for Spain and, fearing a backlash, Spanish Prime Minister Jose Luiz Rodriguez Zapatero has joked he will offer state protection to Paul!

Discussion

Read more about Paul here and see if you would trust Paul in your bets.

Submitted by Laurie Snell and suggested by Dan Rockmore

A golf oddity

“Paul Goydos and the Odds of Shooting 59”
by John Paul Newport, The Wall Street Journal, July 10, 2010

In a July 8, 2010 golf tournament, Paul Goydos shot a 59, only the fourth such score in 612,489 rounds on the PGA Tour.

Those odds of 153,123 to 1 compare with 2,139 to 1 for baseball no-hitters and 21,084 to 1 for perfect games during the same period. A 59 is 1/300th as likely as a hole-in-one on the PGA Tour; [it is] 1/25th as likely as a double eagle.

Submitted by Margaret Cibes

Tuesday’s child

The famous nursery rhyme proclaims: “Tuesday’s child is full of grace.” Well, factoring in Tuesday for a birth date as discussed in Chance News 64 and Andrew Gelman’s blog produced a flood of comments.

Without Tuesday muddying the waters, the well-known answer to

I have two children.
One is a boy.
What is the probability that I have two boys?

is 1/3, rather than 1/2 as many are prone to say. William Feller in his famous book (Introduction to Probability Theory and Its Applications, Volume I, Third Edition, page 117) says the value of 1/2 is the solution to a much simpler problem: “A boy is chosen at random and comes from a family with two children; what is the probability that the other child is a boy?” He explains why: The 1/3 “might refer to a card file of families,” while the 1/2 “might refer to a file of males. In the latter, each family with two boys will be represented twice, and this explains the difference between the two results.”

Many of the comments focused on the intuitively irrelevant aspect of Tuesday and yet, a careful laying out of the sample space indicates that the day of the week for the birth of a boy turns out to be relevant. Some of the comments tried to explain the cognitive dissonance by referring to similarities to the so-called Monty Hall Problem, in the sense that available information needs to be accounted for.

With Tuesday thrown into the mix, the answer to

I have two children.
One is a boy born on Tuesday.
What is the probability that I have two boys?

surprisingly, turns out to be 13/27, which is close to 1/2, the answer to the simpler problem.

Consider a different physical situation, where “boy” now represents a successful knee operation and “girl” now represents an unsuccessful knee operation--we have, after all, but two knees. Ignoring the “Tuesday” aspect, knowing there is a successful knee operation implies a 1/3 chance of two successful knee operations. But this seems especially the wrong-way round because knowing of an unsuccessful knee operation implies a 2/3 chance of a successful knee operation.

When “Tuesday” is added to knee replacement, the implication is closer to 1/2. In fact if we recorded time of day to the nearest minute of the day, rather than to the particular day of the week, we would be even much closer to 1/2. But that is bothersome too because this allows for manipulation of the data keeping/presentation merely by tacking on what might be deemed a "spurious" variable that can take on many values.

Discussion

Expanding on Feller’s explanation, what is the proper “card file” to use here?

Submitted by Paul Alper

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