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− | <blockquote>Their final profit after the four days of playing ended up within $100 of what they had originally computed to be their expected payoff. | + | <blockquote>Their final profit after the four days of playing ended up within $100 of what they had originally computed to be their expected payoff.</blockquote> |

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+ | How would you decide if this is about what you would expect? | ||

Written by Laurie Snell | Written by Laurie Snell |

## Revision as of 09:16, 25 March 2007

## Contents

## Quotations

Do not put faith in what statistics say until you have carefully considered what they do not say. William W. Watt

## Forsooths

These Forsooth's are from the March 2007 RSS News.

Hundreds of jobs to go at factory.

Almost 200 workers are to lose their jobs at Lincolnshire factory after rescue attempts to keep it open failed, the trade union Amicus has confirmed.

BBC news website

12 December 2006Despite the ceaseless terrorist attacks on the country's infrastructure and particulary the oil industry, the value of the Iraqi dinar has continued to rise-in November, from D1,410 to the doller to D1,480. That is obviously good for the vast majority of people whose pay comes in dinars.The Spectator

30 December 2006

Paul Campbell provided the following Forsooth:

The population of the USA has topped 300 million for the first time.It reached the figure sometime in October. It passed the 200 million mark in 1967. The U.S. census bureau, which reports the figure, calculates that, if current trends continue, it is expected to reach 400 billion by 2043. This makes it an acceleration of growth...

Significance2 (4) (Dec. 2006) 146## Statistics in the Doctors Office

This is an unscientific look at a number of medical statistics I have run into, so far. It is inspired by the great title of the article in Chance News 24 that included the words "medical research", and "rot" in the same breath.

When I was born, quite premature, the doctors said I had a 50 50 chance of staying alive. My father told my mother that this meant they did not know what the probability was.

I met my husband at 39, got married over the age of 40, and gave birth with my own eggs to a healthy child at the age of 43. Statistically speaking, chance was on my side.

In January 2006, I had a large node on my thyroid, and was told by my doctor to have it removed in 2 months. I then went to a specialist, who said there was a 30 percent chance it was Cancer, although if it wasn't yet cancer, it would most likely develop into cancer because of its size. He said there was no chance it would shrink. I went to another specialist, who said surgery should be done by Labor Day. I went back to the first specialist, who agreed with this timetable. These days I tend to ask, not "what is my chance" but, "how long do I have before I have to make a permanent decision?"

To pass the time before this surgery, that was beginning to seem inevitable, I went to a Tibetan medicine doctor, researched yoga poses to help the thyroid, and altered my diet. I also got more childcare help for my child. Come Labor Day, I did my pre-op, and then insisted on having a final meeting and sonogram with the endocrinologist. I figured if they did a sonogram right before my going into surgery, it would be statistically highly unlikely for them to cancel surgery once everyone had been called into the room, and the surgeon had taken that hour or two just for me.

I scheduled the final sonogram one week before the surgery, with an endocrinologist who works closely with the surgeon. They are on the same team. She was one of the coldest doctors I have ever met, and she had no regard for alternative medicine, so I figured she was the one to go to. Without any emotion or hint in her face, the endocrinologist scanned my throat over and over again, and then suddenly said, "Cancel the surgery. Nothing is over 1 cm. There are no nodes large enough to even have another biopsy on. (My node had been 2.6 cm, and had previously flunked a biopsy)

I have no data to support any alternative medicine I went through. I go to this same endocrinologist every six months for check ups. I continue to be a non-advocate for both western and eastern medicine, but have recently become a certified yoga teacher just in case someone else wants to, if nothing else, distract themselves while they are procrastinating.

Submitted by Mary Snell

## Are beautiful politicians more likely to be elected?

Pretty vacancies, Tim Harford, Undercover Economist, FT magazine, 23 Feb 2007.

Beauty and the Geek - Maybe good looks do make you smarter, Tim Harford, Slate, 3 Mar 2007.

This article considers correlations between subjective beauty and electoral success. It cites a paper by Amy King and Andrew Leigh who, when studying Australian elections, wondered whether the results were driven by ageism or racism. They conclude that a candidate's beauty is the best explaination.

Beautiful candidates are indeed more likely to be elected, with a one standard deviation increase in beauty associated with a 1.5-2 percentage point increase in voteshare.

King and Leigh highlight that their results are adjusted for potential biases, such as:

- adding party fixed effects,
- dropping well-known politicians,
- using a non-Australian beauty rater,
- omitting candidates of non-Anglo Saxon appearance,
- controlling for age,
- analyzing the 'beauty gap' between candidates running in the same electorate.
They also conclude that, consistent with the theory that returns to beauty reflect discrimination, there is 'suggestive evidence that beauty matters more in electorates with a higher share of apathetic voters'.

Hartford is persuaded that beautiful people are better at their jobs.

There is no mystery as to why we want decorative Hollywood stars, but the same logic might apply to sales staff. Even a bureaucrat might be more persuasive if he or she is good-looking, and who wouldn't want persuasive employees instead of charmless ones?

Hartfold also speculates that, as beautiful people have probably been treated well all their lives, this might affect abilities that have nothing to do with appearance. For example, if handsome kids get all the attention from teacher, why would they not do better at school?

Another study (Mobius and Rosenblat) found that attractive people were more self-confident about how they might perform in a maths test but they did not actually do any better. Hartford also speculates that perhaps the self-confidence of the beautiful helps them fool employers into paying more.

Beautiful people could well be genuinely more productive but American economist Daniel Hamermesh devised a clever way to demonstrate that whatever lies behind our preference, our choices are based on skin-deep evidence. He showed that when candidates stood for election on more than one occasion, their chances of success rose simply when they used a more flattering photograph.

## Questions

- In Australia, voting is compulsory and voters are given
How to Votecards depicting photos of the major party candidates as they arrive to vote. Do you think these features might affect the outcome of the test?- A priori, would you expect the marginal effect of beauty to be larger for male candidates than for female candidates?
- Can you think of any other background factors that might ideally be controlled for in a beauty test? Might the outcome depend the underlying profession in question or on how beauty is defined and who defines it?
- How might it be possible to test for explanations such as
employers like to be surrounded by pretty staff,orvoters like to see pretty politicians on TVor that we irrationally conflate beauty with useful qualities such as honesty or intelligence?## Further reading

- Beautiful Politicians, Amy King, University of South Australia and Andrew Leigh, Australian National University. (One conclusion is that the marginal effect of beauty is larger for male candidates than for female candidates.)
- Links to six studies, many involving American economist Daniel Hamermesh, which assert that 'ugly' people earn less. The beauty premium seems to apply even in professions where there is no reason to expect that beauty counts.
- Why Beauty Matters, Markus M. Mobius, Harvard University and Tanya S. Rosenblaty, Wesleyan University, 14 Sep 2003.
## The importance of statistics

Ministering to the truth, The Economist, 1 Mar 2007.

The importance of statistics, Leader section, The Economist, 1 Mar 2007.The UN requires every country to have a national statistics office, governed by a statistics law, to guarantee quality and independence. The OECD compares national statistics on health, education and economic activity to encourage laggards. Despite this, an editorial in The Economist claims that a chance to make UK government numbers more trustworthy is being missed. It claims that three things are needed to make any nation's national statistics trustworthy:

- Pay statisticians well, to attract good candidates away from other fields. Good statistics are not cheap: Britain's next decennial census will cost £500m ($1bn), America's $12bn.
- Statistics should be free from political interference. For example, the article quotes an extreme example where the director of Argentina's statistics agency resigned following government interference in the calculation of inflation rates.
- Figures and their accompanying explanatory text should be published on an independent timetable, free from any political spin. For example, in Norway, ministers do not see statistics in advance of their publication, as happens in the UK.
The Economist claims that this issue matters more in the UK than in other countries because the UK is fondest of setting targets, such as hospital waiting times or the number of new schools built, and it is

the country where statistics are most obviously spun by politicians,such as crime figures coming from the government's crime fighting department, with the best gloss on hard-to-interpret figures. For these reasons, fewer than 20% of the UK population believes official statistics. The Economist claims.If governments tweak some of the numbers that they are judged by, they deprive themselves of their best guide to future policymaking and create distruct of all national statistics.

This topic was covered previously in Chance News: Pick a number, any number (Chance News 9) and Independence for national statistics (Chance News 22).

Coincidently, there is a three-part BBC documentary, called The Trap, which argues (2nd programme aired on BBC2, 18 March 2007) that the UK government's obsession with setting performance targets turns people into the calculating machines, with disasterous consequences. Bizarrely, the programme argues that this all started with game theory, Nash equilibrium and the cold-war arms-race.

## Further reading

- The Trap: This series consists of three one-hour programmes which explore the concept and definition of freedom, specifically: "how a simplistic model of human beings as self-seeking, almost robotic, creatures led to today's idea of freedom." It relies heavily on game theory, including the Nash equilibrium. (See Solution to the Car Talk problem (Chance News 24) for another example of Nash equlibrium.)

- What Happened To Our Dream Of Freedom? BBC press office.
- Cry freedom, The Guardian, 3 March 2007.
Submitted by John Gavin.

Paul Cambell suggested this article.

## Mixing a night out with probability & making a fortune

Math Horizons

February 2007

Kari Lock, Williams CollegeOh, New York bring back those big dippers. August 1, 1999

Donald CatlinBoth of these articles tell us how two lottery players took advantage of their knowledge of probability theory to win a lot of money.

As part of the lottery program the New York State Lottery allows you to play Quick Draw (Keno) in bars, restaurants, bowling alleys and other places. To play their version of Quick Draw you buy a ticket for $1 which has the numbers from 1 through 80 on it. Then you pick a number r between 1 and 10 numbers. The lottery then randomly chooses 20 of the 80 numbers. The object, for the player, is to match as many of the 20 'house' numbers with the player's r numbers as possible. A new game is played every 4 or 5 minutes so a lot of plays can be made while drinking a few beers.

Catlin states that in the month of November in 1997, the New York Lottery had a promotion using the Quick Draw game. He writes, "The following is a direct quote taken from a table card advertising the special promotion"

Win a double dip on Big Dipper Wednesdays. During our 'Big Dipper Wednesday Special' promotion November 5, 12, 19, and 26, prizes for all winning Quick Draw 4-spot tickets will be doubled!A 4-spot ticket means that the player chooses r = 4. The two players realized that if you bought a Quick Draw 4-spot ticket you would be playing a favorable game. In his book "Lottery Book: The truth behind the numbers" Catlin says that the players were graduate students in mathematics. Kari Lock refers to them as former students.

Let's see why this would be a favorable game.

When you play Quick Draw on an ordinary day the payoffs are:

4 Spot Game

Numbers Matched Prize per $1 played 4 $55 3 $5 2 $1The probability p(x) of x matches is given by the hypergeometric distribution:

[math] p(x) = {{{20 \choose x} {{60} \choose {4-x}}}\over {80 \choose 4}}[/math] From this we find the expect payoff per dollar for the 4-spot game is

p(4}*55 p(3)*5 + p(2)*1 =$.597361. So on ordinary days if you choose the 4-spot game you can expect to win about 60 percent of the amount you spent. When the payoffs are doubled your expected payoff becomes twice as much which is $1.19472 so you can expect to make about 19.45 percent of the amount that you bet making this a favorable bet

Kari Lock writes:

When the bar opened at 10 am the first Wednesday in November, they were there and ready to go. From opening until the deal expired at midnight, for all four Wednesdays in November, these two guys feverishly played 4 Spot Quick Draw. Purchasing around 1500 tickets a day, they played the maximum amount of 20 games with each ticket, betting $5 a game. As they played more and more games, they started making a profit as predicted, and were able to use their winnings to keep purchasing more tickets. The only factors limiting the number of tickets they played were the printer--it took a certain amount of time for the matching to process and print out a ticket--and the actual process of cashing in the tickets..

After purchasing a new house and a new car, one of the guys was asked to comment on the experience. His words of wisdom after the whole event:” It shows that paying attention in math class can, in fact, be useful."Neither author told us who the students were nor any evidence that the story was not an urban legend. We wrote to the New York Lottery and they said that their records did not go back to 1997 but they did remember the promotion. However further research resulted convinced us that this is a true story and at the same time to find our "source" Kari Lock.

We found an interview by Joan Garfield, of "chance enhanced course" fame, of statistician Robin Lock in the "Newsletter for the Section on Statistical Education, Volume 7, Number 1, (Winter 2001)". Joan's interview started with:

How many statistics instructors learn that their former students have applied their statistical skills to earn over $100,000 playing a lottery game? This happened to Robin Lock, Professor of Mathematics at St. Lawrence University in New York. Lock's former student and a friend applied their knowledge of probability in figuring out that the expected value of a Quick Draw lottery game at a local restaurant was greater than $0 during a special promotion.

According to Lock, these students "first raised enough cash to start play with little chance of going bust before the law of large numbers took effect to assure their expected winnings." They computed the probabilities and expectations by hand, then simulated the game many times on a computer to confirm the long run behavior. Putting the theory into practice for the remaining three days of the promotion netted the pair a profit of more than $100,000, matching almost exactly what the theory had predicted. Lock noted "Not only did they understand the application of mathematical expectation to this problem, but they had confidence in what they learned and the free time to sit all day in the restaurant playing the game." After hearing about these students' success, Lock invited them to visit his class and share the information about how they worked out the expected value, simulated the game, and decided how much to gamble.Anyone who knows Robin Lock

http://it.stlawu.edu/~rlock/photo1.gif

will not be surprised to learn that his daughter Kari Lock has a gold medal in ice dancing from the US Figure Skating Association.

## Discussion questions

(1) Does winning $100,000 seem plausible?

(2) Kari Lock writes:

Their final profit after the four days of playing ended up within $100 of what they had originally computed to be their expected payoff.How would you decide if this is about what you would expect?Written by Laurie Snell

## Extra Extraordinary Knowing

Extraordinary Knowing: Science Skepticism, and the Inexplicable Powers of the Human Mind

Elizabeth Lloyd Mayer,

Random House 2007"In nonstatistical language, the odds that pure chance was reponsible for 50 percent of women getting preganant in the prayed-for group but only 26 percent in the non-prayed-for group were less than 13 out of ten thousand. The odds that pure chance explained why 16.3 percent of the embryos successfully implanted in the prayed-for group versus only 8 percent in the non-prayed-for group were less than five out of ten thousand." --page 155 in Extraordinary Knowing: Science Skepticism, and the Inexplicable Powers of the Human Mind by Elizabeth Lloyd Mayer. The above quotation gives the reader barely an indication of the credulity of Mayer. In statistical terms, she is confusing p-value with the probability that prayer had no effect. Further, the study to which she is referring has been thoroughly debunked; one of the authors,Daniel Worth, was convicted for unrelated bank and mail fraud and another author, Rogerio Lobo, arrived on the scene after the study was done and now has withdrawn from the study. A better indication of the strange collection of events depicted in this book comes from how Mayer first became interested in her quest for evidence for the occult, ESP, telekinesis. When her daughter's hand-carved harp was stolen in Oakland she eventually turned to a dowser (whom she had not met) some 2000 miles away in Arkansas who told her where the harp would be found. From then on, her gullibility knew no bound. About the only element missing in the book is astrology.

Discussion 1. What evidence would make you believe in dowsing, astrology, or telekinesis?

2. What evidence would make you disbelieve in dowsing, astrology, or telekinesis?

3. On the back cover of the book may be found the following quotation from Judith Orloff, M.D.: "A fascinating look at the power of non-local awareness to transcend the limits of the linear mind." Translate that into English focusing on the words "non-local" and "linear."

Submitted by Paul Alper