Sandbox

Quotations

"It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so."
--Mark Twain

Quoted by Richard H. Thaler in The overconfidence problem in forecasting, New York Times, 21 August 2010.

Submitted by Paul Alper

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"Nine out of 10 ‘SHOCKING’ poll results aren’t shocking if you’re paying attention." --Nate Silver

writing in his FiveThiryEight blog on September 22 (he was making a point about random variation, and technical difficulties in polling, that are often overlooked in a unscientific reading of polling results).

Craps record math

A world record in Atlantic City and the length of the shooter’s hand at craps,
by S.N. Ethier and Fred M. Hoppe, Mathematical Intelligencer, published online 13 August 2010

In an earlier post (see CN 59), we discussed the story of a New Jersey woman who established a new world record in craps, rolling the dice 154 consecutive times before "sevening out." To find the probability of this event, we numerically computed transition probabilities for a Markov chain model of the play (Ethier and Hoppe credit Peter Griffin with first proposing this model for craps).

The Intelligencer article (a pre-publication version is available here), presents an elegant algebraic solution of model, based on eigenvalue analysis and even some Galois theory. With the help of Mathematica, the authors obtain a closed-form expression for the distribution of the duration of play as a linear combination of four geometric distributions. Readers interested in seeing some nifty mathematics should have a look at the full paper.

Submitted by Bill Peterson

Is the United States a religious outlier

Religious outlier by Charles Blow, The New York Times, September 4, 2010.

The following image was published on the New York Times website.

http://graphics8.nytimes.com/images/2010/09/04/opinion/0904OPEDBLOW_600sub.jpg

The author, Charles Blow, is the visual OpEd columnist for the New York Times. His comments about the graph are rather brief.

With all of the consternation about religion in this country, it’s sometimes easy to lose sight of just how anomalous our religiosity is in the world. A Gallup report issued on Tuesday underscored just how out of line we are. Gallup surveyed people in more than 100 countries in 2009 and found that religiosity was highly correlated to poverty. Richer countries in general are less religious. But that doesn’t hold true for the United States.

Questions

1. Does the United States look like an outlier to you? Are there any other outliers on this graph?

2. Why would there be a relationship between GDP and percentage of people who call themselves religious? Does a higher GDP cause lower religiosity? Does a lower religiosity cause a higher GDP? What sort of data could you collect that might help answer this question?

3. Do you like how Mr. Blow presented this data? What would you change, if anything, in this graph?

Submitted by Steve Simon

Additional Discussion

Notice how many dimensions are included in addition to the axes (percentage who say religion is important and G.D.P. per capita). The Gallup poll from which the graph came can be found here. Gallup says:

Results are based on telephone and face-to-face interviews conducted in 2009 with approximately 1,000 adults in each country. For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error ranges from ±5.3 percentage points in Lithuania to ±2.6 percentage points in India. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.

What might be "practical difficulties in conducting surveys"? "wording difficulties"? Ignoring population size, the regression line is downward sloping so that the higher the religiosity, the poorer the people monetarily. One is tempted to say that money "causes" people to be less religious. Reversing the axes, one is tempted to say that religion "causes" people to be poor. Defend and criticize these supposed causes.

Paul Alper