Chance News 80

Quotations

“The role of context. .... The focus on variability naturally gives statistics a particular content that sets it apart from from mathematics itself and from other mathematical sciences, but there is more than just content that distinguishes statistical thinking from mathematics. Statistics requires a different kind of thinking, because data are not just numbers, they are numbers with a context. .... In mathematics, context obscures structure. .... In data analysis, context provides meaning. .... [A]lthough statistics cannot prosper without mathematics, the converse fails.”

"What About Probability? .... In the ideal Platonic world of mathematics, we can start with a probabilistic chicken and use deductive logic to lay a statistical egg, but in the messier world of empirical science, we must start with the egg as observed data and construct a prior probabilistic chicken as an inference."

George Cobb and David Moore (authors' emphasis)

in “Mathematics, Statistics, and Teaching”

The American Mathematical Monthly, 1997

Submitted by Margaret Cibes

Forsooth

“[A researcher] has been funded in part by the U.S. government’s Monty Python-esquely named Office of Research Integrity’s Research on Research Integrity Program.[1]

David H. Freedman, in Wrong, 2010, p. 106

Submitted by Margaret Cibes

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“[A] political science professor at Southern Connecticut State University … has developed a mathematical formula to assess presidential success. … Her model, she said, ‘explains 50 percent in the variance in the quality of the president, which is awfully good ….’"

in “Southern Professor Links Presidential Success To Prior Experience”
The Hartford Courant, January 2, 2012

Submitted by Margaret Cibes

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"When I was in NYC I went to this party by group of Japanese bio-scientists. There, one guy told me about how the biggest pharmaceutical company in Japan did their statistics. They ran 100 different tests and reported the most significant one. (This was in 2006 and he said they stopped doing this few years back so they were doing this until pretty recently…) I’m not sure if this was 100 multiple comparison or 100 different kinds of test but I’m sure they wouldn’t want to disclose their data…"

posted by a colleague on Andrew Gelman's blog, 24 December 2011

Submitted by Paul Alper

Weirdness

Why People Believe Weird Things: Pseudo-Science, Superstition, and Other Confusions of Our Time
by Michael Shermer, MIF Books, 1997, p. 54

Shermer is founding publisher of Skeptic magazine and a Scientific American columnist. This book contains his list of “Twenty-five Fallacies That Lead Us to Believe Weird Things.” The fallacies are not new, but are well illustrated by many interesting historic and contemporary stories.

See Shermer's 13-minute TED Talk[2], including a demonstration of a $900 “dowser” designed to find marijuana in kids’ lockers. Shermer states:

Science is not a thing, it’s a verb. It’s a way of thinking about things. It’s a way of looking for natural explanations for all phenomena.

Question

Shermer states:

[M]ost people have a very poor understanding of the laws of probability. …. The probability that two people in a room of thirty people will have the same birthday is .71.

Ignoring issues such as leap years or twins, and assuming a uniform distribution of real-life birthdays, do you agree with the probability as stated – or could you modify the statement to make it more accurate?

Submitted by Margaret Cibes

Improving IQs

“Ways to Inflate Your IQ”
by Sue Shellenbarger, The Wall Street Journal, November 29, 2011

This is a report about a potpourri of research projects that claim to show that an IQ can change over time. Some sample IQ test questions, with suggestions about how to increase an IQ, are also provided. There is no discussion about what an IQ test measures.

In the latest study, 33 British students were given IQ tests and brain scans at ages 12 to 16 and again about four years later …; 9% of the students showed a significant change of 15 points or more in IQ scores.
On a scale where 90 to 110 is considered average, one student's IQ rose 21 points to 128 from 107, lifting the student from the 68th percentile to the 97th compared with others the same age, [according to a co-author] of the study, published last month in Nature.

Questions

1. We are told that 33 British students took an IQ test twice. It is conceivable that there were additional students who participated in the first test administration but not the second. Would it be helpful, for inference purposes, to have information about any such students, such as reasons for their non-participation in the second administration?
2. When people are IQ tested over time, do you think that they are given the same test (or a parallel version), or might a subsequent test include different skills/concepts appropriate for an older group?
3. On one commonly used IQ test, scores are standardized to mean 100 and standard deviation 15. This is consistent with the claim that a 107 score rising to 128 corresponds to a 68th percentile score rising to the 97th. How would you equate the test scores from two administrations if the tests were different, in order to account for the two tests' possibly different difficulty levels? (See “Equating Test Scores”,”by Samuel Livingston, Educational Testing Service, 2004.)

Submitted by Margaret Cibes

Winning the fight against crime by putting your head in the sand

Police Tactic: Keeping Crime Reports Off the Books Al Baker and Joseph Goldstein, The New York Times, December 30, 2011.

Police officers are joining just about every other profession in trying to skew the statistics to make themselves look good.

Crime victims in New York sometimes struggle to persuade the police to write down what happened on an official report. The reasons are varied. Police officers are often busy, and few relish paperwork. But in interviews, more than half a dozen police officers, detectives and commanders also cited departmental pressure to keep crime statistics low.

The message about reducing police reports comes in many subtle ways.

Officers sometimes bend to pressure by supervisors to eschew report-taking. “Cops don’t want a bad reputation, and stigma,” one commander said. “They know they have to please the sergeants.”

This pressure comes from even higher up.

The sergeants, in turn, are acting on the wishes of higher-ups to keep crime statistics down, a desire that is usually communicated stealthily, the commander said. As an era of low crime continues, and as 2011 draws to a close with felony numbers running virtually even with last year’s figures, any new felony is a significant event in a precinct and a source of consternation to commanders.

Part of the problem is the broad discretion that police officers apply.

In one case, Sandra Ung, 37, went to the Fifth Precinct in Chinatown after her wallet disappeared at a Starbucks. "I had it and then it was gone," she said of the Feb. 23 episode. She said she believed her wallet had been stolen, but could not prove it. She assumed the police had recorded it as pickpocketing, but when she retrieved a copy of the report days later, she saw it was recorded not as a crime, but as lost property that had gone "missing in an unknown manner."

The report noted that the victim had not felt anything that would indicate the actions of a pickpocket. But interestingly, the standards for categorizing the event as a crime were not this strict.

The guidelines focused on the very words that the police used to discount her suspicions: "The victim does not need to have witnessed, felt or otherwise been aware of being bumped or jostled in order to properly record the occurrence as grand larceny."

Questions

1. The report discusses ways in which the underreporting of crimes could be measured. Discuss those approaches and suggest any additional approaches that could be used to detect the extent of this problem.

2. Why is the desire to keep crime statistics low a short sighted policy?

Submitted by Steve Simon

Marilyn's 'Oops' on a drug testing question

Jerry Grossman wrote to point out an error in a recent "Ask Marilyn" column.

Ask Marilyn: What's the Probability of Being Chosen for a Drug Test?

by Marilyn vos Savant, Parade, 25 December 2011

A reader asks:

I manage a drug-testing program for an organization with 400 employees. Every three months, a random-number generator selects 100 names for testing. Afterward, these names go back into the selection pool. Obviously, the probability of an employee being chosen in one quarter is 25 percent. But what’s the likelihood of being chosen over the course of a year?

Marilyn responds, "The probability remains 25 percent, despite the repeated testing. One might think that as the number of tests grows, the likelihood of being chosen increases, but as long as the size of the pool remains the same, so does the probability." Jerry observes that she has answered the wrong question (What is the chance of being chosen in any given quarter?), rather than the one the reader clearly intended (What is the chance of being chosen at least once?), for which the answer would be <math>1-(3/4)^4</math>, or about 68 percent. He adds that Marilyn's readers quickly began commenting here.

Dom Rosa wrote with a link to the next week's column:

Ask Marilyn: Did Marilyn Make a Mistake on the Drug-Testing Question?

by Marilyn vos Savant, Parade, 2 January 2012

Here Marilyn prints Jerry's correction, swears off eggnog, and promises a followup on January 22. Check back here for the update!