Chance News 61

Census errors

Can you trust Census data?
Freakonomics blog, New York Times, 2 February 2010
Justin Wolfers

Bureau obscured personal data—Too well, some say
Numbers Guy blog, Wall Street Journal, 6 February 2010
Carl Bialik

To be continued...

Submitted by Bill Peterson

Height bias or data dredging?

Soccer referees hate the tall guys
Wall Street Journal, 8 Feburary 2010

According to the article, "Niels van Quaquebeke and Steffen R. Giessner, researchers at Erasmus University in Rotterdam, compiled refereeing data from seven seasons of the German Bundesliga and the UEFA Champions League, as well as three World Cups (123,844 fouls in total)" and found:

Height Difference	Probability of Foul Against Taller Player
1-5 cm	52.0%
6-10 cm	55.4%
> 10 cm	58.8%

Avg. Height of Perpetrator	Avg. Height of Victim
182.4 cm	181.5 cm

Note that the height difference on average is only 0.9 cm!

To be continued... Submitted by Paul Alper

Poll question wording affects results

“New Poll Shows Support for Repeal of ‘Don’t Ask, Don’t Tell’”
by Dalia Sussman, The New York Times, February 11, 2010
"Support for Gays in the Military Depends on the Question"
by Kevin Hechtkopf, CBS News, February 11, 2010

These articles describe how the wording of a February 5-10, 2010, NYT/CBS News poll affected the results.

When half of the 1,084 respondents were asked their opinions about permitting “gay men and lesbians” to serve in the military, 70% said that they strongly/somewhat favored it. Of the other half of respondents who were asked about permitting “homosexuals” to serve, only 59% said that they strongly/somewhat favored it. The gap was much wider (79% to 43%) for respondents identifying themselves as Democrats.

For more detailed poll results, see the CBS News website [1].

Discussion
1. The margin of error for each half sample was said to be +/- 4 percentage points. Would you consider the difference between 70% and 59% statistically significant? If not, why? If so, at what level? What about the difference for Democrats?
2. Can you suggest any reason for the difference between 70% and 59% for the half samples? For the difference between 79% and 43% for the Democratic half samples?
3. What implication(s) do these results have, if any, for ballot-question writers?

Submitted by Margaret Cibes based on a suggestion of Jim Greenwood and an ISOSTAT posting by Jeff Witmer

Disability to present accurate statistics

The Odds of a Disability Are Themselves Odd Ron Lieber, The New York Times, February 5, 2010.

What are your chances of needing disability insurance?

You have an 80 percent chance of becoming disabled during your working years. Or maybe it’s 52 percent. Or possibly 30 percent. But it could be much lower. Unless you get injured, of course. And did you realize that 31 million people experience a disabling injury each year? Welcome to the disability insurance funhouse, where the odds of an injury or illness that would keep you out of work for more than three months range wildly, depending on where you look for guidance.

Why all the variation? Part of it depends on your definition of disability. One quoted statistic was too high because

the statistic comes from the National Safety Council, which describes “disabling” pretty loosely. “It interferes with normal daily activity one day beyond the day of injury,” said Amy Williams, a spokeswoman for the National Safety Council. “It doesn’t mean they weren’t able to go to work. It may mean that they twisted their ankle and couldn’t go to Pilates that night.”

A good estimate of disability, one that defines the duration of the disability (an injury that keeps you out of work for 90 days or more) and a time frame for the individual (probability of a disability event between the ages of 25 and 65), appears to be around 30%. But even that number needs to be qualified.

Numbers for white-collar workers are usually lower than for assembly line workers. If you have no chronic conditions, eat decent food and avoid cigarettes, your odds may drop to 10 percent, according to the “Personal Disability Quotient” quiz on the Web site of the Council for Disability Awareness.

And there are even more qualifiers.

Here are a few other things to keep in mind if you’re running your own numbers. Some people lie about being disabled, and their fake claims skew the actuarial data, though no one knows by how much. Lower your odds a bit to account for the cheaters. Lower them some more in recognition of the fact that people who buy their own policies also tend to actually use them.

This is not to imply that disability insurance is a bad deal. The article failed to make this point, but insurance makes sense for covering catastrophic events of whatever probability, that would otherwise bankrupt an individual. It is the magnitude of the potential loss, rather than the probability, that determines whether you should buy insurance.

Submitted by Steve Simon