Number SensePart II – Computations and Benchmarks

This video is designed to accompanypages 1-12

in Making Sense of UncertaintyActivities for Teaching Statistical

ReasoningVan-Griner Publishing Company

Implausible Numbers

An article in the journal Science on insects attacking plants, mentioned a California field that produces 750,000 melons per acre

1 acre = 43,560 ft2

750,000 melons/acre = 750,000 melons/43,560 ft2

That’s a little over 17 melons per square foot.

Percentages or Absolutes?

Probably not. Comair is only on-time 62% of the time compared to 71% for Atlantic Southeast. Makes obvious sense to look at rates in this case..

Lexington’s Bluegrass Field – July, 2007

Airline Total flights On time

Pinnacle Airlines Inc.

141 122

Skywest Airlines Inc.

123 88 Atlantic Southeast Airlines

91 65 Expressjet Airlines Inc.

84 55

American Eagle Airlines Inc.

155 97 Comair Inc.

255 158 Delta Air Lines Inc.

28 13

Have a look at this flight table regarding the airport in Lexington, Kentucky. Is it fair to say Comair, with 158 on time flights is much superior to Atlantic Southeast with only 65?

Percentages or Absolutes?

Baby cured of HIV: What does this mean for the future of treatment?Published March 04, 2013FoxNews.comAbsolute: That’s one baby cured out of one baby treated.

Percent: That’s a 100% success rate.

Details: Would be the same regardless but we have to be ready to uncover them.

Percentages or Absolutes?Maternal Health in the U.S.It's more dangerous to give birth in the United States than in 49 other countries. African-American women are at almost four times greater risk than Caucasian women. A safe pregnancy is a human right for every woman regardless of race or income.

Maternal mortality ratios have increased from 6.6 deaths per 100,000 live births in 1987 to 13.3 deaths per 100,000 live births in 2006.

Absolute: That’s an increase of 6.7 deaths per 100,000 live births.

Percent: An increase of (13.3/6.6)= 2.02, so just over a 100% increase since 1987.Could both be useful. But sometimes one creates a more extreme picture than does the other. Be wise, be aware.

United States - 82 United Kingdom - 44In a 2007 campaign advertisement, former New York City mayor Rudy Giuliani said, “I had prostate cancer, five, six years ago. My chances of surviving prostate cancer—and thank God, I was cured of it—in the United States? Eighty-two percent. My chances of surviving prostate cancer in England? Only 44 percent under socialized medicine.”

He apparently used data from the year 2000, when 49 British men in every 100,000 were diagnosed with prostate cancer, of whom 28 died within five years — about 44 percent. Using a similar approach, he cited a corresponding 82 percent five-year survival rate in the U.S ….

Endless Possibilities!

The PSA is widely used in the U.S. but not in the U.K. Prostate cancer is a cancer that often develops slowly and is not the cause of death in an elderly male. So in the U.S. we have detection coming at 50 and the patient living to 70; in the U.K. detection might come at 67 and the patient lives to 70. Both have same time of death, but U.S. looks better with a stronger “five-year” survival rate.

Five-year Survival Rates

What Can You Do?

Be alert, and be aware.Be ready and willing to question what you

read and hear.Be comfortable with fractions and

percentages.Be well-versed in some basic

“benchmarks.”

Benchmarks to Know

1. U.S. population is about 300 million2. Each year about 4 million babies are born in

the U.S.3. About 2.4 million Americans die each year4. Roughly 1 in 4 who die, do so of heart

disease5. Roughly 1 in 4 who die, die from cancer,

more or less.*From Joel Best’s book Stat-Spotting …

Benchmarks to Know

6. About 43,000 die in traffic accidents7. About 17,000 deaths are homicides8. About 16,000 deaths are from AIDS9. There are about 40 million black Americans10.About 14% of Americans identify themselves

as Latino

Useful? How?

Claim has been made that over 4 million women in the U.S. are battered to death each year by a spouse or boyfriend.

Hmmm, only about 2.4 million people die in the U.S. per year … all together!

One-Sentence Reflection

Competence with fractions, percentages, and a knowledge of common benchmarks go a long way toward the goal of correctly forming human inferences from statistical constructs.