Chapter 9 1

Chapter 9

Do the Numbers Make Sense?

Chapter 9 2

Thought Question 1

In 1994, according to the Department of Labor, the median salary for government workers was $29,528, while the median salary for private workers was $26,494. Conservative groups have claimed that this shows that government workers are an overpaid “privileged class.” Does this make sense?

Chapter 9 3

Thought Question 1: Answer

The nature of salaried jobs in the public and private sectors is so different that a comparison of median salaries can be misleading. For example, government doctors and lawyers receive salaries; most private-sector doctors and lawyers are self-employed, so their income is not used in the Department of Labor’s calculations, even though they often earn much more than government employees.

Chapter 9 4

Thought Question 2

Two papers were written on similar topics and it turned out that identical data points appeared in each paper, but the actual number of subjects cited was different for each paper. Do you have any questions as to whether or not these are legitimate results?

Chapter 9 5

Thought Question 2: Answer

The suspicious regularity of the identical data points and the inconsistency in the number of subjects should make one wonder if the data have been falsified (or at least reported inaccurately).

Chapter 9 6

Ask the following questions What didn’t they tell us?

– missing data or information Are the numbers consistent / plausible / too good

to be true?– distorted information– fake or falsified data– too much precision or regularity in the numbers– data from a biased sample

Is the arithmetic correct? Is there a hidden agenda?

Chapter 9 7

What didn’t they tell us?Consumer Reports (April 1985)

A.R.M. Allergy Relief Medicine switched to “new formula maximum strength.”

Old formula had 37.5 mg of active ingredient. New formula had only 25 mg. FDA limited dosage to 25 mg. Company complied by lowering its dosage,

and called the new tablet “maximum strength” because it contained the federal maximum dosage.

Chapter 9 8

Are the numbers consistent? Durham NC Morning Herald (Feb. 23, 1982)

“Of 258 persons who answered the survey [on Chapel Hill parks], 96 percent were white. Thirty-eight percent of the 10 non-whites surveyed said they were satisfied with recreation services; 73 percent indicated they used the parks.”

What is 38% of 10 people?3.8 people (10 x 0.38 = 3.8)

What is 73% of 10 people?7.3 people

Chapter 9 9

Are the numbers plausible? Lafayette Journal and Courier (June 12, 2000)

“Southwest does, however, carry a far greater number of passengers, 65,288 in 1999 to TWA’s 25,790.”

Do these values seem believable? The 2000 Statistical Abstract says that 600

million passengers flew in the U.S. in 1997. The author meant to write 65,288,000 and

25,790,000.

Chapter 9 10

Are the numbers too good? Student project (Fall 2000)

A sample of 1000 M&M Peanut candies was investigated to determine the proportion of each color produced.

Results:20% Brown20% Yellow 20% Red 20% Blue 10% Orange 10% Green

The results match EXACTLY with what the M&M manufacturer states.

Chapter 9 11

Is the arithmetic correct? Forbes (April 8, 1996)

“Packard Bell had sales of $20 billion over ten years and $45 million in profits, a profit margin of 2% of sales.”

What percent of 20,000,000,000 is 45,000,000?

(45,000,000 / 20,000,000,000 = .00225)

0.225%

Chapter 9 12

Is there a hidden agenda? Gloria Steinem’s Revolution from Within

She claims that in the United States “150,000 females die of anorexia each year.”

The National Center for Health Statistics says about 50 die per year.

The American Anorexia and Bulimia Foundation (an advocacy group) claims that roughly 150,000 to 200,000 women suffer from anorexia.

Be wary of numbers reported by an individual or group with a cause to support.

Chapter 9 13

Case Study

Affirmative Action Poll

appeared in The Press of Atlantic City on March 25, 1995 p. A6.

Chapter 9 14

Case Study

Headline: “Poll: 75 % of Americans are against affirmative action”

Actually: only 28% of respondents would abolish affirmative action programs. The additional 47% of the reported 75% in the headline would change them. – DISTORTED INFORMATION– HIDDEN AGENDA?

Chapter 9 15

Case Study

Microwave Choice

Surveying Subjective Phenomena, by Turner and Martin, 1984, Sage.

Objective:To determine most preferred

brand of microwave.

Chapter 9 16

Case Study

Litton industries claimed: “76% of independent microwave oven technicians surveyed recommended Litton.”

PROBLEM: survey included only technicians who serviced Litton ovens and at least one other brand, some of whom were actually Litton dealers. – BIASED SAMPLE– HIDDEN AGENDA?

Chapter 9 17

A health club reports that of its members over 50 years of age, 45% are men and 25% are women– what about the other 30%? (45%+25% = only 70%)

– CHECK THE ARITHMETIC

Case Study

Percents

Chapter 9 18

Samples of 20 individuals were taken from five different age groups at the health club. For each sample of 20 individuals, the percentage that used the swimming pool for exercise was reported as follows: 8% 14% 16% 21% 37%– percents from 20 individuals must be multiples of 5– what is 8% of 20? [ 20 x 0.08 = 1.6 people ]

– INCONSISTENT DATA

Case Study

Chapter 9 19

Key Concepts

Critical thinking about believing the data Missing information Inconsistencies in data Implausible data Incorrect arithmetic Hidden agendas