1.3: Uses and Abuses of Statistics

Objective: To identify common errors and misuses of statistics

CHS Statistics

Practical Uses of Statistics

Poll results are used to determine the television shows we watch and the products we purchase.

Manufacturers provide better products at lower costs by using statistical control tools, such as control charts.

Diseases are controlled through analyses designed to anticipate epidemics.

Endangered species of fish and other wildlife are protected through regulations and laws that react to statistical estimates of changing population sizes.

Through statistical analysis of fatality rates, legislators can better justify laws, such as those governing air pollution, auto inspections, seat belt and air bag use, and drunk driving.

These are just a few examples of the many practical uses of statistics!

Abuses of Statistics

Some people will use statistics in which the data are presented in ways that are designed to be misleading.

Some abuses are not intentional, but some are!

“Statistics show far fewer skateboarding injuries in the winter, while sledding injuries are more common.”

Does this seem like a valid statement? What could be a reason for such misleading statistics?

Abuses of Statistics (continued)

Common ways in which data are misleading:

1) Bad samples

A major source of deceptive statistics is the use of inappropriate methods to collect data.

Self-selected survey – (voluntary response sample) is one in which the respondents themselves decide whether to be included

In such surveys, people with strong opinions are more likely to participate, so the obtained responses are not necessarily representative of the whole population.

Abuses of Statistics (continued)

Common ways in which data are misleading:

2) Small Samples

It can be very misleading to make broad conclusions or inferences based on samples that are far too small.

Example: Children’s Defense Fund’s publication of Children Out of School in America reported that among secondary school students suspended in one region, 67% were suspended at least three times. That statistic was based off of only three students, and the media reports failed to mention that!

Abuses of Statistics (continued)

Common ways in which data are misleading:

3) Loaded Questions

Survey questions can be worded to elicit a desired response.

A “loaded” item uses emotionally charged words – words that have a strong negative or positive.

Example: The University of Pittsburgh should stop wasting student activities funds on elitist organizations such as fraternities and sororities.

A. strongly agree B. agree C. neutral D. disagree E. strongly disagree

This is a loaded item because of the use of the phrases “wasting funds” and “elitist organizations.” It would be improved by making the wording more neutral.

Abuses of Statistics (continued)

Common ways in which data are misleading:

4) Misleading Graphs

Many visual graphs (especially bar charts and pie charts) exaggerate or hide the true meaning of the data. Using different increments or not following the Area Principle is a key way to exaggerate, so be careful when reading charts!

Abuses of Statistics (continued)

Common ways in which data are misleading:

4) Misleading Graphs – More examples

Abuses of Statistics (continued)

Common ways in which data are misleading:

5) Pictographs Using pictures and three-dimensional objects as bars in histograms and bar

charts can be misleading and, again, not follow the Area Principle.

Abuses of Statistics (continued)

Common ways in which data are misleading:

6) Precise Numbers

Being precise is not always accurate. Saying there are 203,144,036 vehicles in the Southeast region. Since this number is an estimate, it would be better to say about 203 million.

Abuses of Statistics (continued)

Common ways in which data are misleading:

7) Distorted Percentages

Be careful with interpretation of percentages:

An ad from Continental Airlines referring to lost baggage; “… an area where we’ve already improved 100% in the last six months.”

The New York Times took this to mean there is no lost baggage, which has never been achieved by Continental Airlines.

Abuses of Statistics (continued)

Common ways in which data are misleading:

8) Partial Pictures

“Ninety percent of all our cars sold in this country in the last 10 years are still on the road.”

Consumers were impressed; however, the dealer failed to mention that 90% of the cars that the dealer sold were in the last 3 years.

Abuses of Statistics (continued)

Common ways in which data are misleading:

9) Deliberate Distortions

Be careful to accurately interpret survey results. Hertz sued Avis because Avis said they were the winner of the survey among car rental companies. When Hertz requested the actual survey results, the responses disappeared and the magazine coordinator who published the survey result statement resigned.

Homework

Pp. 15 – 16 # 1 – 6, 8 – 12, 14