1. 10 Chapter Data Analysis/Statistics: An Introduction
Copyright © 2016, 2013, and 2010, Pearson Education, Inc.

2. 10-5 Abuse of Statistics
Students will be able to understand and explain
• Misuses and abuses of statistics based on samples and populations;
• Valid and invalid inferences;
• Misuses of graphs; and
• Misuses of numerical data.

3. Abuses of Statistics
“There are three kinds of lies: lies, damned lies, and statistics.”
-Benjamin Disraeli (1804−1881)

4. Abuses of Statistics
People sometimes deliberately use statistics to mislead others. This can be seen in advertising.
More often, however, the misuse of statistics is the result of misinterpreting what the data and statistics mean.

5. Abuses of Statistics
Consider an advertisement reporting that of the people responding to a recent survey, 98% said that Buffepain is the most effective pain reliever of headaches and arthritis.
To certify that the statistics are not being misused, the following information should have been reported:
1. The questions being asked
2. The number of people surveyed
3. The number of people who responded

6. Abuses of Statistics
4. How the people who participated in the survey were chosen
5. The number and type of pain relievers tested
6. How the answers were interpreted
Without the information listed, many following situations are possible, all of which could cause the advertisement to be misleading.

7. Abuses of Statistics
1. Suppose 1,000,000 people nationwide were sent the survey, and only 50 responded. This would mean that there was only a 0.005% response, which would certainly cause us to mistrust the ad.
2. Of the 50 responding in (1), suppose 49 responses were affirmative. The 98% claim is true, but 999,950 people did not respond.

8. Abuses of Statistics
3. Suppose a survey sentence read, “Buffepain is the best pain reliever I’ve tried for headaches and arthritis,” and there were no questions about the kind and type of other pain relievers tried.
4. Suppose all the people who received the survey were chosen from a town in which the major industry was the manufacture of Buffepain. It is very doubtful that the survey would represent an unbiased sample.

9. Abuses of Statistics
5. Suppose only two “pain relievers” were tested: Buffepain, whose active ingredient is 100% aspirin, and a placebo containing only powdered sugar.

10. Abuses of Statistics
A different type of misuse of data and statistics involves graphs. Among the things to look for in a graph are the following. If they are not there, then the graph may be misleading.
1. Title
2. Labels on both axes of a line or bar chart and on all sections of a pie chart
3. Source of the data

11. Abuses of Statistics 4. Key to a pictograph
5. Uniform size of symbols in a pictograph
6. Scale: Does it start with zero? If not, is there a break shown?
7. Scale: Are the numbers equally spaced?

12. Abuses of Statistics
A line graph, histogram, or bar graph can be altered by changing the scale of the graph.

13. Abuses of Statistics
The statistics presented are the same, but these graphs do not convey the same psychological message.

14. Abuses of Statistics
Another error that frequently occurs is the use of continuous graphs to depict data that are discrete (a finite number of data values).
Many points along the line are meaningless.

15. Abuses of Statistics
Another way to distort graphs is to omit a scale.

16. Abuses of Statistics
Suppose that the number of boxes of cereal sold by Sugar Plops last year was 2 million and the number of boxes of cereal sold by Korn Krisps was 8 million.

17. Abuses of Statistics
The area of the bar representing Korn Krisps is 16 times the comparable area representing Sugar Plops, rather than 4 times the area, as would be justified by the original data.

18. Abuses of Statistics
Circle graphs easily become distorted when attempts are made to depict them as three-dimensional.

19. Abuses of Statistics
The final examples of the misuses of statistics involve misleading uses of mean, median, and mode.
All these are “averages” and can be used to suit a person’s purposes.
The important thing to watch for when a mean is reported is disparate cases in the reference
group. If the sample is small, then a few extremely high or low scores can have a great influence on the mean.