This document discusses critical thinking in statistics and common misuses of statistics. It identifies 13 common misuses: 1) bad samples, like voluntary response samples where conclusions can only be made about respondents, 2) small samples where conclusions shouldn't be based on too small a sample, 3) misleading graphs that exaggerate differences, 4) pictographs that also exaggerate differences, 5) percentages that can be unclear or misleading, and 6) other issues like loaded questions, order of questions, refusals, confusing correlation with causation, biased studies, imprecise numbers, and partial pictures. The purpose is to illustrate how common sense is needed to properly interpret data and statistics.

1. SlideSlide 1Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Created by Tom Wegleitner, Centreville, Virginia
Edited by Olga Pilipets, San Diego, California
Critical Thinking

2. SlideSlide 2Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Key Concepts
 Success in the introductory statistics
course typically requires more common
sense than mathematical expertise.
 This section is designed to illustrate how
common sense is used when we think
critically about data and statistics.

3. SlideSlide 3Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Misuses of Statistics

4. SlideSlide 4Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Misuse # 1- Bad Samples
Voluntary response sample
(or self-selected sample)
one in which the respondents themselves
decide whether to be included
In this case, valid conclusions can be
made only about the specific group of
people who agree to participate.

5. SlideSlide 5Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Misuse # 2- Small Samples
Conclusions should not be based
on samples that are far too small.
Example: Basing a school
suspension rate on a sample of
only three students

6. SlideSlide 6Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
To correctly interpret a graph, you must analyze the numerical
information given in the graph, so as not to be misled by the
graph’s shape.
Misuse # 3- Graphs

7. SlideSlide 7Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Part (b) is designed to exaggerate the difference by increasing
each dimension in proportion to the actual amounts of oil
consumption.
Misuse # 4- Pictographs

8. SlideSlide 8Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Misuse # 5- Percentages
Misleading or unclear percentages are
sometimes used. For example, if you
take 100% of a quantity, you take it all.
Example: a certain airline company
claimed that they increased the
recovery of missing luggage by up to
100%

9. SlideSlide 9Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
 Loaded Questions
 Order of Questions
 Refusals
 Correlation & Causality
 Self Interest Study (who is
paying for the study?)
 Precise Numbers
 Partial Pictures
 Deliberate Distortions
Other Misuses of Statistics

10. SlideSlide 10Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
Recap
 Reviewed 13 misuses of statistics
 Illustrated how common sense can play a
big role in interpreting data and
statistics
In this section we have:

11. SlideSlide 11Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

12. SlideSlide 12
Percentages
Key principal: Percentage of
• What is 34% of 500?
Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

13. SlideSlide 13
Percentages
Fraction to a percentage
• Convert to percentage.
Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
20
3

14. SlideSlide 14
Percentages
Decimal to a percentage
• Convert 0.789 into percentage.
Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

15. SlideSlide 15
Percentages
Percentage to a decimal
• Convert 56.7% to an equivalent decimal..
Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.