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Created by Tom Wegleitner, Centreville, Virginia

Section 1-3 Critical Thinking. Created by Tom Wegleitner, Centreville, Virginia. Success in Statistics. Success in the introductory statistics course typically requires more common sense than mathematical expertise.

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Created by Tom Wegleitner, Centreville, Virginia

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  1. Section 1-3 Critical Thinking Created by Tom Wegleitner, Centreville, Virginia

  2. Success in Statistics • 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. Misuses of Statistics • Bad Samples

  4. Definitions • Voluntary response sample (or self-selected survey) 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. Misuses of Statistics • Misleading Graphs • Bad Samples • Small Samples

  6. Figure 1-1

  7. To correctly interpret a graph, we should analyze the numericalinformation given in the graph instead of being mislead by its general shape.

  8. Misuses of Statistics • Bad Samples • Small Samples • Misleading Graphs • Pictographs

  9. Double the length, width, and height of a cube, and the volume increases by a factor of eight Figure 1-2

  10. Misuses of Statistics • Bad Samples • Small Samples • Misleading Graphs • Pictographs • Distorted Percentages • Loaded Questions

  11. 97% yes: “Should the President have the line item veto to eliminate waste?” 57% yes: “Should the President have the line item veto, or not?”

  12. Bad Samples Small Samples Misleading Graphs Pictographs Distorted Percentages Loaded Questions Order of Questions Refusals Correlation & Causality Self Interest Study Precise Numbers Partial Pictures Deliberate Distortions Misuses of Statistics

  13. Recap In this section we have: • Reviewed 13 misuses of statistics. • Illustrated how common sense can play a big role in interpreting data and statistics

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