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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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Section 1-3

Critical Thinking

Created by Tom Wegleitner, Centreville, Virginia


Success in statistics
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.



Definitions
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.


Misuses of statistics1
Misuses of Statistics

  • Misleading Graphs

  • Bad Samples

  • Small Samples



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


Misuses of statistics2
Misuses of Statistics

  • Bad Samples

  • Small Samples

  • Misleading Graphs

  • Pictographs


Double the length, width, and height of a cube, and the volume increases by a factor of eight

Figure 1-2


Misuses of statistics3
Misuses of Statistics volume increases by a factor of eight

  • Bad Samples

  • Small Samples

  • Misleading Graphs

  • Pictographs

  • Distorted Percentages

  • Loaded Questions


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?”


Bad Samples eliminate waste?”

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


Recap eliminate waste?”

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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