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Created by Tom Wegleitner, Centreville, VirginiaEdited by Olga Pilipets, San Diego, California

Critical Thinking

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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.

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Misuses of Statistics

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Misuse # 1- Bad SamplesVoluntary 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.

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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

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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

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Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption.

Misuse # 4- Pictographs

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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%

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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

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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:

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PercentagesKey principal: Percentage of

• What is 34% of 500?

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PercentagesFraction to a percentage

• Convert to percentage.

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203

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PercentagesDecimal to a percentage

• Convert 0.789 into percentage.

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PercentagesPercentage to a decimal

• Convert 56.7% to an equivalent decimal..

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