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

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.

Misuses of Statistics  Bad Samples

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 Statistics  Misleading Graphs  Bad Samples  Small Samples

Figure 1-1

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

Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs

Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs

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

Misuses of Statistics  Bad Samples  Small Samples  Misleading Graphs  Pictographs  Distorted Percentages  Loaded Questions

Loaded Questions Too little money is being spent on welfare Too little money is being spent on assistance to the poor.

Order of Questions Would you say that traffic contributes more or less to air pollution than industry? Would you say that industry contributes more or less to air pollution than industry? When traffic was presented first, 45% blamed traffic and 27% blamed industry; when industry was presented first, 24% blamed traffic and 57% blamed industry.

Self-Interest Study Kiwi Brands, a maker of shoe polish, commissioned a study that resulted in this statement: “ According to a nationwide survey of 250 hiring professionals, scuffed shoes was the most common reason for a male job seeker’s failure to make a good first impression.”

 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

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:

After the last national Census was conducted, the Poughkeepsie Journal ran this front page headline: “281,421,906 in America.” What is wrong with this headline? The census is not 100% accurate, especially among those(such as illegal aliens) who may not wish to be counted.

In a ABC Nightline poll, 186,000 viewers each paid 50 cents to call a “900” telephone number with their opinion about keeping the United Nations in the United States. The results showed that 67% of those who called were in favor of moving the United Nations out of the United States.

A client received a survey from the investment firm of Merrill Lynch. It was designed to gauge his satifaction as a client, and it had specific questions for rating the client’s personal Financial Consultant. The cover letter included this statement: “Your responses are extremely valuable to your Financial Consultant, and the Merrill Lynch… We will share your name with your Financial Consultant.

What is wrong with this survey?