1. Quick Check
In 2002, Consumer Reports published an article evaluating refrigerators. It listed 41 models, giving the brand, cost, size (cu ft), type (such as top- freezer), estimated annual energy cost, an overall rating (good, excellent, etc.), and the history for that brand (percentage requiring repairs over the past five years).
State the W's. if not given state not specified. Be sure to tell whether the variables are categorical or quantitative. If quantitative state the units.
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2. Chapter 3 Displaying and Describing Categorical Data
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3. Objective
Understand how to display and describe a single categorical variable.
Read Chapter 3 pages 15 – 18
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4. Employment History
Which of the following best describes your employment history?
Currently employed
Employed in summer but not currently employed
Never had a job
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5. Example 1: Displaying a Categorical Variable
Produce a graph that displays the Employment History data effectively.
What is the most common Employment History? Least Common?
Write a few sentences describing the class distribution.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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6. Example 2: Movies Which movies below have you have seen this year?
Guardians of the Galaxy
Captain America: The Winter Soldier
The Lego Movie
Transformers: Age of Extinction
Maleficent
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7. Bad Graphs
When you draw bar graphs, draw the bars equally wide (area principle). Don't get fancy! People sometimes add features to graphs that don’t help to convey their information.
What's wrong with these graphs?
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8. Partner Work
A survey of college freshmen asked what field they planned to study. The results: 25.2% arts and humanities, 19.3% business, 7.1% education, 16.6% engineering and science, 7.8% professional, and 15.3% social science.
What percent planned to study fields other than those listed?
Make a graph that compares the percents of college freshman planning to study various fields.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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9. Assignment Ch 3 Do #5, 7, & 12 Slide 3- 11
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10. Quick Check
What's wrong with this graph? Sketch a more appropriate graph.
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11. Two-way or Contingency Tables
This is a contingency or two-way table because it describes two categorical variables.
Name the two variables and categories for each.
Freshmen
Sophomores
Juniors
Seniors
No AP Courses
311
296
277
133
1 AP Course 1 23 65 51
2 AP Courses 4 48 83
3 or More AP Courses 54
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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12. Marginal Distributions
The row totals and column totals in a two-way table give the marginal distributions of the two individual variables. The marginal distribution summarizes one of the variables at a time.
Find the marginal distributions.
Freshmen
Sophomores
Juniors
Seniors
Total
No AP Courses
311
296
277
133
1 AP Course 1 23 65 51
2 AP Courses 4 48 83
3 or More AP Courses 54
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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13. Marginal Distributions Again
Determine the marginal distribution of grade in terms of percents.
Determine the marginal distribution of class in terms of percents.
Freshmen
Sophomores
Juniors
Seniors
Total
No AP Courses
311
296
277
133
1017
1 AP Course 1 23 65 51
140
2 AP Courses 4 48 83
135
3 or More AP Courses 54 58
312
323
394
321
1350
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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14. Describing Relationships
What percent of Freshmen were in No AP Courses?
What percent of students in No AP Courses were Freshmen?
What percent of students were Freshmen in No AP Courses?
Freshmen
Sophomores
Juniors
Seniors
Total
No AP Courses
311
296
277
133
1017
1 AP Course 1 23 65 51
140
2 AP Courses 4 48 83
135
3 or More AP Courses 54 58
312
323
394
321
1350
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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15. Conditional Distributions
To find the conditional distribution of the row variable, look only at that one column in the table. Find each entry in the column as a percent of the column total.
Calculate the conditional distribution of AP status among Freshmen.
Calculate the conditional distribution of AP status among Sophomores, Juniors, and Seniors.
Freshmen
Sophomores
Juniors
Seniors
Total
No AP Courses
311
296
277
133
1017
1 AP Course 1 23 65 51
140
2 AP Courses 4 48 83
135
3 or More AP Courses 54 58
312
323
394
321
1350
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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16. Segmented Bar Charts
Conditional distributions can be represented visually with segmented bar graphs.
Each category of the explanatory variable is represented by a rectangle with a total height 100%, but each rectangle contains segments whose lengths correspond to the conditional proportions.
Construct a segmented bar chart of the conditional distributions by Grade.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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17. Assignment Categorical Variables WS Slide 3- 20
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18. Quick Check
In 1993, one of the first studies aimed at preventing maternal transmission of AIDS to infants gave the drug AZT to pregnant, HIV- infected women (Connor et al., 1994). Roughly half of the women were randomly assigned to receive the drug AZT, and the others received a placebo. The HIV-infected status was then determined for 363 babies.
What percent were HIV-infected and given a placebo?
What percent of those with HIV were given a placebo?
What percent of those given a placebo were HIV-infected?
HIV-Infected
Treatment
Yes No
Total
AZT 13
167
180
Placebo 40
143
183 53
310
363
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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19. Partner Activity
In 1993, one of the first studies aimed at preventing maternal transmission of AIDS to infants gave the drug AZT to pregnant, HIV-infected women (Connor et al., 1994). Roughly half of the women were randomly assigned to receive the drug AZT, and the others received a placebo. The HIV- infected status was then determined for 363 babies.
Determine the marginal distribution of HIV status in percents.
Determine the conditional distribution of HIV status for each treatment group in percents.
Sketch a segmented bar graph.
HIV
Yes No
Total
AZT 13
167
180
Placebo 40
143
183 53
310
363
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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20. Independence and Association
Comparing conditional distributions reveals the nature of the association between two categorical variables.
Two categorical variables are said to be…
Associated if the distributions are different for at least two categories.
Independent if the conditional distributions of one variable are similar for every category of the other variable.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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21. Independence and Association
Does this data suggest there is an association between HIV-infected status and treatment? Give statistical evidence to support your conclusion.
Can the researchers conclude that AZT prevents HIV- transmission for pregnant women? Explain.
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22. Discussion
With which issue does opinion about government spending come closer to being independent of political viewpoint – environment or space program? Explain how you can tell.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

23. Independence
Complete the table so that treatment and HIV-infected status are independent.
Make a segmented bar chart.
Describe the association.
HIV
Yes No
Total
AZT
180
Placebo
183 53
310
363
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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24. Concept Check
What does the display suggest about the association between gender and feeling about weight? Give statistical evidence to support your conclusion.
The data provide evidence that feeling about weight and gender are associated. More females feel overweight (55%) than males (30%). More males feel their weight is about right (50%) than females (40%).
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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25. Assignment Finish Reading Chapter 3 Do #15 & 23
Investigative Task/Review Next Class
Quiz 1 in 2 Classes (No Notes)
Ch 2 & 3
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26. Quick Check Determine whether each statement is true or false.
The number of college graduates is greatest in 2004.
The percent with only a High school diploma is decreasing.
In 2004, more than half had at least some college.
There is no association between year and education level.
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27. Investigative Task Group Task – graded (due next class).
Complete a single report summarizing your data.
Be sure to complete all parts.
Quiz next class (chapter 1 – 3):
No notes
Calculator expected
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