1. Smart Start
In June 2003, Consumer Reports published an article on some sport-utility vehicles they had tested recently. They had reported some basic information about each of the vehicles and the results of some tests conducted by their staff. Among other things, the article told the brand of each vehicle, its price, and whether it had standard or automatic transmission. They reported the vehicle’s fuel economy, its acceleration (number of seconds to go from 0 to 60 mph), and its breaking distance to stop from 60 mph. The article also rated each vehicle’s reliability as much better than average, better than average, average, worse, or much worse than average.
Describe the W’s of the information
List the variables and indicate whether each variable is categorical or quantitative. If the variable is quantitative tell its units.

2. Chapter 1.1 Analyzing Categorical Data

3. The Titanic – The data
Here are some data about the passengers and crew on board.
Survival
Age
Sex
Class
Dead
Alive
Adult
Male
Female
Third
Crew
First

4. Review from Chapter 1 Identify the 5 W’s and how about the data: Who –
What –
When –
Where –
Why –
How –

5. Frequency Tables Example:
A _____________ like ticket class with only a few categories is easy to read. For a variable with dozens or hundreds of categories is much harder to read.
Class
Count
First
Second
Third
Crew
325
285
706
885

6. Frequency Tables
Counts are useful, but sometimes we want to know the fraction or _______________of the data in each category. Multiply by 100 to express the proportion as a _____________.
_________________ _________________ table: Displays the _____________________ rather than the _____________ of the values in each ____________________.
They describe the distribution of ______________ variable because they name possible categories and tell how frequently each occurs.
Class %
First
Second
Third
Crew

7. Frequency Table Example
Fill in the table with your M&M data.
Color
Frequency
Relative Frequency
Percent
Blue
Red
Green
Orange
Yellow
Brown
Total

8. Bar Chart - Characteristics
Definition: Bar chart –
Should always obey the _____________________. That is their widths have to be the _______ so their ____________ determine the area and is _________________ to the count.
Should have _______________between the bars to indicate that they are freestanding bards that could be ________________ into any order
They can be vertical or horizontal

9. Bar Chart - Example
Create a bar chart for your M&M data:

10. Bar Chart – Relative Frequency
You can replace the counts with percentages and create a _______________ ________________bar chart.
The sum of the relative frequencies is 100%
Here is the relative frequency bar chart of the titanic data:

11. Relative Frequency Bar Chart - Example
Create a relative frequency bar chart for your M&M data:

12. Pie Charts
Often difficult to construct by hand.

13. Misleading Graphs: Example
In the regular season, basketball player Dwayne Wade averaged 7.5 assists per game and 2.2 steals per game. Explain what is wrong with the following graph and how to make it better.
Although the heights of the basketballs are correct, our eyes respond to the areas of the basketballs. The area of the basketball representing assists is over 9 times as big. It would be better to use equally wide bars for assists and steals so that only the height of the bars determines the area.

14. Misleading Graphs: Example
Here are two possible bar graphs of the data table. Which one could be considered deceptive? Why?
Previous Ownership
Count
Percent (%)
None 85
17.0 PC 60
12.0
Macintosh
355
71.0
Total
500
100.0

15. Chapter 2 - Continued
Two-Way Tables and Marginal Distributions, Relationships between Categorical Variables: Conditional Distributions

16. Two-Way Tables
To answer this question, our first step is to _________________
______________
Two-Way Table:
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201

17. Each cell of the table gives the ________________________
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201
Each cell of the table gives the ________________________
_______________________________________
The ___________ of the table, both on the right and at the bottom, give _____________.
The bottom line of the table is the ____________________ of the __________________.
The right column is the _________________________of the variable ____________.
When presented like this, in the _____________ of a contingency table, the __________________________of one of the variables is called ________________________

18. Find the cell containing 118. Find the cell containing 178.
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201
Find the cell containing 118.
Find the cell containing 178.
More third class survived, but does that mean that third class passengers were more likely to survive?
Keep in mind, there were more third class passengers on the ship. Therefore, to compare them fairly we need to express them as __________.

19. Percent of what …?
For every cell there are three choices of percent:

20. Percent of What?
Each different percent affects the ________ of the problem
What percent of survivors were in 2nd class?
Who –
What percent were 2nd class passengers who survived?
What percent of 2nd class passengers survived?
Key words -

21. Super Bowl Example
A recent Gallup poll asked 1,008 Americans age 18 and over whether they planned to watch the upcoming Super Bowl. The pollster also asked those who planned to watch whether they were looking forward more to seeing the football game or the commercials. The results are summarized in the table.

22. Example – Finding Marginal Distributions
Male
Female
Total
Game
279
200
479
Commercials 81
156
237
Won’t Watch
132
160
292
492
516
1,008
Question: What’s the marginal distribution of the responses?

23. Conditional Distributions
A ___________ ______________ shows the _______________ of one variable, for only the individuals who ___________________________________________
_______________________________________
The conditional distribution of ______ ______ conditional on _____________
The conditional distribution of ticket class, conditional on _______________:
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
First
Second
Third
Crew
Total
Dead
122
167
528
673
1490

24. Conditional Distributions
What is the conditional relative distribution of survival status among the third class?
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201

25. Independence
If the ____________ ______________are the ______, we conclude that the variables are _____ _______________. Therefore, they are ______________ of each other
If the conditional distributions _________, we conclude that the variables are somehow associated. Therefore, they are ______ ____________of one another.

26. Conditional Distributions
We can create a picture of this table by using two pie charts. We want to restrict the ______ in the problem to ____________ and then restrict the ________to _______________.

27. Segmented Bar Charts
We can display the Titanic information by dividing up bars rather than using circles.
The resulting segmented bar chart

28. Segmented Bar Charts

29. Super Bowl Example – Finding Conditional Distributions
Male
Female
Total
Game
279
200
479
Commercials 81
156
237
Won’t Watch
132
160
292
492
516
1,008
Question: How do the conditional distributions of interest in the commercials differ for men and women?
Answer:
Conclusion:

30. Titanic Example – Conditional Distribution
We can turn our Titanic question around and look at the distribution of survival for each ticket class (column percent)
What is the conditional distribution of survival status among ticket classes?
First
Second
Third
Crew
Total
Alive
203
118
178
212
711
Dead
122
167
528
673
1490
325
285
706
885
2201

31. Titanic Example – Column %
Conclusion: Looking at how the percentages across each row it looks like your class mattered.

32. Super Bowl Example – Association between Variables
Question: Does it seem that there is an association between interest in Super Bowl TV coverage and a person’s gender?
Steps:
Male
Female
Total
Game
279
200
479
Commercials 81
156
237
Won’t Watch
132
160
292
492
516
1,008

33. Example – Association between Variables

34. Just Checking
A Statistics class reports the following data on Sex and Eye Color for students in the class.
Blue
Brown
Green/
Other
Total
Males 6 20 32
Females 4 16 12 10 36 18 64

35. Just Checking What percent of females are brown-eyed?
What percent of brown-eyed students are female?
What percent of students are brown-eyed females?
What’s the distribution of Eye Color?
What’s the conditional distribution of eye color for the males?
Compare the percent who are female amount the blue-eyed students to the percent of all students who are female.
Does is seem that Eye color and sex are independent? Explain.