1. Variability and Associations in Categorical Data
Investigation #5

2. Every roller coaster had wooden frames
Every roller coaster had wooden frames. Now, most roller coasters have steel frames, even though wood is still popular. A recent roller coaster census counted 174 wood-frame coasters, with 129 in North America.

3. How can people compare wood- and steel-frame roller coasters
How can people compare wood- and steel-frame roller coasters? Wood and steel are types of frames, not numbers. Types of roller coaster is what statisticians call a categorical variable that has values of wood and steel.
What could be some other types of categorical data we could use?

4. A study comparing popularity of dogs would investigate the categorical variable breed of dog with values standard poodle, Irish setter, German pointer, Chihuahua, whippet, and so on.

5. Wood or steel? That is the Question Relationships in categorical data
Problem 5.1
Wood or steel?
That is the Question
Relationships in categorical data

6. What does a two-way table show you about preferences among groups?
Focus Question:
What does a two-way table show you about preferences among groups?

7. To plan a new amusement park, a team of coaster designers asked customers “Do you prefer wood or steel frames in roller coasters?” The table below shows the preference by age group.

12. Politics of Girls and Boys Analyzing data in two-way tables
Problem 5.2
Politics of Girls and Boys
Analyzing data in two-way tables

13. Focus Question:
Suppose you have recorded the counts of different preferences by group in a two-way table. How can you use those counts, or percents from the counts, to decide if two groups have the same preferences or not?

14. Every four years social studies teachers at the middle school hold a mock election. Each student registers as a Democrat, Independent, or Republican, all of which are categorical data values. Then the classes hold primary and final elections for President.
The table shows the student registrations in one class.

19. Frequency table vs. relative frequency table
Why do we change to percents?

22. After-school jobs and homework
Problem 5.3
After-school jobs and homework
Working Backwards: Setting up a Two-Way Table

23. Focus Question:
What does a correlation coefficient of 1, 0, or -1 suggest to you about the relationship between the two variables?

24. The teachers at the high school did a study to see whether students who had jobs after school were more or less likely to turn in homework on time than students who did not have after-school jobs. Each student was categorized as usually on time or often late with homework and as having a job or not having a job. The results are on the next slide.