2. Displaying Categorical Data THINK SHOW TELL

3. What is categorical data? Bar, Segmented Bar, and Pie Charts Frequency vs. Relative Frequency Tables/Charts Area Principle Contingency Tables Marginal Distributions Conditional Distributions

4. What is categorical data? Data that can be separated into “piles”/categories that are not numerically based. Example: Eye color, T-shirt size, type of vehicle, …

5. Titanic Who: People on Titanic What: Survival status, age, gender, ticket class When: April 14, 1912 Where: North Atlantic How: Variety of resources Why: Historical interest

6. Distribution of Categorical Data Frequency Table Relative Frequency Table ClassCount First325 Second285 Third706 Crew885 Class% First14.766 Second12.949 Third32.076 Crew40.209 COUNTS!PERCENTAGES!

7. Bar, Segmented Bar, & Pie Charts

8. Area Principle—How to Lie Purpose of chart is to help see patterns, but a bad chart (violating the area principle) can distort pattern or imply another relationship (really not happening). See page 3-3 in textbook.

9. Contingency Table LivedDiedTOTAL Crew212673885 First202123325 Second118167285 Third178528706 TOTAL71014912201 Survival Ticket Class

10. LivedDiedTOTAL Crew212 24.0 673 76.0 885 100.0 First202 62.2 123 37.8 325 100.0 Second118 41.4 167 58.6 285 100.0 Third178 25.2 528 74.8 706 100.0 TOTAL710 32.3 1491 67.7 2201 100.0 Survival Marginal Distribution Row % Ticket Class

11. LivedDiedTOTAL Crew212 29.9 673 45.1 885 40.2 First202 28.5 123 8.25 325 14.8 Second118 16.6 167 11.2 285 12.9 Third178 25.1 528 35.4 706 32.1 TOTAL710 100.0 1491 100.0 2201 100.0 Ticket Class Survival Marginal Distribution Column%

12. LivedDiedTOTAL Crew212 9.63 673 30.6 885 40.2 First202 9.18 123 5.59 325 14.8 Second118 5.36 167 7.59 285 12.9 Third178 8.09 528 24.0 706 32.1 TOTAL710 32.3 1491 67.7 2201 100.0 Survival Marginal Distribution Table % Ticket Class

13. Did chance of surviving depend on ticket class? Let’s look at our marginal distribution with row percentages. Does the distribution of survivors’ ticket class look the same for non-survivors? To do this, we first restrict our attention to the survivors. Conditional distribution ALIVECount% 1 st 20262.2 2 nd 11841.4 3 rd 17825.2 Crew21224.0 Total71032.3

14. Survivors Non-survivors Are Ticket Class and Survival are associated? This was an important part of the movie.

15. Same data  Segmented Bar Chart Conditional distribution based on ticket class.

16. Same data  Segmented Bar Chart Conditional distribution based on survival or not.

17. Displaying Categorical Data THINK Variable: Identify the variables and report the W’s. Be sure the data are counts and categories do not overlap. SHOW Mechanics: Make an appropriate display. Be sure “bars” are of equal width. TELL Interpretation: Discuss the patterns in the table and displays. Any possible real-world consequences?

18. Simpson’s Paradox AlfredSuccessesAttempts%Success 1 st half8010080% 2 nd half204050% BubbaSuccessesAttempts%Success 1 st half7810078% 2 nd half2540%

19. Simpson’s Paradox Total for year SuccessesAttempts%Success Alfred10014071.4% Bubba8010576.2% Does it follow that Alfred’s percentage of successes was greater than Bubba’s for the whole year? Aggregate data means to combine data into one group.