1.  Display Categorical Variables appropriately  Find and interpret marginal and conditional distributions for 2 Categorical Variables  Determine if 2 Categorical Variables have a possible association AP Statistics Objectives Ch3

2.  frequency table  relative frequency table  variable distribution  bar chart  relative frequency bar chart  pie chart  segmented bar chart Vocabulary

3.  contingency table  marginal distribution  conditional distribution  Independent  Simpson’s paradox Vocabulary

4. Simpson’s Paradox Vocabulary Chapter 2 Assignment Answers Segmented Bar Chart showing possible association Pie Chart showing possible association Chapter 3 Assignment Contingency Table and Independence

5. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 2. According to an article in Fortune (Dec. 28, 1992), 401(k) plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. U.S. employers typically match 50% of the employees’ contribution up to about 6% of salary. One company, concerned with what it believed was a low employee participation rate in its 401(k) plan, sampled 30 other companies with similar plans and asked for their 401(k) participation rates.

6. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 2. According to an article in Fortune (Dec. 28, 1992), 401(k) plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. U.S. employers typically match 50% of the employees’ contribution up to about 6% of salary. One company, concerned with what it believed was a low employee participation rate in its 401(k) plan, sampled 30 other companies with similar plans and asked for their 401(k) participation rates. 30 similar companies 401K Participation Rates Quantitative Sometime after reading the 1992 article United States Company is concerned that their 401K participation rates are low.

7. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 8. A study was conducted to compare the abilities of men and women to perform the strenuous tasks required of a shipboard firefighter (Human Factors 24 [1982]). The study reports the pulling force (in newtons) that a firefighter was able to exert in pulling the starter cord of a P-250 water pump. The study also gives the weight and, of course, the gender of the firefighters.

8. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 8. A study was conducted to compare the abilities of men and women to perform the strenuous tasks required of a shipboard firefighter (Human Factors 24 [1982]). The study reports the pulling force (in newtons) that a firefighter was able to exert in pulling the starter cord of a P-250 water pump. The study also gives the weight and, of course, the gender of the firefighters. Shipboard firefighters pulling force weight gender quantitative categorical Sometime before the 1982 article was written To compare the abilities of men and women

9. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 20. The Environmental Protection Agency (EPA) tracks fuel economy of automobiles. Among the data they collect are the manufacturer (Ford, Toyota, etc.), vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving.

10. 20. The U.S. Environmental Protection Agency (EPA) tracks fuel economy of automobiles. Among the data they collect are the manufacturer (Ford, Toyota, etc.), vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving. All automobiles in the United States manufacturercategorical Vehicle typecategorical weightquantitative horsepowerquantitative gas mileage for cityquantitative gas mileage for highwayquantitative

11. For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative (list under appropriate type). 24. The 2.5-mile Indianapolis Motor Speedway has been the home to a race on Memorial Day nearly every year since 1911. Even during the first race there were controversies. Ralph Mulford was given the checkered flag first but took three extra laps just to make sure he’d completed 500 miles. When he finished, another driver, Ray Harroun, was being presented with the winner’s trophy, and Mulford’s protests were ignored. Harroun averaged 74.6 mph for the 500 miles. In 2003 the winner, Gil de Ferran, averaged 153.6 mph. Here are the data for the 1915-1920 Indianapolis 500 races.(Note: The race wasn’t run in 1917 or 1918 due to World War I.) Included are the pole winners (the winners of the trial the day before, when each driver drives alone to determine the position on race day).

12. Indy 500 races (not racers) year winner pole position average speed pole winner average pole speed categorical quantitative categorical quantitative 1915 - 1920 Indianapolis, Indiana

13. Class Notes – Independent Are survival status and ticket class of Titanic riders independent? It doesn’t appear that survival status and ticket class for Titanic riders are independent, because the distributions of Ticket Class for those who lived doesn’t match those who died. For instance, over 28% of the survivors had first class tickets. However, of those that died, fewer than 10% had first class tickets. 28.6% 8.2% 16.6% 11.2% 25.0% 35.4% 29.8% 45.2%

14. Class Notes –Segmented Bar Chart Create a segmented bar chart from the Titanic information given below. FirstSecondThirdCrew Alive 28.6%16.6%25.0%29.8% Dead 8.2%11.2%35.4%45.2% Survival T i c k e t C l a s s Alive Dead

15. Class Notes –Simpson’s Paradox The data below is for on-time flights for two pilots. Why is the data given below an example of Simpson’s paradox? Day NightOverall Moe 90/100 90% 10/20 50% 100/120 83% Jill 19/20 95% 75/100 75% 94/120 78% Pilot Time of Day Jill has the best on-time percentage for both daytime and nighttime flights. However, she flies more of the difficult nighttime flight so Moe has a better overall on-time percentage.

16. Assignment : Chapter 3 pp. 36-41 #7,10,18,31

17. Chapter 3 Vocabulary 2. Relative Frequency Table - Displays the counts for each value of a categorical variable 1. Frequency Table - Displays the proportion of the total for each value of a categorical variable

18. Chapter 3 Vocabulary Gives the relative frequency (proportion) of all possible values for a variable 3. Distribution of a variable-

19. Chapter 3 Vocabulary 5. Relative frequency bar chart - A graphical display the distribution of a categorical variable using counts 4. Bar chart - A graphical display the distribution of a categorical variable using proportions CAUTION: Do not violate the AREA PRINCIPLE

20. Chapter 3 Vocabulary 6. Pie chart a circular display of the distribution of a categorical variable using proportions (Note: proportions must add to 100%)

21. Chapter 3 Vocabulary 8. Marginal Distribution a table that shows how two categorical variables are related to each other 7. Contingency Table - the frequency distribution of one categorical variable found in the margin of a contingency table

22. Chapter 3 Vocabulary one row or column of a contingency table (including marginal total) 9. Conditional distribution -

23. Chapter 3 Vocabulary Two variables are independent if the distribution of one variable is the same for all values of another variable (HINT: Check relative frequency.) 10. Independent - NOTE: If two variables are not independent, we say there is a possible association between the variables. Do not say they are dependent.

24. Chapter 3 Vocabulary 11. Segmented Bar Chart a rectangular display of the distribution of a categorical variable using proportions (Note: proportions must add to 100%) Similar to pie chart, but makes it easier to see small differences when comparing two categorical variables

25. Chapter 3 Vocabulary 12. Simpson’s Paradox -

26. Chapter 3 Vocabulary When averages are taken across different groups, they can appear to contradict the overall averages. 12. Simpson’s Paradox -

27. Are Gender & Political Affiliation Independent? Yes, Gender and Political Affiliation are independent, because their conditional distributions are identical.

28. Are Gender & Political Affiliation Independent? Yes, Gender and Political Affiliation are independent, because their conditional distributions are identical.