1. Relations and Categorical Data Target Goal: I can describe relationships among categorical data using two way tables. 1.1 cont. Hw: pg 24: 20, 21, 23, 26, 27 - 32

2. Now we will look at describing relationships between two or more categorical variables. Ex. Gender, race, occupation Ex. Gender, race, occupation

3. To analyze categorical data, use counts or percents of individuals that fall into various categories. To analyze categorical data, use counts or percents of individuals that fall into various categories.

4. Example : Education and Age Table presents Census Bureau data on the years of school completed by Americans at different ages. Table presents Census Bureau data on the years of school completed by Americans at different ages.

5. Two Way Table: Describes Two Categorical Variables Row and column variable: least to most Row and column variable: least to most Marginal distributions: totals that appear at the right and bottom margins for each individual variable. Marginal distributions: totals that appear at the right and bottom margins for each individual variable. Round off error: There is round off error depending on groupings. Round off error: There is round off error depending on groupings.

6. Percents To describe relationships among categorical variables, calculate the appropriate percents from the counts given. To describe relationships among categorical variables, calculate the appropriate percents from the counts given. Percents: are often more informative than counts. Percents: are often more informative than counts.

7. The percent of people 25 years of age or older that have at least 4 years of college is:

8. Tip for deciding on what fraction gives the percent you want: Tip for deciding on what fraction gives the percent you want: Ask, “What group represents the total that I want a percent of?” Ask, “What group represents the total that I want a percent of?” Can be tricky! Can be tricky!

9. Exercise:Percents Give the marginal distribution of age among people 25 years or older in percents, starting from the counts in table 4.6. Give the marginal distribution of age among people 25 years or older in percents, starting from the counts in table 4.6. Which totals do we use? Which totals do we use?

10. Find each one and the total: Age 25 to 34: 37,786/175,230 = 21.6% Age 25 to 34: 37,786/175,230 = 21.6% Age 35 to 54: Age 35 to 54: Age 55+: Age 55+: Total = 100.1% due to rounding Total = 100.1% due to rounding 46.5% 32.0%

11. Exercise: Using Percents to Make Bar Graph Using the counts in table 4.6, find the percent of people in each age group who did not complete high school. Using the counts in table 4.6, find the percent of people in each age group who did not complete high school.

12. Percent of people in each age group who did not complete high school. age 25 to 34: age 25 to 34: age 35 to 54: age 35 to 54: age 55+: = 11.8% 4,474/37,786 11.2% 25.4%

13. Draw a bar graph that compares these percents. State briefly what the data show. (3 min) Draw a bar graph that compares these percents. State briefly what the data show. (3 min) Conclusion: Conclusion: The percentage of people who did not finish high school is about the same for the 25 - 34 and the 35 – 54 age groups 11.8 and 11.2 % respectively. The percentage of people who did not finish high school is about the same for the 25 - 34 and the 35 – 54 age groups 11.8 and 11.2 % respectively. But, the percentage almost doubles to 25.4% for the 55 and over age group. But, the percentage almost doubles to 25.4% for the 55 and over age group.

14. Marginal distribution: compare each variable separately. (Denominator is the grand total.) Conditional distribution: refers to only “people” who satisfy a certain condition (age 25-34). Look only at column (or row). Look only at column (or row). Column (or row) total is the denominator. Column (or row) total is the denominator.

15. Result: comparing conditional distributions of “education” in different “age groups” describes the association between age and education. Bar graphs to compare the education levels of three age groups. Bar graphs to compare the education levels of three age groups. Each graph compares the percents of three groups who fall in one of the four education levels. Each graph compares the percents of three groups who fall in one of the four education levels.

16. Young adults by gender and chance of getting rich FemaleMaleTotal Almost no chance9698194 Some chance, but probably not426286712 A 50-50 chance6967201416 A good chance6637581421 Almost certain4865971083 Total236724594826 Analyzing Categorical Data Two-Way Tables and Marginal Distributions Two-Way Tables and Marginal Distributions ResponsePercent Almost no chance 194/4826 = 4.0% Some chance 712/4826 = 14.8% A 50-50 chance 1416/4826 = 29.3% A good chance 1421/4826 = 29.4% Almost certain 1083/4826 = 22.4% Example, p. 13 Examine the marginal distribution of chance of getting rich.

17. Young adults by gender and chance of getting rich FemaleMaleTotal Almost no chance9698194 Some chance, but probably not426286712 A 50-50 chance6967201416 A good chance6637581421 Almost certain4865971083 Total236724594826 Analyzing Categorical Data Two-Way Tables and Conditional Distributions Two-Way Tables and Conditional Distributions ResponseMale Almost no chance 98/2459 = 4.0% Some chance 286/2459 = 11.6% A 50-50 chance 720/2459 = 29.3% A good chance 758/2459 = 30.8% Almost certain 597/2459 = 24.3% Example, p. 15 Calculate the conditional distribution of opinion among males. Examine the relationship between gender and opinion. Female 96/2367 = 4.1% 426/2367 = 18.0% 696/2367 = 29.4% 663/2367 = 28.0% 486/2367 = 20.5%

18. Describes the value of that variable among individuals who have a specific value of another variable. The conditional dist of ______________ among _____________. hw. 29) What percent of females thought they were going to be married in the next ten years. The conditional dist of _________________ among ___________________________. You will be asked to express the Conditional Distribution

19. Analyzing Categorical Data Organizing a Statistical Problem As you learn more about statistics, you will be asked to solve more complex problems. As you learn more about statistics, you will be asked to solve more complex problems. Here is a four-step process you can follow. Here is a four-step process you can follow. State: What’s the question that you’re trying to answer? Plan: How will you go about answering the question? What statistical techniques does this problem call for? Do: Make graphs and carry out needed calculations. Conclude: Give your practical conclusion in the setting of the real- world problem. See pg. 18 for an example. Hw question on 4 step process. How to Organize a Statistical Problem: A Four-Step Process

20. Looking Ahead… We’ll learn how to display quantitative data. Dotplots Stemplots Histograms We’ll also learn how to describe and compare distributions of quantitative data. In the next Section…