Section 4.3 2-Way Tables and Marginal Distributions

1. Section 4.32-Way Tables and Marginal Distributions AP Statistics October 20, 2010

2. What about Categorical Data? • Whenever we have looked at data so far, it has quantitative vs. quantitative • What tools do we use if we are faced with categorical data? AP Statistics, Section 4.3, Part 1

3. 2-Way Tables • First, think of data where each member of the distribution belongs to only one category. • Education Level: • Did not complete high school • Completed high school • 1 to 3 years of college • 4 or more years of college AP Statistics, Section 4.3, Part 1

4. 2-Way Tables • First, think of data where the member of the distribution belongs to only category. • Age: • 25 to 34 years • 35 to 54 years • 55+ years AP Statistics, Section 4.3, Part 1

5. Each number represents a “count”, or the number of data points that meet the criteria Sample 2-Way Table Education is considered “row variables” Age is considered “column variables” AP Statistics, Section 4.3, Part 1

6. Calculating Marginal Distributions • When we do a marginal distribution, we only look at totals (the values found on the right margin or bottom margin) • In marginal distributions, we divide by “Grand Total” AP Statistics, Section 4.3, Part 1

7. Calculating Marginal Distributions AP Statistics, Section 4.3, Part 1

8. Calculating Marginal Distributions AP Statistics, Section 4.3, Part 1

9. Graph of Marginal Distribution AP Statistics, Section 4.3, Part 1

10. Calculating Conditional Distributions • The “conditional” part sounds like • “on the condition the respondents are 35 to 54” • “among those who have completed high school but did not go to college” • “for those respondents over 55 years of age” AP Statistics, Section 4.3, Part 1

11. Calculating Conditional Distributions • When we look at conditional distributions, we are restricted to a particular column or row (but not “margins”) • In conditional distributions, we divide by “Total” of the column or row. AP Statistics, Section 4.3, Part 1

12. Calculating Conditional Distributions AP Statistics, Section 4.3, Part 1

13. Calculating Conditional Distributions AP Statistics, Section 4.3, Part 1

14. Round-off Error • Occurs when tables round numbers in each entry and the totals don’t actually match up to what they really are. AP Statistics, Section 4.3, Part 1

15. Graph of Conditional Distribution AP Statistics, Section 4.3, Part 1

16. Simpson’s Paradox • A paradox is “a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true” • Simpson’s Paradox involves percentages… AP Statistics, Section 4.3, Part 1

17. Among the patients of Hospital B, what percentage survived? On the condition you were admitted to Hospital A, what is your chance of surviving? Which Hospital Will You Choose? SR=97% SR=98% AP Statistics, Section 4.3, Part 1

18. Amongst Hospital B patients in good condition, what percentage lived? If you were admitted to Hospital A in good condition, what is your chance of surviving? What if you are in “good” condition? SR=99.0% SR=98.6% AP Statistics, Section 4.3, Part 1

19. Among Hospital B patients in poor condition, what percentage lived? If you were admitted to Hospital A in poor condition, what is your chance of living? What if you are in “poor” condition? SR=96.2% SR=96.0% AP Statistics, Section 4.3, Part 1

20. Simpson’s Paradox • Refers to the reversal of the direction of a comparison or an association when data from several groups are combined to form a single group. • The lurking variables in Simpson’s Paradox are categorical. • This happens very rarely! AP Statistics, Section 4.3, Part 1

21. Assignment • Complete Worksheets • 4.2A and 4.2B AP Statistics, Section 4.3, Part 1