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Section 4.3 2-Way Tables and Marginal Distributions

Section 4.3 2-Way Tables and Marginal Distributions. AP Statistics October 20, 2010. 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?. 2-Way Tables.

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Section 4.3 2-Way Tables and Marginal Distributions

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  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

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