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Section 4.3.2 Conditional Distributions and Simpson’s Paradox

Section 4.3.2 Conditional Distributions and Simpson’s Paradox. AP Statistics www.toddfadoir.com/apstats. Calculating Conditional Distributions. The “conditional” part sounds like “on the condition the respondents are 35 to 54”

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Section 4.3.2 Conditional Distributions and Simpson’s Paradox

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  1. Section 4.3.2Conditional Distributions and Simpson’s Paradox AP Statistics www.toddfadoir.com/apstats

  2. 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 2

  3. 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 2

  4. Calculating Conditional Distributions AP Statistics, Section 4.3, Part 2

  5. Calculating Conditional Distributions AP Statistics, Section 4.3, Part 2

  6. Graph of Conditional Distribution AP Statistics, Section 4.3, Part 2

  7. Simpson’s Paradox • A paradox is “a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true” (m-w.com) • Simpson’s Paradox involves percentages… AP Statistics, Section 4.3, Part 2

  8. 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 2

  9. 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 2

  10. 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 2

  11. The choice reverses… • when we add the third variable. • This happens very rarely. AP Statistics, Section 4.3, Part 2

  12. Assignment • Exercises: 4.59-4.61 AP Statistics, Section 4.3, Part 2

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