4.3 Reading Quiz (second half) 1. In a two way table when looking at education given a person is 55+ we refer to it as ____________ distribution. 2. True or False. No single graph portrays the form of the relationship between categorical variables. 3. This section explains _________ paradox. 4. Name the lurking variable in the example used to explain the Paradox. AP Statistics, Section 4.3, Part 2 1
Section Conditional Distributions and Simpson’s Paradox AP Statistics
AP Statistics, Section 4.3, Part 2 3 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” 25 to 3435 to 5455+Total Did not complete HS4,4749,15514,22427,853 Completed HS11,54626,48120,06058,087 1 to 3 years of college10,70022,61811,12744, years of college11,06623,18310,59644,845 Total37,78681,43556,008175,230
AP Statistics, Section 4.3, Part 2 4 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. 25 to 3435 to 5455+Total Did not complete HS4,4749,15514,22427,853 Completed HS11,54626,48120,06058,087 1 to 3 years of college10,70022,61811,12744, years of college11,06623,18310,59644,845 Total37,78681,43556,008175,230
AP Statistics, Section 4.3, Part 2 5 Calculating Conditional Distributions Years of school completed, by age, 2000 (thousand of persons) 25 to 3435 to 5455+Total Did not complete HS4,4749,15514,22427,853 Completed HS11,54626,48120,06058,087 1 to 3 years of college10,70022,61811,12744, years of college11,06623,18310,59644,845 Total37,78681,43556,008175,230
AP Statistics, Section 4.3, Part 2 6 Calculating Conditional Distributions Years of school completed, by age, 2000 (thousand of persons) 25 to 3435 to 5455+Total Did not complete HS4,4749,15514,22427,853 Completed HS11,54626,48120,06058,087 1 to 3 years of college10,70022,61811,12744, years of college11,06623,18310,59644,845 Total37,78681,43556,008175,230
AP Statistics, Section 4.3, Part 2 7 Graph of Conditional Distribution
AP Statistics, Section 4.3, Part 2 8 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 9 Which Hospital Will You Choose? Hospital AHospital BTotal Died Survived Total On the condition you were admitted to Hospital A, what is your chance of surviving? Among the patients of Hospital B, what percentage survived? SR=97%SR=98%
AP Statistics, Section 4.3, Part 2 10 What if you are in “good” condition? Hospital AHospital BTotal Died6814 Survived Total If you were admitted to Hospital A in good condition, what is your chance of surviving? Amongst Hospital B patients in good condition, what percentage lived? SR=99.0% SR=98.6%
AP Statistics, Section 4.3, Part 2 11 What if you are in “poor” condition? Hospital AHospital BTotal Died57865 Survived Total If you were admitted to Hospital A in poor condition, what is your chance of living? Among Hospital B patients in poor condition, what percentage lived? SR=96.2%SR=96.0%
AP Statistics, Section 4.3, Part 2 12 The choice reverses… when we add the third variable. This happens very rarely.
AP Statistics, Section 4.3, Part 2 13 Assignment Exercises: Review: 4.74,4.76,4.79,4.81,4.83