Question

14 Simpson's paradox. Recently, the king of the mythical nation of Pcoria was diagnosed with cancer. He noticed that many other nobles in his court had also been diagnosecd with cancer recently. He dispatched his two best health economists to study can cer rates in Pcoria's two towns. Their results are recorded in Table 4.6. Before you begin, recall that Pcoria's two towns are very different. Eastville is a poor area, home to numerous factories that produce prodigious amounts of pollution. Weston is the home of the king's court and is filled with pristine parks and hiking trails. Table 4.6. Information from the cancer rate study commissioned by the King of Pcoria Eastville Weston Population 100 1,000 Cancer rate 50% 40% Population 900 500 Cancer rate Nobles 10% Peasants 8% a The king's economists conclude that there is a health disparity between nobles and b Calculate the nationwide cancer rate for nobles and the nationwide cancer rate for c This effect is called Simpson's paradox or the amalgamation paradox. Explain how peasants when it comes to cancer rates. Succinctly state the health disparity peasants. What do you find? the distribution of nobles and peasants and the geography of Pcoria contribute to the paradoxical result. Which health disparity hypothesis from the chapter does this exemplify? d Consider Table 4.7, which substitutes variable names for the cancer rate data. Simpson's paradox occurs when the cancer rate is higher for nobles in each town but higher for peasants nationwide. Express these three conditions in terms of the variable names in the table Use your answer from Exercise d to prove that Simpson's paradox cannot occur if the populations of nobles and peasants are the same in both towns (that is, a c and b-d) e

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Answer 1

a) In both the regions chances of nobles contracting cancer is 25% more than that for Peasants.

Eastville- Helath disparity=(50-40)/40=0.25

For Weston, it is (10-8)/8=0.25

b) Number of nobles in having cancer in Eastville and Weston=0.5x100+0.1x900=140

Total number of nobles in both areas=100+900=1000

Cancer rate for nobles=140/1000=.14 ---->14%

Number of peasants in having cancer in Eastville and Weston=400+40=440

Total number of peasants in both areas=1000+500=1500

Cancer rate for peasants=440/1500=0.2933 ---->29.33%

Nationawide cancer rate is more for peasants.

c) We observe Simpson's paradox because number of peasants is more than number of nobles. So even a small % of peasants having cancer translates to larger absolute numbers. Absolute number of nobles is 1000 whereas it is 1500 for peasants. Similarly geographical division implies absolute number of peasants is very high for Eastville,so even though rate of getting cancer in Eastville is smaller for peasants,it turns out that 400 peasants have cancer and only 50 nobles have cancer. This exemplifies health disparity due to socioeconomic status.