The following two-way table classifies hypothetical hospital patients with a certain disease, according to the hospital that treated them and whether they survived or died:

a. Calculate the proportion of Hospital A€™s patients who survived and the proportion of Hospital B€™s patients who survived. Which hospital saved the higher percentage of its patients?
Suppose that we further classify each patient according to a third variable: whether they were in fair condition orpoor condition prior to treatment. We obtain the following two-way tables:

Fair condition

Poor condition

b. Show that when the €œfair€ and €œpoor€ condition patients are combined, the totals are indeed those given in the table above.
c. Among those in fair condition, compare the recovery rates for the two hospitals. Which hospital saved the greater percentage of its patients who had been in fair condition?
d. Among those in poor condition, compare the recovery rates for the two hospitals. Which hospital saved the greater percentage of its patients who had been in poor condition?
Th is phenomenon is called Simpson€™s paradox: An association or comparison that holds for all of several groups can reverse direction when the data are merged to form a single group.
e. Explain (arguing from the data given) the apparent €œparadox€ here. (Hints: Do fair or poor patients tend to survive more often? Does one hospital tend to treat one type of patient?)

f. Which hospital would you rather go to if you were sick with this disease? Explain.

Transcribed Image Text:

Hospital A Hospital B Survived 800 900 100 Died 200 Total 1,000 1,000 Hospital A Hospital B 870 590 Survived Died 30 30