Discussion Question 2: Simpson’s Paradox In this project, we investigate an interesting phenomenon known as Simpson’s Paradox. A study on the survival rate of patients recorded whether hospital patients lived or died, which of two hospitals the patients were admitted to, and the condition (poor or good) of the patient when admitted to the hospital. One way to examine three categorical variables is to give multiple two-way tables: one for each category of the third variable. Tables 1 and 2 give two-way tables for the status and the hospital variables, with the subjects separated based on the condition on admittance. Table 1. Good Condition Hospital A Hospital B Died Survived 6 594 8 592ACTIVITIES AND ASSIGNMENTS FOR WEEK 2 Table 2. Poor Condition Hospital A Hospital B Died Survived 57 1443 8 192 Table 3. Let’s ignore the condition of the patient Hospital A Hospital B Died Survived (1) Considering only patients in good condition, which hospital has a lower death rate? (2) Considering only patients in poor condition, which hospital has a lower death rate? 3 (3) Which hospital is the best choice for good condition patients? Which hospital is the best choice for poor condition patients? (4) Suppose the researchers decided the condition of the patient was not relevant, and looked only at the two variables of the survival statusand the two hospitals. Complete Table 3 to include all patients (in either condition). (5) Use Table 3 to determine which hospital has a lower death rate. Is your result surprising? (6) Discuss the discrepancy in your answers to parts (3) and (5). This discrepancy is an example of Simpson’s Paradox, in which the existence of a confounding variable– in this case, the condition of the patient can actually reverse the interpretation of an observed effect. Which hospital really is the best choice? (7) Do a web search and find another example of Simpson’s Paradox. Give the details of the example and explain how it demonstrates this paradox. Give reference.
