The Book of Why: The New Science of Cause and Effect

by Judea Pearl

The study was observational, not randomized, with sixty men and sixty women. This means that the patients themselves decided whether to take or not to take the drug. Table 6.4 shows how many of each gender received Drug D and how many were subsequently diagnosed with heart attack. Let me emphasize where the paradox is. As you can see, 5 percent (one in twenty) of the women in the control group later had a heart attack, compared to 7.5 percent of the women who took the drug. So the drug is associated with a higher risk of heart attack for women. Among the men, 30 percent in the control group had a heart attack, compared to 40 percent in the treatment group. So the drug is associated with a higher risk of heart attack among men. Dr. Simpson was right. TABLE 6.4. Fictitious data illustrating Simpson’s paradox. But now look at the third line of the table. Among the control group, 22 percent had a heart attack, but in the treatment group only 18 percent did. So, if we judge on the basis of the bottom line, Drug D seems to decrease the risk of heart attack in the population as a whole. Welcome to the bizarre world of Simpson’s paradox!