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

by Judea Pearl

Suppose we want to know the effect of an online advertisement (X) on the likelihood that a consumer will purchase the product (Y)—say, a surfboard. We have data from studies in five different places: Los Angeles, Boston, San Francisco, Toronto, and Honolulu. Now we want to estimate how effective the advertisement will be in Arkansas. Unfortunately, each population and each study differs slightly. For example, the Los Angeles population is younger than our target population, and the San Francisco population differs in click-through rate. Figure 10.1 shows the unique characteristics of each population and each study. Can we combine the data from these remote and disparate studies to estimate the ad’s effectiveness in Arkansas? Can we do it without taking any data in Arkansas? Or perhaps by measuring merely a small set of variables or conducting a pilot observational study? FIGURE 10.1. The transportability problem. Figure 10.2 translates these differences into graphical form. The variable Z represents age, which is a confounder; young people may be more likely to see the ad and more likely to buy the product even if they don’t see the ad. The variable W represents clicking on a link to get more information. This is a mediator, a step that must take place in order to convert “seeing the advertisement” into “buying the product.” The letter S, in each case, stands for a “difference-producing” variable, a hypothetical variable that points to the characteristic by which the two p...