The Book of Why: The New Science of Cause and Effect (Penguin Science)

by Judea Pearl

we can see that the front-door criterion would apply if there were no arrow from Motivation to Showed Up, the “shielding” I mentioned earlier. In many cases we could justify the absence of that arrow. For example, if the services were only offered by appointment and people only missed their appointments because of chance events unrelated to Motivation (a bus strike, a sprained ankle, etc.), then we could erase that arrow and use the front-door criterion. Under the actual circumstances of the study, where the services were available all the time, such an argument is hard to make. However—and this is where things get really interesting—Glynn and Kashin tested out the front-door criterion anyway. We might think of this as a sensitivity test. If we suspect that the middle arrow is weak, then the bias introduced by treating it as absent may be very small.