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

by Judea Pearl

Around 1923 or 1924, Fisher began to realize that the only experimental design that the genie could not defeat was a random one. Imagine performing the same experiment one hundred times on a field with an unknown distribution of fertility. Each time you assign fertilizers to subplots randomly. Sometimes you may be very unlucky and use Fertilizer 1 in all the least fertile subplots. Other times you may get lucky and apply it to the most fertile subplots. But by generating a new random assignment each time you perform the experiment, you can guarantee that the great majority of the time you will be neither lucky nor unlucky. In those cases, Fertilizer 1 will be applied to a selection of subplots that is representative of the field as a whole. This is exactly what you want for a controlled trial. Because the distribution of fertility in the field is fixed throughout your series of experiments—the genie can’t change it—