Inferring and Explaining

ChaPter twelVe Correlations and Causes Most of you will have heard the maxim “correlation does not imply causation.” Just because two variables have a statistical relationship with each other does not mean that one is responsible for the other. For instance, ice cream sales and forest fres are correlated because both occur more ofen in the summer heat. But there is no causation; you don’t light a patch of the Montana brush on fre when you buy a pint of Haagan-Dazs. —nate sIlver 1 Correlations Te Concise Oxford Dictionary ofers two defni- tions of the term correlation : 1. Mutual relationship between two or more things. 2. Interdependence of variable quantities, quantity measuring extent of this. 2 Te latter defnition gets most of the attention in statistics courses. But the more generic def- nition is at the heart of reasoning from a cause to an efect. What is the relationship between two things—a car accident on Tuesday and a backache on Wednesday morning? “Obviously” the crash caused the back injury. Well, maybe, but maybe not. Perhaps the back injury (caused from too much of a workout at the gym on Mon- day) resulted in the crash because of a muscle spasm as the driver was trying to hit the brakes. Or suppose some third thing—say, a small seizure—simultaneously caused the crash by distracting the driver and caused the back injury as the driver wrenched in surprise. And maybe the relationship is one of simple coincidence. Te injury occurred at the gym and the crash from foolishly texting while driving—there was 107