Exercise: The spurious speed camera

speed camera
Goal: To illustrate regression to the mean
 
Materials needed: 2 dice per person, a “speed camera” (i.e. cardboard cutout).
 
Estimated time: 5-8 minutes
 
 
Regression to the mean is another way of saying things return to normal. However, it’s not always easy to spot.  This exercise demonstrates a common situation where regression to the mean can be confused with a causative effect.
 
Give a pair of dice to everyone in the room.  Tell them they are all members of your constituency, who are worried about road safety.  To find out how many people were knocked down on the road outside each of their houses that year, everyone rolls the dice.
 
Explain that the council can only afford a single speed camera – who should get it?  Typically the class will agree that the person who rolled the highest number – an eleven or twelve – will have the strongest claim.  Place the fake speed camera on the table in front of them.
 
Have everyone roll the dice again to signify another year in the constituency. Ask the person with the speed camera whether they rolled a lower number this time.  Almost certainly, the answer will be yes.
 
"So the question for the class is: are they happy with the demonstration of this speed camera?  Does it work? Point out that others in the room saw a bigger number on their second roll.  They didn’t have cameras on their roads, so isn’t this proof that the camera it works?"
 
Presented in this way, in such a familiar narrative, it can be tricky to identify this as regression to the mean.  Most will figure out though that the person who rolls a high number the first time round will almost certainly roll a lower number the second time round.  Because events that are unusually dire tend to attract our attention (and intervention), it’s can be tricky  to separate the success of that intervention from simple regression.
 
"Can the class think of other similar narratives that mask regression to the mean?  What about “momentum” in sports? Or the tendency of athletes to suffer misfortune after a winning streak? What about expensive interventions into failing schools or high crime areas?"
 
 

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