Regression toward the Mean

Regression toward the mean simply put is that extreme events will be followed by less extreme events. This observation was found by Sir Francis Galton using a bean machine where balls were dropped through a series of panels that could bounce them randomly before falling into columns at the bottom of the machine. Galton observed what is called a normal distribution would occur where most balls were in the middle with some balls on the far right and left. A simulation can be found here,   

In one of my favourite books written by Daniel Kahneman, Thinking, Fast and Slow he discusses the concept of Regression toward the mean whilst assisting the Israeli air force. Kahneman recalled one of the flight instructors scoffing at the concept of luck determining extreme events from the average and reported that when his pilots were not performing well, he would yell at them which motivated them to do better, Kahneman reasoned that if a Pilot were to perform a manoeuvre to below their average skill level, then it was likely to the next manoeuvre would be closer to their average. So not necessarily a yelling instructor willing them on to a better performance. 

In another favourite book, Alex's Adventures in Numberland by Alex Bellos, Alex also discuss the concept of Regression toward the mean using the infamous, Sports Illustrated curse. The curse dictates that an athlete who makes it to the front cover will inevitably perform poorly following the publishing. Could it be the athlete is overwhelmed with the pressure that distress takes over and they underperform? or more likely they have been performing above their average (hence being put on the cover) so naturally, they will return to their average performance. The point is also made by Alex in relation to parenting techniques where parents will often praise their child for behaviour that is desirable and above the norm then punish undesirable behaviour that is below the norm. Perhaps reinforcement techniques should be focused on the mean behaviours as this is where the majority of behaviours are in a normal distribution. 

So how is Regression to the mean relevant in Psychology? The studies of Psychology involve the measurement of variables between a control group and experimental group. Changes between groups and variables are measured to ascertain the effectiveness of therapeutic interventions. Without controlling for the natural phenomenon of Regression toward the mean, it can be easy to interpret natural variation as meaningful change and attribute that change to a false positive. 

Fortunately, this and many other statistical phenomena can be controlled through rigid study designs and statistical methods. However, Regression toward the mean is a part of our everyday life and if we are not mindful we could be attributing a casual narrative to something that is no more than pure luck or lack thereof. 



Bellos, Alex. & Riley, Andy.  (2011).  Alex's adventures in numberland.  London :  Bloomsbury

Kahneman, D. (2015). Thinking, fast and slow. New York: Farrar, Straus and Giroux.