Regression to the Mean: A Two-Systems View
System 1 naturally produces extreme predictions and overconfidence based on weak evidence, while System 2 finds regression to the mean difficult to understand and apply, requiring special training.
THE IDEA
A TWO-SYSTEMS VIEW OF REGRESSION
Extreme predictions and a willingness to predict rare events from weak evidence are both manifestations of System 1. It is natural for the associative machinery to match the extremeness of predictions to the perceived extremeness of evidence on which it is based—this is how substitution works. And it is natural for System 1 to generate overconfident judgments, because confidence, as we have seen, is determined by the coherence of the best story you can tell from the evidence at hand. Be warned: your intuitions will deliver predictions that are too extreme and you will be inclined to put far too much faith in them.
Regression is also a problem for System 2. The very idea of regression to the mean is alien and difficult to communicate and comprehend. Galton had a hard time before he understood it. Many statistics teachers dread the class in which the topic comes up, and their students often end up with only a vague understanding of this crucial concept. This is a case where System 2 requires special training. Matching predictions to the evidence is not only something we do intuitively; it also seems a reasonable thing to do. We will not learn to understand regression from experience. Even when a regression is identified, as we saw in the story of the flight instructors, it will be given a causal interpretation that is almost always wrong.
When to use it
Evaluating employee performance after a particularly good or bad quarter.
Predicting sports performance after an exceptional game.
Interpreting changes in student test scores after an intervention.
Analyzing the effectiveness of a new treatment when patients show extreme symptoms.
FROM THEORY TO EVERYDAY LIFE
In practice
Galton's Height Observation
Francis Galton observed that parents of extreme height (very tall or very short) tend to have children whose heights are closer to the average. This is a classic example of regression to the mean.
Flight Instructor Misinterpretation
An instructor sees an exceptional landing followed by a more ordinary one after praise, and a poor landing followed by improvement after criticism. The instructor concludes that criticism works better. Regression to the mean offers another explanation for both changes, so the sequence alone does not establish the effect of either response.
A MOMENT TO REFLECT
Put it to work.
Think of a time you made an extreme prediction based on limited evidence. How might regression to the mean have influenced the outcome?
Why is it difficult to learn about regression from personal experience?
How can you adjust your predictions to account for regression to the mean?
References
- Regression towards mediocrity in hereditary stature — Francis Galton (1886)
CONTINUE THE CONVERSATION
Source texts
- Thinking, Fast and Slow (Daniel Kahneman)