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Regression to the mean
1. Regression to the mean
The phrase "regression to the mean" means that, due to the central limit theorem, any result or sample that is far from the mean tends to be nearer to the mean on the next result or sample.
2. History
Francis Galton (1822-1911) was the first to recognized, study, and name this phenomena.
3. Experiment
One experiment performed by Francis Galton was with small balls falling though a series of obstacles to form what is today called a normal distribution pattern.
4. Mediocrity
This phenomena was originally called "regression to mediocrity", "reversion to mediocrity", or "reversion to the mean".
This phenomena happens naturally but sometimes is erroneously associated with a causative effect.
5. Sports Illustrated cover jinx
It as often noted that athletes who appear on the cover of Sports Illustrated then suffer a "
jinx".
A Wikipedia article at
https://en.wikipedia.org/wiki/Sports_Illustrated_cover_jinx is devoted to this "
jinx".
There are examples presented on both sides of the "
jinx" claim.
It appears that regression to the mean explains many of the instances. But not all. But that is how statistics works.
6. Other areas
Some other areas where this phenomena has been noted include the following.
NFL head coaches, MLB managers, etc.
Movie producers, etc.
Stock market brokers, etc.
7. Bias
It appears that people focus in on certain events that support their bias while ignoring other events that would not support their bias.
The "regression to the mean" can be used to explain phenomena in general but does not work as well for prediction of individual cases.
8. Counterfactual reasoning
Counter-factual reasoning, or logic, is reasoning that is "
counter to fact" and is one of the basic ways in which humans reason and is part of the field called "
casual reasoning".
Human beings tend to reason using counter-factual (counter to fact, or what if) logic, as pointed out by famous computer scientist Judea Pearl.
9. Speed cameras
The following has been noticed.
A lot of accidents at an intersection.
A speed camera installed.
Accidents at that intersection go down.
Claim than speed camera installation caused intersection to be more safe.
Is this a causal relationship? Did the speed camera cause the accidents to decrease?
What are other reasons why accidents might have gone down at this intersection?
10. Counterfactual claim
For causation, the following argument is often used.
If the speed camera had not been installed, the accident rate at that intersection would not have gone down.
How do we know what might have happened if the speed camera were not installed?
11. End of page
