Regression fallacy
Encyclopedia
The regression fallacy is an informal fallacy
. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.
. The logical flaw is to make predictions that expect exceptional results to continue as if they were average (see Representativeness heuristic
). People are most likely to take action when variance is at its peak. Then after results become more normal they believe that their action was the cause of the change when in fact it was not causal.
The word "regression" was coined by Sir Francis Galton
in a study from 1885 called "Regression Toward Mediocrity in Hereditary Stature". He showed that the height of children from very short or very tall parents would move towards the average. In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable may not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that the distribution of heights of their children will be centered somewhere between the average of the parents and the average of the population as whole. Thus, any single child can be more extreme than the parents, but the odds are against it.
The pain subsiding a little after it has gotten worse is more easily explained by regression towards the mean. Assuming it was caused by the doctor is fallacious.
Often exceptional performances are followed by more normal performances, so the change in performance might better be explained by regression towards the mean. Incidentally, some experiments have shown that people may develop a systematic bias for punishment and against reward because of reasoning analogous to this example of the regression fallacy.
Speed cameras are often installed after a road incurs an exceptionally high number of accidents, and this value usually falls (regression to mean) immediately afterwards. Many speed camera proponents attribute this fall in accidents to the speed camera, without observing the overall trend.
Some authors have claimed that the alleged "Sports Illustrated Cover Jinx
" is a good example of a regression effect: extremely good performances are likely to be followed by less extreme ones, and athletes are chosen to appear on the cover of Sports Illustrated
only after extreme performances. Assuming athletic careers are partly based on random factors, attributing this to a "jinx
" rather than regression, as some athletes reportedly believed, would be an example of committing the regression fallacy.
Fallacious evaluation: "Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies." This is clearly not the case. The reason is that political power and occupation of territories is not primarily determined by random events, making the concept of regression to the mean inapplicable (on the large scale).
In essence, misapplication of regression to the mean can reduce all events to a "just so" story
, without cause or effect. (Such misapplication takes as a premise that all events are random, as they must be for the concept of regression to the mean to be validly applied.)
Informal fallacy
An informal fallacy is an argument whose stated premises fail to support their proposed conclusion. The deviation in an informal fallacy often stems from a flaw in the path of reasoning that links the premises to the conclusion...
. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.
Explanation
Things like stock market prices, golf scores, the earth's temperature, and chronic back pain fluctuate naturally and usually regress towards the meanRegression toward the mean
In statistics, regression toward the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on a second measurement, and—a fact that may superficially seem paradoxical—if it is extreme on a second measurement, will tend...
. The logical flaw is to make predictions that expect exceptional results to continue as if they were average (see Representativeness heuristic
Representativeness heuristic
The representativeness heuristic is a psychological term describing a phenomenon wherein people judge the probability or frequency of a hypothesis by considering how much the hypothesis resembles available data as opposed to using a Bayesian calculation. While often very useful in everyday life, it...
). People are most likely to take action when variance is at its peak. Then after results become more normal they believe that their action was the cause of the change when in fact it was not causal.
The word "regression" was coined by Sir Francis Galton
Francis Galton
Sir Francis Galton /ˈfrɑːnsɪs ˈgɔːltn̩/ FRS , cousin of Douglas Strutt Galton, half-cousin of Charles Darwin, was an English Victorian polymath: anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician...
in a study from 1885 called "Regression Toward Mediocrity in Hereditary Stature". He showed that the height of children from very short or very tall parents would move towards the average. In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable may not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that the distribution of heights of their children will be centered somewhere between the average of the parents and the average of the population as whole. Thus, any single child can be more extreme than the parents, but the odds are against it.
Examples
When his pain got worse, he went to a doctor, after which the pain subsided a little. Therefore, he benefited from the doctor's treatment.
The pain subsiding a little after it has gotten worse is more easily explained by regression towards the mean. Assuming it was caused by the doctor is fallacious.
The student did exceptionally poorly last semester, so I punished him. He did much better this semester. Clearly, punishment is effective in improving students' grades.
Often exceptional performances are followed by more normal performances, so the change in performance might better be explained by regression towards the mean. Incidentally, some experiments have shown that people may develop a systematic bias for punishment and against reward because of reasoning analogous to this example of the regression fallacy.
The frequency of accidents on a road fell after a speed camera was installed. Therefore, the speed camera has improved road safety.
Speed cameras are often installed after a road incurs an exceptionally high number of accidents, and this value usually falls (regression to mean) immediately afterwards. Many speed camera proponents attribute this fall in accidents to the speed camera, without observing the overall trend.
Some authors have claimed that the alleged "Sports Illustrated Cover Jinx
Sports Illustrated Cover Jinx
The Sports Illustrated Cover Jinx is an urban legend that states that individuals or teams who appear on the cover of the Sports Illustrated magazine will subsequently be jinxed...
" is a good example of a regression effect: extremely good performances are likely to be followed by less extreme ones, and athletes are chosen to appear on the cover of Sports Illustrated
Sports Illustrated
Sports Illustrated is an American sports media company owned by media conglomerate Time Warner. Its self titled magazine has over 3.5 million subscribers and is read by 23 million adults each week, including over 18 million men. It was the first magazine with circulation over one million to win the...
only after extreme performances. Assuming athletic careers are partly based on random factors, attributing this to a "jinx
Jinx
A jinx, in popular superstition and folklore, is:* A type of curse placed on a person that makes them prey to many minor misfortunes and other forms of bad luck;...
" rather than regression, as some athletes reportedly believed, would be an example of committing the regression fallacy.
Misapplication
On the other hand, dismissing valid explanations can lead to a worse situation. For example:After the Western Allies invaded Normandy, creating a second major front, German control of Europe waned. Clearly, the combination of the Western Allies and the USSR drove the Germans back.
Fallacious evaluation: "Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies." This is clearly not the case. The reason is that political power and occupation of territories is not primarily determined by random events, making the concept of regression to the mean inapplicable (on the large scale).
In essence, misapplication of regression to the mean can reduce all events to a "just so" story
Just-so story
A just-so story, also called the ad hoc fallacy, is a term used in academic anthropology, biological sciences, social sciences, and philosophy. It describes an unverifiable and unfalsifiable narrative explanation for a cultural practice, a biological trait, or behavior of humans or other animals...
, without cause or effect. (Such misapplication takes as a premise that all events are random, as they must be for the concept of regression to the mean to be validly applied.)