Regression fallacy

The regression (or regressive) 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.

Explanation

Things like stock market prices, golf scores, and chronic back pain can fluctuate naturally and may regress towards the mean. 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 will 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 children's height will fall somewhere between the average of the parents and the average of the population as whole.

It also should be noted that a line fitted to data incorrectly will produce the regression toward the mean effect. When error exists on the horizontal X axis variable, the sum of squared [perpendicular] distances between points and the fitted line should be used in the least squares math formulas instead of [vertical] distances. This is called orthogonal, Deming or Type II regression. If this method was used for Galton's data, the regression toward the mean fallacy would disappear. More accurately, if the X and Y variables have equal error [perpendicular] distances are ideal. If the X variable error is much larger than the Y variable error, [horizontal] distances are best. Vertical distances should only be used when the Y variable error is much larger than for X. A simple option is to fit a line using all three directional distances and determine which is best for your case. If the X and Y errors are known, closed form solutions are available as well. This topic however is not well published.

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 [Schaffner, 1985; Gilovich, 1991 pp. 27–28] .

:"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 the alleged "Sports Illustrated Cover Jinx" is a good example of a regression effect: extremely good performances are likely to be following by relatively 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 [Gilovich, 1991 pp. 26–27; Plous, 1993 p. 118] .

Mis-application

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.

In essence, mis-application of regression to the mean can reduce all events to a "just so" story, without cause or effect.

External links

* [http://www.fallacyfiles.org/regressf.html Fallacy files: Regression fallacy]

Notes

References

*citation |last=Schaffner |first=P. E. |title=Specious learning about reward and punishment |journal=Journal of Personality and Social Psychology |volume=48 |year=1985 |pages=1377–86 |url=http://psycnet.apa.org/index.cfm?fa=search.displayRecord&uid=1985-28051-001
*citation |last=Gilovich |first=Thomas |authorlink=Thomas Gilovich |title=How we know what isn't so: The fallibility of human reason in everyday life |location=New York |publisher=The Free Press |year=1991
*citation |last=Plous |first=Scott |authorlink=Scott Plous |title=The Psychology of Judgment and Decision making |publisher=McGraw-Hill |location=New York |year=1993