# Regression fallacy:

Definition | Example |

When the cause of some apparent phenomenon is assumed to be some factor outside statistical noise and artifacts, when natural and expected statistical dynamics may in part or wholly account for the apparent phenomenon. | Last year we had 12 car accidents on main street, double the previous year’s figures! The frequency of accidents on Main Street fell to only 6 again after a speed camera was installed early this year. Therefore, the speed camera has improved road safety. |

Notes | |

This is similar to the post hoc ergo propter hoc fallacy, but is based on the statistical principle of “regression to the mean” principle in which certain phenomena naturally fluctuate in volume or intensity. This statistical “noise” in the data is natural and expected. |

**Case Study One**

In 1999 the Massachusetts Department of Education gave it’s school improvement goals, then subsequently tested those districts for any detectable improvement. Unsurprisingly, the bottom 50% of the schools made notable improvement. What was not so heavily emphasized was that the top 50% of their schools fell about the same degree as the bottom 50% gained. An apparent improvement of the bottom half and an apparent drop of the top half is what is statistically expected, and does not necessarily show the efficacy of any policy in effect at the time.

**Case Study Two**

Two very tall parents will most likely have children who are taller than the average child. However, due to the natural regression to the mean, the children will also likely be shorter than the average height of their parents. To attribute the shortness of the child relative to their parents to anything other than a statistical expectation without accompanying evidence would be a regression fallacy.

^{Keep in mind that a fallacious argument does not entail an erroneous position.}