Can you have causation without correlation? (Surprisingly, yes)

Here are five ways you can have correlation without causation:

1. Averaging: increasing A sometimes causes increasing B, but other times, it causes B to decrease. The two balance out. Since correlation measures the average relationship, the correlation is zero.

For example, if you drive up a symmetrical hill and then down the other side, there’s no correlation between how many times the wheels have revolved on the hill and the car’s height above sea level, even though the revolving of the wheels causes the altitude to change.

2. Confounders: when A increases, that causes B to increase, but change is coming from C, and increasing C both causes A to increase AND causes B to decrease. The decrease in B from more C is the right amount to counteract the increase in B caused by C causing A to increase.

Example: A is in love with B and best friends with C. When C is happy, that makes A happy. When B compliments someone in front of A, that makes A unhappy. When B complements C, that makes C happy, making A happier, but the complement itself makes A unhappier, balancing it out.

3. Control: a system is designed to stabilize the value of B. Even though increases in A normally cause an increase in B, the system resists this change by exerting the opposite effect on B with the goal of keeping B constant.

For example, opening the vents would normally cool down the house, but when the heating system detects a draft, it causes the heating system to start working harder in order to keep the house at the desired 70 degrees.

4. Multiple causation: while A does cause C, C is also caused by B (so either A or B on its own is sufficient to cause C). Since A and B are both active, deactivating one has no effect on C. A and B never get deactivated at the same time, so the relationship between A and C is 0.

Example: on death row in a certain country, they administer a lethal dose of two different poisons. They have experimented with removing one or the other poison, and this did not affect whether the inmate died.

5. Deactivated causation: an increase in A causes an increase in B normally, but only if C is active. Since C is not active, there is no correlation measured between A and B. For example, force on the gas peddle only causes the car to increase speed when the car is turned on

All of this being said, while causation does not NECESSARILY imply correlation, causation USUALLY DOES imply correlation. Some software that attempts to discover causation in observational data even goes so far as to make this assumption of causation implying correlation.

---

This piece was first written on March 14, 2022, and first appeared on this site on December 7, 2023.