Reverse causation

What it is

Reverse causation is when we get the arrow backwards. Two things are linked, and it looks as if X causes Y. But really, Y causes X.

Here is an imaginary example. Suppose you notice that people who use walking sticks fall more often than people who don't. Do walking sticks cause falls? Almost certainly not. People who are unsteady on their feet are more likely to use a stick, and more likely to fall. The unsteadiness comes first.

The Correlation vs causation entry introduces reverse causation as one of four ways a link can fool you. This entry looks at how to work out which way the arrow points.

Why it matters

If we get the direction wrong, we may give the wrong advice. Imagine telling unsteady people to stop using walking sticks so they fall less often. The advice would be backwards, and could do harm.

A real example, about alcohol, is described in the Correlation vs causation entry. Men who didn't drink seemed to die sooner than light drinkers, but many of them had stopped drinking because they were already ill.¹

Reverse causation vs a hidden third factor

Reverse causation is not the same as a hidden third factor, called a confounder. With a confounder, something else causes both X and Y. With reverse causation, the arrow between X and Y simply points the other way. The two can happen together, though. In the alcohol example, illness is behind both. See the Confounding variable entry.

How to check the direction

• Timing. Did X really come before Y? Austin Bradford Hill, who wrote about how to judge causes, stressed that the cause has to come first.² See the Indicators of causation entry.
• Measure before it starts. Following people over time helps, but only if X was measured before Y began. If the illness had already started when drinking habits were recorded, following people for years won't fix the problem.
• Leave out people who were already affected. If a link disappears when you exclude people who were already ill at the start, reverse causation is a likely explanation.¹
• Assign X at random. In a randomized controlled trial, chance decides who gets X. Then Y can't have caused X, so the direction is settled by the design. See the Randomized controlled trial entry.

In everyday life

For each of these, ask which way the arrow might point:

• "People who sleep more are less stressed." Does sleep reduce stress? Or does stress ruin sleep?
• "Children who read more get better grades." Does reading improve grades? Or do children who find school easier enjoy reading more?
• "Cities with more police have more crime." Do police cause crime? Or do cities with more crime hire more police?

Each of these could run in either direction, or both.

The common trap

The trap is assuming that the obvious direction must be the right one. When two things are linked, our minds jump to the story that feels most natural. That story may be backwards.

Some ways out:

• Always say the link out loud both ways: "X causes Y" and "Y causes X." Which fits the facts better?
• Ask what came first, and how anyone knows.
• Ask whether a randomized trial has been done.

Try it

Take the three examples above. For each one, describe a fact that would tell you which direction is right. For example, for sleep and stress: what happens to people's stress when their sleep is disturbed by something unrelated, like a new baby or roadworks outside?

Related concepts

Correlation vs causation · Indicators of causation · Confounding variable · Randomized controlled trial

Sources

1. Shaper, A. G., Wannamethee, G., & Walker, M. (1988). Alcohol and mortality in British men: Explaining the U-shaped curve. The Lancet, 332(8623), 1267–1273. https://doi.org/10.1016/S0140-6736(88)92890-5

2. Hill, A. B. (1965). The environment and disease: Association or causation? Proceedings of the Royal Society of Medicine, 58(5), 295–300. https://doi.org/10.1177/003591576505800503