Correlation Does Not Imply Causation
The principle that an observed association between two variables does not prove a cause-and-effect relationship. The logical fallacy occurs when one incorrectly infers causality from correlation alone.
THE IDEA
Correlation Does Not Imply Causation
One of the first things taught in introductory statistics textbooks is that correlation is not causation. It is also one of the first things forgotten.
—Thomas Sowell
Correlation does not imply causation refers to the inability to legitimately deduce a cause-and-effect relationship between two variables based solely on an observed association or correlation between them.
The complementary idea that correlation implies causality is a logical fallacy, where two events occurring together are considered to have established a cause-and-effect relationship. This idea creates two related fallacies: post hoc ergo propter hoc (one event occurs after another, then it is because of that other) and cum hoc ergo propter hoc (one event occurs at the same time as another, then is caused by that other).
Correlation measures how variables vary together. A positive correlation means that higher values of one tend to accompany higher values of the other; a negative correlation means that higher values tend to accompany lower values. Zero linear correlation does not rule out every kind of relationship. Measurements can be paired across time as well as taken simultaneously. Estimates from small samples can be unstable, and a larger sample does not by itself establish causation.
This confusion runs through many studies, especially in the social sciences, so one must be especially careful with interpretations of statistical data so as not to imply causal relationships where there might be nothing more than a spurious correlation or mere coincidence.
Common Misleading Headlines
News headlines often imply causation from correlation, such as:
- "A study states that the more A, the more B."
- "A study states that those who are A have less B."
- "A study states that since A is like this then B is this other way."
The first two headlines can describe associations without asserting causation. The question is whether the article goes on to claim that changing A would change B, and whether the study supports that claim.
Illustrative Examples
- The source describes a 1999 Nature study associating childhood night-light use with myopia, followed by research examining parental myopia. Parents’ vision could be related both to their use of night lights and to their children’s myopia, illustrating a possible confounder.
- The crowing of the rooster does not cause the sunrise.
- Carrying an umbrella does not prevent rain.
- Ancient peoples believed lightning was caused by human actions that angered the gods.
- Changes in economic variables are often attributed solely to government actions, ignoring other factors.
Almost all great records eventually dwindle…
—Charlie Munger
Complexity and Nonlinearity
In a nonlinear system, effects need not be proportional to changes in an input. Feedback and interactions can make causal relationships difficult to isolate. These complications call for a better model and evidence; a correlation alone still does not identify the causal mechanism.
This idea is closely related to the models of Chaos Theory, Power Laws, and Complex Adaptive Systems.
When to use it
Evaluating health claims in media (e.g., 'coffee drinkers have lower risk of X' without controlling for confounders).
Interpreting economic indicators and policy outcomes by considering multiple interacting variables.
Assessing social science research to avoid overstating causal conclusions from observational studies.
Debiasing everyday superstitious beliefs (lucky charms, rituals) by examining the underlying false cause-and-effect pattern.
FROM THEORY TO EVERYDAY LIFE
In practice
Night Lights and Myopia
The source cites a 1999 Nature study linking childhood night-light use with myopia. It describes later work on parental myopia as an alternative explanation for the association. The example shows why a possible common cause needs investigation before blaming the light.
Rooster Crowing and Sunrise
The rooster crows before sunrise, but the crowing does not cause the sun to rise. The correlation is due to the rooster's circadian rhythm responding to the approaching dawn.
Umbrella and Rain
Carrying an umbrella on an uncertain day is sometimes thought to prevent rain. In reality, the umbrella does not influence the weather; the belief is based on a spurious correlation (when it doesn't rain, the umbrella was carried).
Government Policies and the Economy
Politicians often claim that economic changes during their term are directly caused by their actions. However, many external factors (global markets, technology, consumer confidence) influence the economy, making it a classic case of mistaking correlation for causation.
A MOMENT TO REFLECT
Put it to work.
Think of a recent news headline that implied causation from a correlation. What alternative explanations could account for the observed association?
In your own life, have you ever mistakenly assumed that because two things happened together, one caused the other? What might you test to avoid this fallacy in the future?
How could you design an experiment to distinguish correlation from causation in a scenario like the relationship between exercise and happiness?
Often confused with
References
- Association of myopia and sleep in children — Unknown (1999)
CONTINUE THE CONVERSATION
Source texts
- Wisdom Theory 100 Mental Models (2020) (Wisdom Theory)