Correlation Versus Causation

For example, suppose you record the height of a growing sunflower and the mass of a growing puppy each day. As the sunflower gets taller, the puppy tends to get heavier. The measurements show positive correlation.

However, this does not establish that making the sunflower taller would make the puppy heavier. Nor does it establish that a heavier puppy makes the sunflower grow. The pattern alone cannot tell us that either variable causes the other.

This is what correlation does not necessarily imply causation means. A causal relationship may exist, but correlation alone is not enough to establish it—even when the pattern is very strong.

Another factor can influence both variables

In the sunflower and puppy example, the passage of time helps explain the relationship. As time passes, both organisms grow. Their measurements can therefore increase together without either organism's growth causing the other's.

Time is a third factor: something other than the two measured variables that helps explain why they are associated.

The arrows show two separate influences, not a causal link from sunflower height to puppy mass. When interpreting a correlation, it is useful to ask whether another factor could affect both variables.

Multiple factors may interact — Higher tier

A relationship need not have just one simple explanation. Several factors may influence the variables, and their effects may combine or depend on one another.

Consider a study that finds rising atmospheric carbon dioxide levels and rising obesity levels over time. That correlation alone would not establish that carbon dioxide causes obesity. One possible explanation involves increasing wealth: richer populations may have both higher emissions and higher obesity levels.

Here, time and wealth are connected rather than being completely separate explanations. Wealth can change over time and may be associated with changes in both measured quantities. Other influences may also contribute, so it would be unjustified to treat one observed correlation as a complete explanation.

Making a justified conclusion

A statistical conclusion should match the evidence. In the sunflower example, you can conclude that greater sunflower height is associated with greater puppy mass in the recorded measurements. You cannot conclude from those measurements alone that increasing sunflower height causes an increase in puppy mass.

Separate what the data show from what might explain the pattern. A plausible third factor is a reason to question a causal claim, not proof that your alternative explanation must be correct.