When two variables are related, we say that there is association between them.

Causal relationships

A causal relationship arises when we can conclude that one variable has a direct influence on the other.

Non-causal relationships

In non-causal relationships, the association between the two variables is not completely the result of one variable directly affecting the other.

If two variables are not causally related, it is impossible to tell whether changes to one variable, X, will result in changes to the other variable, Y.

The scatterplot below shows data from a sample of towns in a region. Neither variable directly affects the other. (The size of the towns is a lurking variable since larger towns have more churches and also more deaths.)