Is a relationship causal?
Investigators usually hope to find causal relationships between the variables that are recorded. If one variable causally affects the other, then adjusting the value of that variable will cause the other to change. For example, if the milk yield of cows is causally affected by a dietary supplement, then yields can be increased by changing this supplement.
Causality can only be determined by reasoning about how the data were collected.
The data values themselves contain no information that can help you to decide.
Lurking variables
Non-causal relationships between two variables usually result from the effect of further variables called lurking variables that are related to the variables under investigation. Causal relationships can only be deduced if it can be reasoned that lurking variables are not present.
Smoking and attendance at college
The following contingency table comes from a survey of 400 males aged 19.
A smaller proportion of male college students smoke than males who do not attend college. Also, a smaller proportion of male smokers attend college than non-smokers.
There are three possible interpretations of this relationship between smoking and college attendance.
The data cannot help to resolve the issue of causation so it would be incorrect to report any causal relationship from these data.