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.

Instruction in technical writing

In order to evaluate instruction in technical writing, a group of firms submit 110 pieces of technical writing done by members of their staff who had received training in technical writing and another 120 piece of technical writing done by others who had no training. A panel of judges rated each article.

  Rating of writing
Attended course? Superior Acceptable Inferior Pr(Superior writing)
Yes 48 39 23 0.44
No 12 36 72 0.10
Pr(attended) 0.80 0.52 0.24

A larger proportion of those who had attended a course were rated as 'superior'. Also, a larger proportion of 'superior' passages were written by staff who had attended a course.

There are two possible interpretations of this relationship.

The data cannot help to resolve the issue of causation so it would be incorrect to report any causal relationship from these data.