What is an example of a positive correlation that has an obvious causal relationship?

Answer 1

The standard answer is that a positive statistical correlation, no matter how strong, never proves anything about the causal relationship. Technically, correlations are symmetric and so the evidence is identical whether you imagine that A causes B or B causes A.

Another problem is that you could have an omitted third factor C which explains both A and B. A correlation between A and B never rules out the possibility of C influencing them both.

What you can sometimes say more realistically is that a strong correlation might make a proposed causal explanation more plausible. It might be evidence as part of an argument, but it's not sufficient by itself.

Other parts of the argument could be exclusion of other factors (through experiments or statistical controls) and logical precedence. For example, if you had evidence that women are smarter than men, it doesn't seem likely that smartness causes gender. Similarly, events from the future don't influence events of the past; thus establishing the time sequence might also help to build a causal explanation.

In short, there are few if any obvious causal relationships based on correlation alone if you want to use rigorous methods. Experiments and replication of results under diverse circumstances are the best way to show a causal relationship.