Question

An observational study determined that there is a strong correlation between eating breakfast and weight loss. Can it be determined that eating breakfast causes weight loss? Explain.
Causation cannot be proven because everyone eats breakfast.
Causation cannot be proven because weight loss can occur for other reasons, such as exercise and eating healthy.
Causation can be proven because it is well known that eating breakfast causes weight loss.
Causation can be proven because an experiment was used to prove this hypothesis.

Answer 1

A common misconception in statistics is confusing correlation with causation. If two events are correlated, it merely means that they share the same behaviour over time, but it doesn't imply in any way that those event are related by a common cause, or even worse, that one implies the other.

You can find several (even humorous) counter examples online. For example, if you plot the number of reported pirates assault against the global temperature in the last years, you'll se that temperature is rising (unfortunately...) while pirates are almost disappearing.

One could observe this strong negative correlation and claim that hotter climate has solved the pirate issue. Of course this is a joke, but it explains why you shouldn't confuse correlation with causation.