Which research method assesses how well one variable predicts another without demonstrating a cause-effect relationship between the variables?

The answer is correlational research.

Explanation:

This approach seeks to measure the extent in which two variables are related. It's important to recognise that correlation does not mean causation. For example, a study might find that 80% of people who passed an exam had breakfast that morning. The variables are correlated, but that doesn't mean the breakfast was the cause of the exam results.