Final answer:
Two variables are said to display correlation if they vary together, measured by a correlation coefficient ranging from -1 to +1, which signifies the strength and direction of their relationship. However, it's important to differentiate correlation from causation, as correlated variables do not necessarily cause changes in each other.
Step-by-step explanation:
Two variables are said to display correlation if they vary together. When we say two variables are correlated, it implies that a change in one variable is associated with a change in the other variable. This relationship is measured using a correlation coefficient, commonly denoted by the letter r, which can range from -1 to +1 indicating the strength and direction of the relationship. A positive correlation coefficient means that both variables move in the same direction, whereas a negative correlation means they move in opposite directions.
It's crucial to understand that correlation does not imply causation. This means that while two variables may display a synchronous change, it does not necessarily mean that one variable's change is causing the change in the other. There might be other variables at play influencing this association.
In the context of observational studies, it's often observed that there may be a strong positive or negative correlation between two variables, which could lead to hypotheses about potential causal relationships. However, these studies can't definitively establish causation because they don't control for all the variables like controlled experiments do.