Understanding Correlations

In psychology, a correlation is a statistical measure that describes the relationship between two variables. When we say two things are correlated, we mean that as one variable changes, the other tends to change as well. We often represent these variables as $x$ and $y$. It is important to remember that correlation does not prove that one thing causes the other; it simply shows that they move together. For example, height and weight are correlated, but growing taller isn't the only reason someone gains weight.

Correlations have two directions. A positive correlation occurs when both variables move in the same direction. If $x$ increases, $y$ also increases. If $x$ decreases, $y$ also decreases. A negative correlation occurs when variables move in opposite directions. As $x$ increases, $y$ decreases. Think of a negative correlation like a seesaw: when one side goes up, the other must go down.

To see a correlation, psychologists use a scatterplot. This is a graph where each dot represents one data point. If the dots form a line pointing from the bottom-left to the top-right, it is a positive correlation. If the line points from the top-left to the bottom-right, it is negative. If the dots are scattered everywhere like spilled glitter, there is a zero correlation, meaning the variables $x$ and $y$ have no relationship at all.

Sometimes, there is absolutely no link between two things. This is a zero correlation. For instance, your shoe size has nothing to do with your intelligence. On a scatterplot, these points would show no discernible pattern or slope. In mathematical terms, the correlation coefficient, represented by the letter $r$, would be $0$.