Correlations

Psychology AS · Research methodology. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A correlation is a relationship between two measured variables, called co-variables. Nothing is manipulated, so there is no independent or dependent variable. The researcher measures both co-variables for each participant and looks for a pattern, usually on a scatter graph.

In a positive correlation both co-variables rise together. In a negative correlation one rises as the other falls. The correlation coefficient, r, shows strength on a scale from −1 to +1: the closer to either end, the stronger the relationship.

A correlation shows that two things are related. It never shows that one causes the other.

Rules to remember

Positive correlation: as one co-variable increases, the other increases. Points slope upwards from left to right.
Negative correlation: as one increases, the other decreases. Points slope downwards from left to right.
Strength: r runs from −1 to +1. Near +1 or −1 is strong; near 0 is weak or no correlation. The sign shows direction, not strength.
Co-variables must be operationalised: state exactly how each is measured, with units or a scale.
No causality: A may cause B, B may cause A, or a third variable may affect both.
Strength of the method: allows study of variables that cannot be manipulated for practical or ethical reasons, and can suggest ideas for experiments.

Common mistake

Students think a negative correlation is a weak one. The sign only gives the direction: r = −0.8 is a stronger relationship than r = +0.5.

Worked example

A study of 50 adults finds r = −0.75 between minutes of exercise per week and score on an anxiety scale (0 to 40). Describe the relationship and say whether exercise reduces anxiety.

The sign is negative, so as exercise increases, anxiety scores decrease.
0.75 is close to 1, so the relationship is strong.
Both were only measured, so cause is unknown: anxious people may exercise less, or a third variable such as health may affect both.

Answer: A strong negative correlation: more exercise goes with lower anxiety, but the study cannot show that exercise causes the lower anxiety.

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