Correlations

Correlational Analysis

A correlation is a statistical technique used to measure the strength and direction of the relationship between two variables — called co-variables — without manipulating either. Rather than asking 'does X cause Y?', correlational research asks 'does X tend to change as Y changes?' Correlations are used when experimental manipulation is impractical or unethical, and are particularly valuable for generating hypotheses, studying naturally occurring relationships, and describing how variables relate in the real world.

Direction of Correlation

A positive correlation exists when both co-variables increase or decrease together — as one goes up, so does the other. For example, there is a positive correlation between hours of revision and exam grade: students who revise more tend to score higher. A negative correlation exists when as one variable increases, the other decreases. For example, there is a negative correlation between stress levels and immune function: higher stress is associated with lower immune response. A zero correlation (no correlation) exists when there is no systematic relationship between the two variables.

Strength of Correlation

The strength of a correlation is expressed as a correlation coefficient, which ranges from −1.00 to +1.00. A coefficient of +1.00 indicates a perfect positive correlation; −1.00 a perfect negative correlation; 0 indicates no linear relationship. The closer the coefficient is to ±1.00 (regardless of sign), the stronger the relationship. In psychology, correlations between ±0.30 and ±0.70 are common.

Displaying Correlational Data: Scattergrams

Correlational data is typically displayed on a scattergram (scatter diagram), in which each participant is represented as a single dot plotted at the intersection of their scores on the two variables. The pattern of dots reveals the direction and approximate strength of the correlation. A line of best fit can be added to summarise the trend. Inspecting the scattergram is important before calculating a correlation coefficient — it can reveal non-linear (curvilinear) relationships or outliers that would distort the coefficient.

Strengths and Limitations

Strengths: allows investigation of variables that cannot be manipulated for ethical or practical reasons; can study naturally occurring relationships with high ecological validity; identifies associations that can then be investigated experimentally; efficient — both variables measured in a single study. Limitations:

• Cannot establish cause and effect: even a strong correlation does not tell us which variable causes which. The directionality problem means we cannot determine from the correlation alone whether X causes Y or Y causes X. The third variable problem means that an unmeasured third variable may cause both co-variables independently, producing the correlation without any direct causal link between them.
• Only detects linear relationships: a Pearson correlation coefficient only measures linear association. A strong curvilinear relationship (e.g. the Yerkes-Dodson inverted-U between arousal and performance) may produce a near-zero coefficient.