Statistics for the Social Sciences A General Linear Model Approach

Pearson’s correlation describes the relationship between two interval- or ratio-level variables. Positive correlation values indicate that individuals who have high X scores tend to have high Y scores (and that individuals with low X scores tend to have low Y scores). A negative correlation indicates that individuals with high X scores tend to have low Y scores (and that individuals with low X scores tend to have high Y scores). Correlation values closer to +1 or –1 indicate stronger relationships between the variables; values close to zero indicate weaker relationships. A correlation between two variables does not imply a causal relationship between them.

It is also possible to test a correlation coefficient for statistical significance, where the null hypothesis is r = 0. This follows the same steps of all NHSTs. The effect size for Pearson’s r is calculated by squaring the r value (r2).

A correlation is visualized with a scatterplot. Scatterplots for strong correlations have dots that are closely grouped together; scatterplots showing weak correlations have widely spaced dots. Positive correlations have dots that cluster in the lower-left and upper-right quadrants of a scatterplot. Negative correlations have the reverse pattern.