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Correlation

Statistics & analysis

Definition

A measure of how strongly two variables move together, from −1 to +1 — Pearson's r for continuous linear relationships, Spearman's rho for ordinal or non-normal data.

Correlation quantifies association, not causation: r = 0.6 between stress and turnover intention says the two travel together, not that one causes the other. Direction, strength and significance are three separate pieces of information — report all three.

Rules of thumb treat |r| around 0.1 as small, 0.3 as medium and 0.5 as large, but interpretation is field-dependent. Always inspect the scatterplot: outliers and non-linearity can manufacture or mask correlations.

Choosing the coefficient is a measurement decision. Pearson's r assumes both variables are continuous, roughly normally distributed and linearly related. Spearman's rho works on ranks, so it suits ordinal data and monotonic but non-linear relationships, and it is far less sensitive to outliers. Kendall's tau is preferred for small samples with many tied ranks. Single Likert items are ordinal and are better handled with Spearman, whereas composite scale scores averaged over several items are usually treated as continuous.

In a thesis, the correlation matrix typically appears in the descriptive section of the results chapter, showing means, standard deviations and inter-construct correlations in one table. Very high correlations between independent variables (above about 0.8) warn of multicollinearity before you run a regression, and very high correlations between constructs that should be distinct raise a discriminant-validity question. Report the coefficient, sample size and p-value — for example, r(248) = 0.42, p < 0.001.

Where it's used

  • Preliminary relationship screening before regression
  • Convergent validity evidence between related scales

Software used

SPSSRPythonJASP

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