Correlation
What question does this help answer?
Whether two measurements are related, and how tightly. It is a descriptive question, and it is a weaker one than most papers using it seem to intend.
Pearson, Spearman, Kendall
Pearson's r measures LINEAR association and assumes roughly bivariate normal data; a single outlier can dominate it. Spearman's rho ranks the data first and measures monotonic association, which makes it robust to outliers and appropriate for ordinal variables. Kendall's tau does something similar with a more interpretable definition based on concordant and discordant pairs, and behaves better with many ties.
What it does not tell you
- Not the magnitude of the relationship: that is a regression slope, in the units a clinician thinks in.
- Not causation, in either direction, and not the absence of a confounder explaining both.
- Not agreement: two methods can correlate at 0.99 while one reads systematically twice the other. That is a Bland-Altman question.
- Not the shape: a strong U-shaped relationship can have a Pearson r near zero.
- Not that the association holds in a subgroup, since a pooled correlation can reverse within groups.
Always plot it
The scatter plot is not decoration. Anscombe's classic quartet is four datasets with the same correlation and utterly different shapes, and the same trap is easy to fall into with real clinical data where a handful of extreme values create or destroy the coefficient.
What the same correlation can look like
Why Mallard may recommend it
Mallard may name correlation when the question is genuinely about association between two continuous measurements, and will prefer regression whenever the question implies a direction or needs adjustment.
What to watch out for
A correlation coefficient describes the strength of a linear or monotonic association and nothing else: it does not say how much the outcome changes per unit of exposure, it is not a test of agreement between two measurement methods, and it is heavily affected by the RANGE of the data, so restricting the sample shrinks r without changing the underlying relationship. A large r with a wide scatter and a small r with a clinically important slope are both routine.
Clinical example
Question: Is serum biomarker concentration related to symptom score? Analysis: Spearman's rho with a confidence interval and a scatter plot, alongside a regression slope in score points per unit of biomarker if the question is really about how much one moves with the other.
- Correlation Coefficients: Appropriate Use and Interpretation (opens in a new tab) · Anesth Analg · doi 10.1213/ANE.0000000000002864
- Statistical methods for assessing agreement between two methods of clinical measurement (opens in a new tab) · Lancet