The practical comparison
| Coefficient | Best read as | Main cautions |
|---|---|---|
| Pearson r | Strength and direction of a linear pattern | Nonlinearity and influential observations can distort it. |
| Spearman rho | Strength and direction of a monotonic rank pattern | Ties and rank compression matter. |
| Kendall tau | Pairwise ordinal concordance | Magnitude is not numerically interchangeable with r or rho. |
An ordinal variable or a clearly monotonic but curved relationship can support a rank coefficient. That is not a license to choose whichever coefficient yields the preferred p-value.
Read Pearson and Spearman together
If Pearson and Spearman are similar, the linear and rank summaries tell a consistent story. If |Spearman| is much larger, inspect for a monotonic curve or influential extremes. If Pearson is larger, inspect clusters, ties, and range restrictions. The scatter plot remains essential.
Correlation strength interpretation covers attributed magnitude conventions. Correlation matrices explains how mixed coefficients and multiple pairs complicate a table. r versus R-squared keeps correlation separate from model fit.
Ties, missingness, and uncertainty
Rank methods need a stated tie treatment. Software can use exact or asymptotic p-values under different conditions. Pairwise missing-data deletion can make coefficients in the same matrix rely on different samples. Report n and an interval where possible.
A defensible reporting sentence
“Pearson r was .34 and Spearman rho was .51. The scatter plot showed a monotonic curve, so rho better summarized the rank pattern; the coefficient type, sample size, interval, and tie handling were reported.”