Spearman Rank Correlation Coefficient
Also known as: Spearman's rho, Spearman rank-order correlation, Spearman Sıra Korelasyonu
The Spearman rank correlation coefficient (ρ) is a nonparametric measure of the monotonic association between two variables. Introduced by Charles Spearman in 1904, it converts raw observations to ranks and measures how consistently one variable increases as the other increases, without assuming a normal distribution or a linear relationship.
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When to use it
Use Spearman's correlation when you want to measure the association between two variables that are at least ordinal in scale and when you cannot confidently assume normality or a linear relationship. It is the preferred choice when the data contain outliers, when the relationship is monotonic but not strictly linear, or when one or both variables are measured on an ordinal scale (e.g. Likert items, ranked preferences). The minimum recommended sample is 10 observations. If n is smaller than 10, Kendall's tau is a more reliable alternative. A scatter plot should always be inspected first: if the relationship appears non-monotonic (U-shaped or cyclical), neither Spearman nor Pearson is appropriate.
Strengths & limitations
- Does not require normality or linearity — applies to any monotonic relationship.
- Robust to outliers because ranks are insensitive to extreme values.
- Works with both continuous and ordinal data, making it broadly applicable across disciplines.
- Widely accepted and available in every major statistical package.
- Detects only monotonic associations; non-monotonic patterns (e.g. U-shaped) yield ρ near zero even when a strong relationship exists.
- Less statistically powerful than Pearson correlation when data are truly bivariate normal.
- With many tied ranks the standard formula is less accurate; the general rank-based Pearson formula should be used instead.
- A sample smaller than 10 produces unreliable results.
Frequently asked
When should I use Spearman instead of Pearson?
Use Spearman when you cannot assume bivariate normality, when one or both variables are ordinal, or when the data contain influential outliers. Pearson is more powerful under normality and linearity, but can be badly distorted by a single extreme value. If in doubt, examine the scatter plot and run a normality check.
What does ρ = 0.45 mean in practice?
It indicates a moderate positive monotonic association: when one variable increases, the other tends to increase as well, but the pattern is not tight enough to be considered strong. By convention, |ρ| < 0.30 is weak, 0.30–0.49 is moderate, and 0.50 or above is strong, though these thresholds depend on the discipline.
How do I handle ties in the data?
When observations share the same value they are assigned the average of the ranks they would have occupied. In the presence of many ties the simplified d² formula becomes inaccurate; use the Pearson formula applied to the rank vectors instead — most statistical software does this automatically.
Can I use Spearman correlation to compare more than two variables at once?
Spearman's ρ is a pairwise measure; it quantifies the association between exactly two variables at a time. For multiple variables, compute a correlation matrix of pairwise ρ values. Adjust p-values for multiple comparisons (e.g. with the Bonferroni or FDR correction) to avoid inflated false-positive rates.
Sources
- Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15, 72–101. DOI: 10.2307/1412159 ↗
How to cite this page
ScholarGate. (2026, June 1). Spearman Rank Correlation Coefficient. ScholarGate. https://scholargate.app/en/statistics/spearman-correlation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Kendall Tau CorrelationStatistics↔ compare
- Mann-Whitney U testStatistics↔ compare
- Pearson CorrelationStatistics↔ compare
- Point-Biserial CorrelationStatistics↔ compare