Measures the strength of a monotonic relationship using ranks — the robust alternative to Pearson for ordinal data, outliers, or curved-but-monotonic trends.
Test AssociationBivariatealso known as: Spearman's rho, ρ, rank-order correlation
✓ When to use
One or both variables are ordinal (single Likert items, ranks, grades).
Continuous data with outliers or clear non-normality.
The relationship looks monotonic but not linear (consistently rising, at a changing rate).
✗ When NOT to use
Both variables continuous, roughly normal, relation linear — Pearson uses more information.
Non-monotonic relationships (U-shaped) — no correlation coefficient captures these; model the curve.
Very small samples with many ties — consider Kendall's tau instead.
Truly nominal variables — use chi-square/Cramér's V.
Data requirements
Dependent / outcome variable
Two variables, each at least ordinal (symmetric measure).
Independent / grouping variable
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Design
One sample, both variables per case, independent observations.
Sample size guidance
Usable from n ≈ 10; same power ballpark as Pearson for moderate effects.
Assumptions
Independent observations.
Both variables at least ordinal.
Monotonic relationship (rho summarizes monotonic trend; check the scatterplot).
Hypotheses
H₀ — No monotonic association in the population (ρs = 0).
H₁ — A monotonic association exists (ρs ≠ 0).
The concept
Spearman's rho is simply Pearson's r computed on the ranks of the data. Converting to ranks discards distances between values, which immunizes the coefficient against outliers and skew, and captures any relationship in which higher X consistently goes with higher (or lower) Y — even when the trend is curved.
Benchmarks parallel Pearson's (.10/.30/.50). With heavily tied data (short Likert scales), Kendall's tau-b handles ties more gracefully and is preferred by some journals.
Worked example
A researcher relates employees' rank in the performance league table (1–80) to a single overall-satisfaction item (1–5), n = 80.
Result: ρs = −.36, p = .001 — better-ranked (lower number) employees report higher satisfaction: a medium monotonic association.
How to run it
cor.test(df$perf_rank, df$satisfaction, method = "spearman")
# with CI via bootstrap
library(confintr)
ci_cor(df$perf_rank, df$satisfaction, method = "spearman", type = "bootstrap")
from scipy import stats
import pingouin as pg
print(stats.spearmanr(df["perf_rank"], df["satisfaction"]))
print(pg.corr(df["perf_rank"], df["satisfaction"], method="spearman"))
Analyze → Correlate → Bivariate.
Move both variables in; untick Pearson, tick Spearman.
Report rho, n, and p; add medians/IQRs as descriptives for ordinal variables.
Create rank columns: =RANK.AVG(A2, A$2:A$81, 1) for each variable.
Then correlate the ranks: =CORREL(rankX_range, rankY_range) — this equals Spearman's rho (tie-corrected because RANK.AVG averages ties).
p-value approximation: t = rho*SQRT(n−2)/SQRT(1−rho^2); =T.DIST.2T(ABS(t), n−2).
Interpreting the output
Sign and magnitude read like Pearson's r, but the claim is about monotonic (not linear) association.
Report medians rather than means for ordinal inputs.
With many ties, note the software's tie handling or prefer Kendall's tau-b.
Same caution: association is not causation.
APA-style reporting
Performance rank was negatively associated with overall satisfaction, Spearman's ρ = −.36, p = .001, n = 80, indicating that higher-ranked employees tended to report greater satisfaction.
Common mistakes
Defaulting to Spearman only because data are 'survey data' — averaged multi-item scales usually justify Pearson.
Interpreting rho as a linear-relationship measure.
Ignoring massive ties on 5-point items (report tau-b as a check).