spearman-rank-correlation · shipping · also Spearman's rho, Spearman rank-order correlation, SRCC

Spearman rank correlation

Spearman rank correlation measures monotonic association by taking the Pearson correlation of paired ranks, using average ranks for ties.

Related Observatory article: Spearman rank correlation on hesela.com

A coefficient near +1 indicates increasing rank agreement and one near -1 decreasing rank agreement; zero does not establish independence. Equal observations receive the average of their occupied rank positions. A constant input has no rank variance, so its correlation is undefined rather than zero. [1] [2] [3]

For a concrete counterexample, take six equally likely invented states with X = (-3,-2,-1,1,2,3) and Y = (1,0,0,0,0,1). Average Y ranks are (11/2,5/2,5/2,5/2,5/2,11/2). Centered rank products sum to zero, although Y is determined by abs(X) = 3. P(Y=1) = 1/3 while P(Y=1 | X=3) = 1. This is a constructed population, not SMART telemetry or a validated predictor. [5]

Han et al. use SRCC to compare SMART attributes with grouped SSD failures. Their section 3 implication from zero SRCC to independence is too strong; section 4.3's reported coefficients are not changed by this mathematical counterexample. Rank association alone neither supplies an alert threshold nor evaluates nonlinear predictive performance. [4]

Relations

related

Matthews correlation coefficient, Probability calibration, Class prevalence, Precision, Recall, Grouped cross-validation, Temporal validation

Limitations

• A small coefficient cannot rule out nonmonotonic dependence or establish that a predictor is useless; a large coefficient does not establish causation. [1, 5]
• Repeated observations from one drive are not automatically independent samples; define the observation unit and evaluation split before interpreting predictive results. [6]

Citations

1. SciPy: spearmanr, monotonic rank association and undefined constant inputs (accessed 2026-11-04)
2. SciPy: rankdata, average tie ranks (accessed 2026-11-04)
3. R stats: cor, rank-based correlation (accessed 2026-11-04)
4. Han et al. An In-Depth Study of Correlated Failures in Production SSD-Based Data Centers. FAST 2021, sections 3 and 4.3 (accessed 2026-11-04)
5. Hesela: exact synthetic rank-association counterexample, method and limitations (accessed 2026-11-04)
6. Hesela: evaluation units and temporal/device splits in failure prediction (accessed 2026-11-04)

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