When should I use Spearman rank correlation instead of Pearson?

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AcadiFi · Accepted Answer

Yes — Spearman rank correlation is specifically designed for that situation. Instead of using raw values, it ranks the data from lowest to highest and then computes Pearson correlation on the ranks. Key properties: - Robust to outliers: extreme values become ordinary ranks like 1 or n. - Captures monotonic (but not strictly linear) relationships. - Works with ordinal data like credit ratings or risk tiers. Formula (when ranks are unique): ρₛ = 1 - 6Σdᵢ² / (n(n² - 1)), where dᵢ = difference in ranks for pair i. Example: You are correlating credit ratings (AAA, AA, A, BBB, BB) with default rates. Credit ratings are ordinal, not cardinal — the 'distance' from AAA to AA isn't the same as from BB to B. Pearson would be meaningless; Spearman handles this naturally by ranking the categories. When to prefer Spearman: - Data include meaningful outliers. - Relationship is monotonic but nonlinear (e.g., y = log(x) or y = x³). - Variables are ordinal. - Distribution is heavy-tailed. When to prefer Pearson: - Relationship is clearly linear. - Outliers are absent or trimmed. - Data are continuous and roughly normal. ```mermaid flowchart LR A[Raw Data] --> B{Linear and
no outliers?} B -->|Yes| C[Pearson] B -->|No| D[Spearman] D --> E[Rank then
correlate] ``` On the CFA exam, if you see ordinal data or the prompt hints at outliers, choose Spearman. If the data are clean and continuous, Pearson is typically fine.

When should I use Spearman rank correlation instead of Pearson?

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