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Spearman Correlation

Spearman rank correlation rs

📊Spearman Rank Correlation

Spearman's rank correlation (rs) measures the strength of the monotonic relationship between two variables using their ranks. It is the non-parametric equivalent of Pearson's r and is more robust to outliers.

  1. 1Rank each variable from 1 to n
  2. 2rs = 1 − (6Σd²) / (n(n²−1))
  3. 3d = difference in ranks for each pair
  4. 4Perfect rank agreement → rs=1; perfect reversal → rs=−1
Two raters rank 5 items: d² values: 1,0,4,1,0=rs = 0.7 — moderate to strong rank correlation1−6×6/(5×24)=0.7

Fun Fact

Spearman correlation is preferred in psychology and social sciences where data is often ordinal (Likert scales, rankings) rather than truly continuous.

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