Spearman Rank Correlation ρ - Monotone relationship between two rankings

Overview

Spearman Rank Correlation ρ - Monotone relationship between two rankings

Output

robustness score, higher is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Sensitivity analysis, uncertainty quantification

How it works

1. 1

   Validate inputs for spearman-rho.

   $${\rho }_s=1-\frac{6\sum d_i^2}{n(n^2-1)}$$

   Spearman 1904, (pending PDF page verification)

Look elsewhere when

Assumptions to verify

• A base ranking method is selected
• Computational budget for repeated runs

Edge cases and pitfalls

• Applying SPEARMAN-RHO without verifying this assumption.

  Requirement: A base ranking method is selected

• Applying SPEARMAN-RHO without verifying this assumption.

  Requirement: Computational budget for repeated runs

• Using SPEARMAN-RHO when: Quick analysis needed → defer robustness check.

  An alternative method is recommended in this situation.

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