Two reviewers score a stack of papers. Do their scores move together — even if not on the same scale? Spearman’s ρ correlates their RANKS, so it catches any monotonic relationship: +1 same order, −1 exact reverse, 0 unrelated. Slide from anti-correlated to aligned.
Spearman’s ρ = 1 − 6Σdᵢ²/(n(n²−1)): rank both variables, take the per-item rank differences dᵢ, and this maps them to [−1,1]. It is Pearson correlation ON THE RANKS, so it measures MONOTONIC agreement and is robust to outliers and nonlinear-but-ordered relationships. +1 identical order, −1 reversed, 0 none. A fail-loud self-check throws unless a strictly increasing pair gives ρ=1 and a reversed pair gives ρ=−1. ◆ real statistics, node-verified.
The paired scores are interpolated for the demo; the rank-difference formula is exact (ties would need the Pearson-on-ranks form). ρ measures MONOTONE association, not agreement on absolute value — two raters can rank identically yet score on wildly different scales.