Lin’s Concordance Correlation Coefficient (CCC): Precision vs. 45-Degree Accuracy

Why Pearson CORREL = 1.00 fails to detect systematic calibration offset or scale drift

Pearson’s correlation coefficient r = CORREL(X, Y) measures tightness around ANY straight line Y = a + b*X, making it completely blind to additive calibration bias (a != 0) and multiplicative scale drift (b != 1). If a new blood-glucose analyzer reads +5 mg/dL high on every single specimen, CORREL(X, Y) still reports a misleading 1.0000.

Lawrence Lin’s (1989) Concordance Correlation Coefficient penalizes departures from the 45-degree identity line Y = X: rho_c = (2 * cov_p) / (var_p(X) + var_p(Y) + (mean_X - mean_Y)^2). Algebraically, rho_c factors into Precision (Pearson r) times Accuracy (C_b = rho_c / r in (0, 1]), immediately diagnosing whether disagreement stems from random noise (low r) or calibration shift (low C_b).

Exact Lin’s CCC Formula via LET & SUMPRODUCT

Compute population means, population variances VARP, and population covariance SUMPRODUCT((X - mx) * (Y - my)) / N inside LET so numerator and denominator share the exact 1/N normalization.

=LET(cnt, COUNT(B2:B6), mx, AVERAGE(B2:B6), my, AVERAGE(C2:C6), vx, VARP(B2:B6), vy, VARP(C2:C6), cov_xy, SUMPRODUCT((B2:B6 - mx) * (C2:C6 - my)) / cnt, ROUND((2 * cov_xy) / (vx + vy + (mx - my) ^ 2), 4))

Accuracy Factor C_b Decomposition

Divide unrounded CCC by CORREL(B2:B6, C2:C6) (guarded for r = 0) to isolate systematic location + scale bias from random scatter.

=IF(F2 = 0, 0, ROUND(F3 / F2, 4))

Further reading

• Lin, L. I.-K. (1989) — A Concordance Correlation Coefficient to Evaluate Reproducibility, Biometrics