Diagnostics › Agreement

Lin's concordance correlation (CCC)

Lin's concordance correlation coefficient adjusts Pearson r for shifts in location and scale, reaching 1 only when two methods agree exactly.

What is Lin's concordance correlation (CCC)?

Pearson r tells you whether two methods rank subjects the same way. CCC tells you whether they *agree* — same value, not just same rank order. CCC = r · Cb, where Cb is a bias-correction factor capturing how far the (mean₁, mean₂) and (SD₁, SD₂) pairs depart from (mean, mean) and (SD, SD).

Two methods can have r = 1 (perfectly correlated) and CCC = 0 (totally different scales). CCC catches the failure mode that correlation misses.

When should I use Lin's concordance correlation (CCC)?

  • Method comparison where you need a single agreement number.
  • Alternative to ICC(2, 1) for two-method studies.

What data does it need?

Two numeric columns measuring the same quantity.

What does it report?

CCC + 95% Fisher-z CI, Pearson r, bias correction Cb, per-method means / SDs.

What does it assume?

  • Independent paired observations.
  • Approximately bivariate normal (for the CI).

Formula

CCC = 2·s_xy / (s_x² + s_y² + (x̄ − ȳ)²)

How do I interpret the result?

CCC > 0.99 substantial agreement; 0.95–0.99 moderate; < 0.90 poor (McBride 2005 anchors).

See also

References

  • Lin (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45(1).