Editverse Free Calculator
Concordance Correlation Calculator (Lin’s CCC)
Quantify agreement between two methods on a continuous scale in a single index — Lin’s concordance correlation coefficient, which rewards closeness to the 45-degree line of identity — with the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
Lin’s concordance correlation coefficient (CCC) measures how closely paired measurements fall on the 45-degree line through the origin — the line of perfect agreement. Unlike Pearson’s correlation, which only checks whether points lie on any straight line, the CCC penalises both scatter and any systematic shift away from identity.
The CCC combines two parts: how tightly the points cluster around a line (precision) and how close that line is to the line of identity (accuracy). It ranges from −1 to 1, where 1 means perfect agreement. This makes it a single-number summary of agreement, complementing the visual detail of a Bland-Altman plot.
When to Use Lin’s CCC
Use the CCC when you want one number summarising agreement between two continuous methods, raters, or assays — for example, in method-validation or reproducibility studies. It is the agreement analogue of a correlation coefficient, corrected for systematic bias.
Report the CCC alongside a Bland-Altman plot, since the coefficient summarises agreement while the plot reveals its pattern across the range. For more than two raters or repeated measures, the intraclass correlation coefficient is the broader tool, and a plain correlation should never be mistaken for agreement. Unsure which fits? Our Test Selector can help.
Expected: 2 columns: Method A values | Method B values
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: 2 columns: Method A values | Method B values
x <- c({x})
y <- c({y})
n <- length(x)
sx <- mean((x-mean(x))^2); sy <- mean((y-mean(y))^2); sxy <- mean((x-mean(x))*(y-mean(y)))
ccc <- 2*sxy/(sx+sy+(mean(x)-mean(y))^2)
ccc
cor(x, y) # precision; Cb = ccc / r (accuracy)User guide
When to use. Quantify agreement (not just correlation) between two methods measuring the same continuous quantity.
Assumptions. Paired measurements on the same subjects; approximately bivariate-normal for the Fisher-z confidence interval; a reasonably wide range of values.
Common mistakes. Do not use Pearson r alone to claim agreement. With very small samples the confidence interval is unreliable; add a Bland-Altman plot.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Lin LI. A concordance correlation coefficient to evaluate reproducibility. Biometrics. 1989;45(1):255-268.
- McBride GB. A proposal for strength-of-agreement criteria for Lin’s concordance correlation coefficient. NIWA Client Report HAM2005-062. 2005.
Worked Examples
Example 1 — Strong concordance
Two assays give very similar values across the range. The CCC is about 0.97, with high precision (tight scatter) and high accuracy (the fitted line sits almost on the line of identity). The methods agree well enough to be treated as interchangeable.
Example 2 — Good correlation, lower CCC
Two methods correlate at r = 0.98 but one runs systematically high. Pearson’s r stays near 0.98, yet the CCC drops to perhaps 0.80 because the points sit on a line parallel to, but offset from, the line of identity — the offset is exactly what the CCC penalises.
Assumptions to Check
Paired continuous measurements. The CCC compares two readings of the same quantity on the same scale for each subject.
A meaningful line of identity. Because the CCC measures closeness to the 45-degree line, the two methods must be on the same units and scale for the index to be interpretable.
Adequate range and sample. A narrow measurement range or very few pairs makes the CCC unstable; report its confidence interval.
Common Mistakes
Treating the CCC like Pearson’s r
Pearson’s r ignores systematic bias; the CCC does not. A high r with a lower CCC signals a real offset between the methods.
Reporting the CCC without a plot
The single number hides the pattern of disagreement. Pair it with a Bland-Altman plot to see where and how the methods diverge.
Comparing methods on different scales
The CCC is anchored to the line of identity, so it is only meaningful when both methods share the same units and scale.
Ignoring the confidence interval
With small samples the CCC point estimate is imprecise; always report its interval so readers can judge the strength of the evidence.
Frequently Asked Questions
How is the CCC different from Pearson’s r?
Pearson’s r measures clustering around any line; the CCC measures clustering around the line of identity, so it penalises systematic bias that r ignores.
What is a good CCC value?
Higher is better, with values approaching 1 indicating strong agreement, but the adequate level depends on the clinical or analytical context.
Should I report a Bland-Altman plot too?
Yes. The CCC summarises agreement in one number, while the Bland-Altman plot shows the bias and how agreement varies across the measurement range.
Does the result match R?
Yes. The calculator uses Lin’s standard formula combining precision and accuracy and shows the R command (epiR or DescTools) so you can reproduce the coefficient.
Related Calculators
References
- Lin LI. A concordance correlation coefficient to evaluate reproducibility. Biometrics. 1989;45(1):255–268. PMID 2720055.
- Barnhart HX, Williamson JM. Modeling concordance correlation via GEE to evaluate reproducibility. Biometrics. 2001;57(3):931–940. PMID 11550947.
- Lin LI. A note on the concordance correlation coefficient. Biometrics. 2000;56(1):324–325.
Need This Analysis Done for Your Manuscript?
Our PhD biostatisticians quantify agreement and reproducibility — Lin’s CCC with confidence intervals alongside Bland-Altman analysis — with reproducible R output.