This article is about **Lin’s concordance correlation coefficient**, which measures bivariate pairs of observations relative to a “gold standard” test or measurement. A similarly named statistic is the coefficient of concordance (often called the “W statistic“), which is used to assess agreement between different raters.

## What is the Concordance Correlation Coefficient?

Lin’s concordance correlation coefficient (ρ_{c}) is

**a measure of how well a set of bivariate data (Y) compares to a “gold standard” measurement or test (X).**You can also compare two sets of measurements without a gold standard comparison. In that case, the second set of measurements would be substituted for the gold standard. The procedure can be performed on data sets with ten or more pairs.

(ρ_{c})measures both precision (ρ) and accuracy (C_{β}).

- (ρ) = Pearson’s correlation coefficient,
- (C
_{Β}) = Bias correction factor, a measure of how far a line of best fit (i.e. the line of perfect concordance) is from a 45 degree angle through the origin.

## Interpretation

(ρ_{c}) ranges from 0 to ±1. Altman (1991) places the interpretation close to other correlation coefficients like Pearson’s, with <20 as “poor” and >80 as “excellent.” This interpretation is by no means set in stone; Other researchers have various interpretations. For example, McBride (2005) suggests the following guidelines for interpreting Lin’s concordance correlation coefficient:

- < 0.90: poor
- 0.90 to 0.95: moderate
- 0.95 to 0.99: substantial
- > 0.99 almost perfect.

What everyone *does *agree on is that near ±1 is perfect concordance (or perfect discordance) and 0 is no correlation; Everything in between should be interpreted with caution.

**See also**: Concordant and discordant pairs.

**References**:

Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.

Lin L.I-K (1989) A [CCC] to evaluate reproducibility. Biometrics 45:255-268

McBride GB (2005) A proposal for strength-of-agreement criteria for Lin’s concordance… NIWA Client Report: HAM2005-062.

Lin L (2000). A note on the concordance correlation coefficient. Biometrics 56: 324 – 325.

**Need help with a homework or test question?** With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. If you rather get 1:1 study help, Chegg Tutors offers 30 minutes of free tutoring to new users, so you can try them out before committing to a subscription.

If you prefer an **online interactive environment** to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

**Comments? Need to post a correction?** Please post a comment on our *Facebook page*.

Check out our updated Privacy policy and Cookie Policy