# Concordant Pairs and Discordant Pairs

Statistics Definitions > Concordant Pairs and Discordant Pairs

## What are Concordant Pairs and Discordant Pairs?

Concordant pairs and discordant pairs refer to comparing two pairs of data points to see if they “match.” The meaning is slightly different depending on if you are finding these pairs from various coefficients (like Kendall’s Tau) or if you are performing experimental studies and clinical trials.

## 1. In Coefficient Calculations

Concordant pairs and discordant pairs are used in Kendall’s Tau, for Goodman and Kruskal’s Gamma and in Logistic Regression. They are calculated for ordinal (ordered) variables and tell you if there is agreement (or disagreement) between scores. To calculate concordance or discordance, your data must be ordered and placed into pairs.

## Example of Tied, Concordant and Discordant Pairs

Let’s say you had two interviewers rate a group of twelve job applicants:

Note that in the first column, interviewer 1’s choices have been ordered from smallest to greatest. That way, a comparison can be made between the choices for interviewer 1 and 2. With concordant or discordant pairs, you’re basically answering the question: did the judges/raters rank the pairs in the same order? You aren’t necessarily looking for the exact same rank, but rather if one job seeker was consistently ranked higher by both interviewers.

Three possible scenarios are possible for these ordered pairs:

• Tied pairs: both interviewers agree. For example, candidate A was marked as a 1st choice for both interviewers, so they are tied.
• Concordant pairs: both interviewers rank both applicants in the same order — that is, they both move in the same direction. While they aren’t the same rank (i.e. both 1st or both 2nd), each pair is ordered equally higher or equally lower. Interviewer 1 ranked F as 6th and G as 7th, while interviewer 2 ranked F as 5th and G as 8th. F and G are concordant because F was consistently ranked higher than G.
• Discordant pairs: Candidates E and F are discordant because the interviewers ranked in opposite directions (one said E had a higher rank than F, while the other said F ranked higher than 6).

## 2. In Experimental Studies and Clinical Trials

The term “concordant pair” is sometimes used (i.e. in case control studies) to mean a pair who are both exposed (or both not exposed) to some factor. In other words, it is based on exposure status. In a matched pairs design, a concordant pair means that the exposure status of one case is the same as a control case.

Reference:
Pennsylvania State University. Epidemiological Research Methods.

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