# Methods and formulas for measures of association

This content applies to the following tools in Minitab:
• Fit Binary Logistic Model
• Analyze Binary Response for Definitive Screening Design
• Analyze Binary Response for Factorial Design
• Analyze Binary Response for Response Surface Design

Concordant and discordant pairs indicate how well your model predicts data. The more concordant pairs you have, the better your model's predictive ability.

The table of concordant, discordant, and tied pairs is calculated by forming all possible pairs of observations with different response values. Suppose the response values are 1 and 0. Minitab pairs every observation with response value 1 with every observation with response value of 0. The total number of pairs equals the number of observations with response of 1 multiplied by the number of observations with the response of 0.

To determine whether the pairs are concordant or discordant, Minitab calculates the predicted probabilities of each observation and compares these values for each pair of observations.

Concordant pairs
A pair of observations is concordant if the observation with the observed response value of 1 has a higher predicted probability of being 1, than the observation with the observed response of 0.
Discordant pairs
A pair of observations is discordant if the observation with the observed response value of 1 has a lower predicted probability of being 1, than the observation with the observed response of 0.
Ties
A pair is tied if the observations have equal predicted probabilities.

## Formula

From the table of concordant, discordant, and tied pairs, Minitab calculates the following summary measures:

## Notation

TermDescription
nc number of concordant pairs
nd number of discordant pairs
nt number of tied pairs
N total number of observations
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