Enter the number of concordant pairs and the number of discordant pairs into the calculator to determine the Gamma Coefficient. This calculator can also evaluate any of the variables given the others are known.

## Gamma Coefficient Formula

The following formula is used to calculate the Gamma Coefficient.

GC = (Nc - Nd) / (Nc + Nd)

Variables:

- GC is the Gamma Coefficient
- Nc is the number of concordant pairs
- Nd is the number of discordant pairs

To calculate the Gamma Coefficient, subtract the number of discordant pairs from the number of concordant pairs. Then, divide the result by the sum of the number of concordant pairs and the number of discordant pairs. The resulting value will range from -1 to 1, indicating the strength and direction of the relationship between the two ordinal variables.

## What is a Gamma Coefficient?

A Gamma Coefficient, also known as Goodman and Kruskal’s gamma, is a statistical measure used to determine the strength and direction of association between two ordinal variables. It ranges from -1 to 1, where -1 indicates a perfect negative relationship, 1 indicates a perfect positive relationship, and 0 indicates no relationship. It is particularly useful when dealing with non-parametric or non-normal data.

## How to Calculate Gamma Coefficient?

The following steps outline how to calculate the Gamma Coefficient.

- First, determine the number of concordant pairs (Nc).
- Next, determine the number of discordant pairs (Nd).
- Next, gather the formula from above = GC = (Nc – Nd) / (Nc + Nd).
- Finally, calculate the Gamma Coefficient.
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Number of concordant pairs (Nc) = 50

Number of discordant pairs (Nd) = 20