Enter the Chi-square statistic and total number of observations into the calculator to determine the Contingency Coefficient. This calculator can also evaluate any of the variables given the others are known.

Contingency Coefficient Formula

The following formula is used to calculate the Contingency Coefficient.

C = sqrt((Chi^2) / (n + (Chi^2)))


  • C is the Contingency Coefficient
  • Chi is the Chi-square statistic
  • n is the total number of observations

To calculate the Contingency Coefficient, square the Chi-square statistic. Divide this result by the sum of the total number of observations and the squared Chi-square statistic. Finally, take the square root of the quotient to get the Contingency Coefficient.

What is a Contingency Coefficient?

A Contingency Coefficient is a statistical measure used to determine the degree of association or dependency between two categorical variables. It ranges from 0 to 1, where 0 indicates no association and 1 indicates a strong association. This coefficient is based on the Chi-square statistic and is used in contingency table analysis, which is a type of non-parametric method used in statistics.

How to Calculate Contingency Coefficient?

The following steps outline how to calculate the Contingency Coefficient.

  1. First, determine the value of the Chi-square statistic (Chi).
  2. Next, determine the total number of observations (n).
  3. Next, gather the formula from above = C = sqrt((Chi^2) / (n + (Chi^2))).
  4. Finally, calculate the Contingency Coefficient.
  5. 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.

Chi-square statistic (Chi) = 25

Total number of observations (n) = 100