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.
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Contingency Coefficient Formula
C = \sqrt{\frac{\chi^2}{n + \chi^2}}Variables:
- C is the Contingency Coefficient
- Chi is the Chi-square statistic (χ²)
- n is the total number of observations
To calculate the Contingency Coefficient, divide the Chi-square statistic (χ²) by the sum of the total number of observations (n) and the Chi-square statistic (χ²). Finally, take the square root of the quotient to get the Contingency Coefficient.
What is a Contingency Coefficient?
A Contingency Coefficient (Pearson’s contingency coefficient) is a statistical measure used to describe the degree of association between two categorical variables in a contingency table. It ranges from 0 (no association) up to a maximum value that is less than 1, and that maximum depends on the size of the table (it increases as the table gets larger).
How to Calculate Contingency Coefficient?
The following steps outline how to calculate the Contingency Coefficient.
- First, determine the value of the Chi-square statistic (Chi).
- Next, determine the total number of observations (n).
- Next, gather the formula from above = C = sqrt(Chi / (n + Chi)).
- Finally, calculate the Contingency 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.
Chi-square statistic (Chi) = 25
Total number of observations (n) = 100
Contingency Coefficient (C) = √(25 / (100 + 25)) = √(0.2) = 0.4472
