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How to Calculate Contingency Coefficient

The contingency coefficient is a statistical term for analyzing different variable categories. The coefficient number describes the distribution of the variables using a matrix format. It is sometimes called a contingency table because of the formatting. For example, contingency coefficients help to understand data when it comes in different categories such as balls that are red or blue and big or small. Each ball falls into two categories but cannot be both red and blue or big and small. The contingency coefficient resolves this data problem.

Instructions

- 1
  Map out your matrix, if possible and reasonable, as this will help you to visualize the problem set. For the sake of expediency, you can also confirm the critical data including the number of cells and number of observations.
- 2
  Apply the Phi Coefficient equation to resolve the problem. It is used in most situations where both variables are nominal. The equation is the square root of Pearson's chi squared test divided by the grand total number of observations. The formula can be represented as follows:
  
  Coefficient = (x^2 / N)^(1/2)
  
  x^2 represents the chi squared test and N represents the number of observations
- 3
  Find the result of the chi squared test. The formula is the square of the difference between observed and expected observations, divided by the expected observations. The formula is as follows:
  
  x^2 = (O - E)^2/ E
  
  O represents observed observations while E is the expected observations.
- 4
  Plug in the result from the chi squared test and the number of observations. Complete the equation and find the result.

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