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### Chi-Square Tests: One Way and Two Way

• For a goodness of fit test, the degrees of freedom are ν = k − 1 where

• k is the number of “groups.” This is always a right-tailed test.

• For a test of independence, the degrees of freedom are ν = (R − 1)(C − 1) where R are the number of rows in the contingency table and C are the number of columns in the contingency table. The null hypothesis is always that the two attributes are independent.

• For a test of homogeneity, the degrees of freedom are ν = (R − 1)(C −1) where R are the number of rows in the contingency table and C are the number of columns in the contingency table. The null hypothesis is always that the two or more populations are the same.

## Chi-Square Tests: One Way and Two Way

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