In the case of the test of independence, the number of degrees of freedom for the appropriate chi-square distribution is computed as

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The number of degrees of freedom for the test of independence is calculated using the formula df = (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. This formula takes into account the number of categories in each variable and the constraint that the row and column totals must add up to a fixed value.

In the Case of the Test of Independence, the Number