For a goodness-of-fit test for a distribution with 5 categories, what are the degrees of freedom for the $\chi^{2}$ distribution for this test? degrees of freedom = x

Step 1 ：The degrees of freedom for a goodness-of-fit test is calculated as the number of categories minus 1.

Step 2 ：In this case, we have 5 categories.

Step 3 ：So, the degrees of freedom would be 5 - 1 = 4.

Step 4 ：Final Answer: The degrees of freedom for the \(\chi^{2}\) distribution for this test is \(\boxed{4}\).