The degrees of freedom for the chi-square goodness-of-fit test are

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The degrees of freedom for the chi-square goodness-of-fit test are calculated using the formula:

$$
\text{Degrees of Freedom} = k - 1 - p
$$

where:
- $$ k $$ is the number of categories or groups in the data,
- $$ p $$ is the number of parameters estimated from the data (if any).

In many cases, if no parameters are estimated, $$ p $$ is 0, and the degrees of freedom simplify to:

$$
\text{Degrees of Freedom} = k - 1
$$

So, for a chi-square goodness-of-fit test, you typically subtract 1 from the number of categories to determine the degrees of freedom, unless you are estimating parameters from the data.
Degrees of freedom for chi-square goodness-of-fit test: $$ k - 1 $$ or $$ k - 1 - p $$ if parameters are estimated.

The degrees of freedom for the chi-square goodness-of-fit test are

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