Quick Question-Degree freedom of Chi Square on Chi-Squared Test

Question

Which is right between

• $df$ of $\chi ^2$ $=k-1$

• $df$ of $\chi ^2$ $=k-3$

Answer 1

For a $\chi^{2}$ goodness of fit test, you want $df = k-1$, where $k$ is the number of groups.

For a $\chi^{2}$ two-way table set up, you want $df = (n-1)(m-1)$, where $n$ and $m$ are the dimensions of the table.