The more categories you have, the larger the chi-square you need for significance. You don't always have 2 groups. If you did ethnic identity in our example, you could have 5 or 6. You can have more than 2 categories.

What about goodness-of-fit? Now that we explained it, this particular chi-square is sometimes called the goodness-of-fit test. We tested whether our "Observed" frequencies "fit" against our "Expected” frequencies.