## Theory-Based Approach

The key advantage of the chi-square statistic is that, under certain validity conditions, the null distribution is well modelled by a mathematical model called the *chi-square distribution*. The degrees of freedom for the appropriate chi-square distribution equal (# rows-1) x (# columns -1), using the number of rows and columns from the original two-way table. We will consider this approximation reasonable as long as we have at least 10 observations in each cell of our two-way table (see Chapter 8 for more details).

(n) Calculate the degrees of freedom for our table. [On the left, check the box that says **Show X ^{2} output** to confirm your calculation of the df, but make sure you verify how it is being calculated for this study.]

(o) Now check the box to also **Overlay** the theoretical chi-square distribution on your simulated null distribution. Does the theoretical model appear to reasonably describe the behavior of the null distribution? Does the p-value from the theoretical distribution appear to be similar to the p-value you estimated from the simulation?

(p) Provide a detailed *interpretation* of this p-value: It's the percentage of what's that do what assuming what?