Easy Steps for Understanding Chi-Square Test Results:

1. Make Hypotheses:

   • Null hypothesis ($H_0$): The two variables have no connection.
   • Alternative hypothesis ($H_a$): The two variables are connected.

2. Calculate the Chi-Square Value:

   • Use this equation:
   $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$

   Here, $O_i$ means what we actually counted, and $E_i$ is what we expected to count.

3. Find the Degrees of Freedom:

   • For checking connection: $(number of rows - 1)(number of columns - 1)$.
   • For testing fit: $k - 1$ (where $k$ is the number of groups).

4. Get the p-value:

   • Check your calculated $\chi^2$ against a key value from the Chi-Square table.

5. Make a Choice:

   • If $p \leq \alpha$ (usually 0.05), then reject $H_0$; if not, keep $H_0$.

6. Explain the Results:

   • Share if there’s a strong link and think about what this means for the group you studied.