To run a Chi-Squared Test for Independence in real-life situations, here's a simple guide to follow:

1. Set Up Your Hypotheses:

   • Null Hypothesis ($H_0$): This means the two groups you are looking at are not connected or related.
   • Alternative Hypothesis ($H_a$): This means the two groups are connected or related in some way.

2. Gather Your Data:

   • Put your data into a table called a contingency table.
   • This table should show how often things happen for each group you are studying.

3. Calculate Expected Frequencies:

   • For each box in the table, figure out how many occurrences we would expect to see, using this formula:
   • $E_{ij} = \frac{(Row \, Total_i)(Column \, Total_j)}{Grand \, Total}$

4. Compute Chi-Squared Value:

   • To find the Chi-Squared statistic, use this formula:
   • $\chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}$
   • Here, $O_{ij}$ stands for the actual counts you collected.

5. Determine Degrees of Freedom:

   • Calculate degrees of freedom using this formula:
   • $df = (r - 1)(c - 1)$
   • Here, $r$ is the number of rows in your table and $c$ is the number of columns.

6. Find the Critical Value:

   • Look in a Chi-Squared distribution table to find the critical value at your chosen level of significance (for example, $\alpha = 0.05$).

7. Make Your Decision:

   • If your Chi-Squared value ($\chi^2$) is greater than the critical value, reject the null hypothesis ($H_0$).
   • If the Chi-Squared value is less than or equal to the critical value, you do not reject the null hypothesis.

8. Conclude Your Findings:

   • Wrap up your results by explaining whether the two groups are independent or dependent. Also, include the p-value where it makes sense.