5. How to Do a Chi-Squared Goodness of Fit Test: A Simple Guide

Doing a Chi-Squared Goodness of Fit Test can be tricky and has lots of chances for mistakes. Let’s make it easier to understand with simple steps:

1. Make Hypotheses:

   • Null Hypothesis ($H_0$): This means the data you have matches what you expected.
   • Alternative Hypothesis ($H_a$): This means the data you have does not match what you expected.

2. Collect Your Data:

   • Gather the data from your sample.
   • Be careful here. If you don’t collect your data well, it might not be accurate.

3. Find Expected Frequencies:

   • Work out what the expected data should look like based on the null hypothesis.
   • This part can get tricky if your data is uneven.

4. Calculate the Chi-Squared Statistic:

   • Use this formula to make your calculation:
   $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$
   • Here, $O_i$ is the observed frequency (what you collected), and $E_i$ is the expected frequency (what you calculated).
   • Mistakes can happen here, so be careful.

5. Find Degrees of Freedom:

   • Calculate this using the formula $df = k - 1$
   • Here, $k$ is the number of categories.
   • People often mess this up, so double-check your count.

6. Compare Your Results:

   • Look at a Chi-Squared distribution table to see if your statistic is bigger than the critical value.
   • Misreading the table can lead to wrong answers.

Even though this process can be hard, taking your time and checking your math can help you make fewer mistakes and get better results.