How to apply the Chi Square Method?

Step 1: Hypotheses Formulation

• H0, Null Hypothesis: Preference for a method is not dependant on the subject taken by students.
• H1, Alternative Hypothesis: Preference for a method is dependant on the subject taken by students.

Step 2: Add numbers across columns and rows:

• Students	Preference for Lecture Method	Preference for Group Discussion Method	Total
  Mathematics	3	12	15
  Literature	5	10	15
  Total	8	22	30

Step 3: Calculate expected numbers for each cell

• 𝐸_𝑣𝑎𝑙𝑢𝑒 = (𝑅𝑜𝑤𝑆𝑢𝑚 × 𝐶𝑜𝑙𝑢𝑚𝑛𝑆𝑢𝑚) / 𝐺𝑟𝑎𝑛𝑑𝑇𝑜𝑡𝑎𝑙

• Students	Preference for Lecture Method	Preference for Group Discussion Method
  Mathematics	4	11
  Literature	4	11

Step 4: Calculate Chi square for each cell

• 𝜒^2 = (𝐸 × (𝑂−𝐸)^2) / 𝐸

• Students	Preference for Lecture Method	Preference for Group Discussion Method
  Mathematics	0.25	0.091
  Literature	0.25	0.091

Step 5: Calculate total Chi square

• 𝜒_𝑡𝑜𝑡𝑎𝑙^2 = 0.25 + 0.25 + 0.091 + 0.091 = 0.682

Step 6: Calculate degrees of freedom, df

• df = (number of rows – 1) x (number of columns – 1) = (2 – 1) x (2 – 1) = 1

Step 7: Check critical values

• Check critical value of Chi-square for df = 1 and α = 0.05.
• χ2 critical = 3.841
• χ2 total (0.682) < χ2 critical(3.841)

Step 8: Interpretation and Decision

• Because χ2 total < χ2 critical, therefore, the null hypothesis is accepted. Therefore, the preference for a method is not dependant on the subject taken by the students.