# Chi Square Method - Numerical

The numerical below is an example of calculations carried out in the Chi Square Method. This approach can be extended to similar cases by replacing the data.

## A research was carried out in which the students of mathematics and literature were asked to express their preference for lecture method and group discussion method. The data obtained is given below. Find out whether the preference for a method is dependent on the subject taken by the students.

 Students Preference for Lecture Method Preference for Group Discussion Method Mathematics 3 12 Literature 5 10

### 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.

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IGNOU Solved Assignments: Q8 - MAPC MPC006 Statistics in Psychology - MPC006/ASST/TMA/2014-15