Chi-square Test of Independence
Calculating the Chi-square value for the association between Gender and Opinion.
Observed Data
| Gender | Agree | Uncertain | Disagree | Row Total |
|---|---|---|---|---|
| Male | 60 | 20 | 15 | 95 |
| Female | 70 | 40 | 10 | 120 |
| Column Total | 130 | 60 | 25 | 215 |
Step 1: Hypotheses
Null Hypothesis (H₀): Gender and opinion are independent (no association).
Alternative Hypothesis (H₁): Gender and opinion are not independent (there is an association).
Step 2: Expected Frequencies
Expected frequency formula: Eij = (Row Totali × Column Totalj) / Grand Total
Grand Total = 215
| Gender | Agree | Uncertain | Disagree |
|---|---|---|---|
| Male | 57.44 | 26.51 | 11.05 |
| Female | 72.56 | 33.49 | 13.95 |
Step 3: Chi-square Statistic
Formula: χ² = Σ [(Oij - Eij)² / Eij]
Male, Agree: (60 - 57.44)² / 57.44 = 0.1141
Male, Uncertain: (20 - 26.51)² / 26.51 = 1.5986
Male, Disagree: (15 - 11.05)² / 11.05 = 1.4118
Female, Agree: (70 - 72.56)² / 72.56 = 0.0903
Female, Uncertain: (40 - 33.49)² / 33.49 = 1.2654
Female, Disagree: (10 - 13.95)² / 13.95 = 1.1184
Total χ² = 0.1141 + 1.5986 + 1.4118 + 0.0903 + 1.2654 + 1.1184 = 5.5986
Step 4: Degrees of Freedom
df = (rows - 1) × (columns - 1) = (2 - 1) × (3 - 1) = 2
Step 5: Interpretation
Chi-square value: 5.60 (rounded to two decimal places)
Critical value (α = 0.05, df = 2): 5.991
Since 5.60 < 5.991, we fail to reject the null hypothesis, suggesting no significant association between gender and opinion.
Final Answer
The Chi-square value is 5.60.