Chi-Square Calculator
Perform chi-square goodness of fit tests to determine if observed data matches expected distributions
Chi-Square Test Calculator
Data Input
| Category | Observed Value | Expected Value | χ² Component | Actions |
|---|---|---|---|---|
| Category 1 | — | |||
| Category 2 | — |
Risk of rejecting true null hypothesis
Leave blank to use standard table values
Chi-Square Test Results
Test Conclusion
Enter data to perform the test
Formula: χ² = Σ[(Observed - Expected)² / Expected]
Calculation: χ² = 0.0000 + 0.0000 = 0.0000
Degrees of Freedom: df = k - 1 = 2 - 1 = 0
Chi-Square Test Assumptions
Example: Student Grade Distribution
Scenario
A teacher expects grade distribution: 15% grade 5, 40% grade 4, 30% grade 3, 15% grade 2
Sample: 60 students
Expected: Grade 2: 9, Grade 3: 18, Grade 4: 24, Grade 5: 9
Observed: Grade 2: 7, Grade 3: 26, Grade 4: 22, Grade 5: 5
Calculation
χ² = (7-9)²/9 + (26-18)²/18 + (22-24)²/24 + (5-9)²/9
χ² = 0.444 + 3.556 + 0.167 + 1.778
χ² = 5.945, df = 3
Critical value (α = 0.05): 7.815
Conclusion: Fail to reject H₀ (5.945 < 7.815)
Critical Values Table
| df | 0.10 | 0.05 | 0.01 |
|---|---|---|---|
| 1 | 2.706 | 3.841 | 6.635 |
| 2 | 4.605 | 5.991 | 9.210 |
| 3 | 6.251 | 7.815 | 11.345 |
| 4 | 7.779 | 9.488 | 13.277 |
| 5 | 9.236 | 11.070 | 15.086 |
Reject H₀ if χ² > critical value
Chi-Square Test Types
Goodness of Fit
Tests if observed data matches expected distribution
Independence
Tests if two categorical variables are independent
Homogeneity
Tests if multiple populations have same distribution
Quick Tips
Ensure all expected frequencies are ≥ 5
Higher χ² values indicate greater deviation
Use continuity correction for small samples
Check independence assumption carefully
Understanding the Chi-Square Test
What is the Chi-Square Test?
The chi-square test is a statistical test used to determine whether observed data differs significantly from expected data. It's commonly used for goodness of fit tests to check if sample data matches a theoretical distribution.
When to Use Chi-Square Test?
- •Testing if data follows a specific distribution
- •Comparing observed vs expected frequencies
- •Categorical data analysis
- •Quality control and process monitoring
Test Formula
χ² = Σ[(Observed - Expected)² / Expected]
- χ²: Chi-square test statistic
- Observed: Actual frequency in each category
- Expected: Theoretical frequency in each category
- Σ: Sum across all categories
Decision Rule
Reject H₀ if: χ² > Critical Value
Fail to reject H₀ if: χ² ≤ Critical Value