Chi-Square Goodness-of-Fit Test
The Chi-Square Goodness-of-Fit Test determines whether sample data matches a population with a specific distribution. It compares observed frequencies with expected frequencies to see if there are significant differences.
Where O is the observed frequency, E is the expected frequency, and the summation is over all categories.
Data Input
Enter your observed values and expected probabilities for each category. Probabilities must sum to 1.
Chi-Square Goodness-of-Fit Results
Chi-Square Statistic
Test statistic
P-Value
Significance level
Degrees of Freedom
(categories - 1)
Result
Hypothesis test
Interpretation
Expected Frequencies
| Category | Observed | Expected | Contribution to χ² |
|---|
Goodness-of-Fit Test Examples in Industrial Engineering
Quality Control Example
Test whether defect types follow the expected distribution.
Defect Types: Minor, Major, Critical
Observed: 50, 30, 20
Expected probabilities: 0.6, 0.3, 0.1
Machine Downtime Example
Test whether machine downtime reasons follow the expected pattern.
Reasons: Maintenance, Operator Error, Material Issue, Other
Observed: 25, 15, 30, 10
Expected probabilities: 0.3, 0.2, 0.4, 0.1
Production Output Example
Test whether production output follows the expected distribution across shifts.
Shifts: Morning, Afternoon, Night
Observed: 120, 95, 85
Expected probabilities: 0.4, 0.35, 0.25