Chi-Square Test of Independence
The Chi-Square Test of Independence determines whether there is a significant association between two categorical variables. It compares the observed frequencies in each category to the frequencies we would expect if the variables were independent.
Where O is the observed frequency, E is the expected frequency, and the summation is over all cells in the contingency table.
Contingency Table Input
Enter your observed values in the table below. You can add more rows and columns as needed.
| Column 1 | Column 2 | Column 3 | |
|---|---|---|---|
| Row 1 | |||
| Row 2 | |||
| Row 3 |
Chi-Square Test Results
Chi-Square Statistic
Test statistic
P-Value
Significance level
Degrees of Freedom
(rows - 1) × (columns - 1)
Result
Hypothesis test
Interpretation
Expected Frequencies
| Column 1 | Column 2 | Column 3 |
|---|
Chi-Square Test Examples in Industrial Engineering
Quality Control Example
Test whether defect rates are independent of production shifts.
Shifts: Morning, Afternoon, Night
Defect Types: Minor, Major, Critical
Example data:
| Minor | Major | Critical | |
|---|---|---|---|
| Morning | 15 | 8 | 2 |
| Afternoon | 12 | 10 | 4 |
| Night | 18 | 14 | 7 |
Supplier Evaluation Example
Test whether product quality is independent of suppliers.
Suppliers: A, B, C
Quality Levels: Excellent, Good, Fair, Poor
Example data:
| Excellent | Good | Fair | Poor | |
|---|---|---|---|---|
| Supplier A | 25 | 40 | 20 | 5 |
| Supplier B | 30 | 35 | 25 | 10 |
| Supplier C | 20 | 30 | 35 | 15 |
Machine Performance Example
Test whether machine performance is independent of maintenance schedule.
Maintenance: Weekly, Bi-weekly, Monthly
Performance: Optimal, Acceptable, Needs Attention
Example data:
| Optimal | Acceptable | Needs Attention | |
|---|---|---|---|
| Weekly | 18 | 10 | 2 |
| Bi-weekly | 12 | 15 | 8 |
| Monthly | 5 | 12 | 13 |