📊 Chi-Square Calculator
Calculate chi-square test statistics
| Col 1 | Col 2 | |
|---|---|---|
| Row 1 | ||
| Row 2 |
Chi-Square Statistic
11.6667
df = 1
Significant at α = 0.05
Step-by-step calculation
- 1.Grand total = 140
- 2.Row totals: 80, 60
- 3.Column totals: 70, 70
- 4.--- Expected values (row total × col total / grand total) ---
- 5.Row 1: 40.00, 40.00
- 6.Row 2: 30.00, 30.00
- 7.--- Chi-square contributions: (O - E)² / E ---
- 8.Cell (1,1): (50 - 40.00)² / 40.00 = 2.5000
- 9.Cell (1,2): (30 - 40.00)² / 40.00 = 2.5000
- 10.Cell (2,1): (20 - 30.00)² / 30.00 = 3.3333
- 11.Cell (2,2): (40 - 30.00)² / 30.00 = 3.3333
- 12.χ² = 11.6667
- 13.Degrees of freedom = (2 - 1) × (2 - 1) = 1
- 14.Critical value at α=0.05: 3.841
- 15.11.6667 > 3.841 → Reject H₀ at α = 0.05
How Chi-Square Testing Works
- 1Enter observed frequencies in the table cells.
- 2Enter expected frequencies (or let the tool compute them for independence tests).
- 3χ² = Σ (O−E)²/E is calculated along with degrees of freedom and the p-value.
About Chi-Square Calculator
Perform chi-square tests for independence and goodness of fit. Enter observed and expected frequencies to get the test statistic and p-value.
Frequently Asked Questions
When do I use chi-square?
Use it to test if observed categorical data differs significantly from expected values, or if two categorical variables are independent.
What are the assumptions?
Expected frequency in each cell should be at least 5, observations must be independent, and data should be counts (not percentages).