Statistics

Chi-Square Calculator

Find the chi-square goodness-of-fit statistic.

Observed 1

Expected 1

Observed 2

Expected 2

Observed 3

Expected 3

Observed 4

Expected 4

Calculated Output

Chi-square statistic 2.72

Degrees of freedom 3

Formula: χ² = Σ (O − E)² ÷ E

Step-by-Step Breakdown

1. Values used:

2. Observed 1 = 30

3. Expected 1 = 25

4. Observed 2 = 20

5. Expected 2 = 25

6. Observed 3 = 28

7. Expected 3 = 25

8. Observed 4 = 22

9. Expected 4 = 25

10.

11. Chi-square statistic = 2.72

12. Degrees of freedom = 3

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The math behind it

χ² = Σ (O − E)² ÷ E. Compare it to the critical value for k − 1 degrees of freedom.

Observed 30/20/28/22 vs 25 each → χ² = 2.72, df 3.

When is it significant?

When χ² exceeds the critical value for your df and chosen α.