Chi-Square Test Calculator
The chi-square test compares observed counts with those expected under independence: the table (20, 30 / 30, 20) gives 4 (df = 1, p = 0.0455).
Each line is a row of the contingency table; separate columns with spaces or commas.
4 (df = 1, p = 0.0455)
- p-value
- 0.0455003
- Degrees of freedom
- 1
- Result at α = 0.05
- Significant: reject independence
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 25 | 25 |
| 2 | 25 | 25 |
Step-by-step solution
- Grand total = 100; expected Eᵢⱼ = (row total × column total) ÷ 100
- χ² = Σ (O − E)² ÷ E = 4
- df = (rows − 1)(columns − 1) = 1; p = P(χ² ≥ 4) = 0.0455003
Chi-Square Test Formula
χ² = Σ (O − E)² ÷ E
O observed count, E = row total × column total ÷ grand total; df = (r − 1)(c − 1)
Worked Example
The 2 × 2 table with rows (20, 30) and (30, 20):
- Grand total = 100; expected Eᵢⱼ = (row total × column total) ÷ 100
- χ² = Σ (O − E)² ÷ E = 4
- df = (rows − 1)(columns − 1) = 1; p = P(χ² ≥ 4) = 0.0455003
Degrees of freedom: 1 · Result at α = 0.05: Significant: reject independence
| Row | Column 1 | Column 2 |
|---|---|---|
| 1 | 25 | 25 |
| 2 | 25 | 25 |
When the chi-square test is valid
The chi-square test compares observed counts with the counts expected if the variables were independent. It needs raw counts, not percentages, and each expected count should be at least 5; otherwise merge categories or use Fisher’s exact test. Degrees of freedom are (rows − 1) × (columns − 1). A small p-value shows an association but not its strength; Cramér’s V measures that.
Frequently asked questions
When can I use the chi-square test?
For counts (not percentages) of independent observations, with expected counts of at least about 5 in most cells. For small 2 × 2 tables use Fisher’s exact test.
How do I interpret the p-value?
If p is below your significance level (usually 0.05), reject the hypothesis that the row and column variables are independent.
What about Yates’ continuity correction?
For 2 × 2 tables some textbooks subtract 0.5 from each |O − E| before squaring. This calculator gives the uncorrected Pearson χ², which is what R’s chisq.test(correct = FALSE) reports.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Chi-Square Test Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/chi-square-calculator/
IEEE
Scientific Converters, "Chi-Square Test Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/chi-square-calculator/