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Free chi-square test calculator for categorical frequency analysis. Enter observed and expected values to compute chi-square statistic, degrees of freedom, estimated p-value, and hypothesis decision in seconds.
Last updated: April 20, 2026
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Chi-square statistic
2.0000
Degrees of freedom
3
Estimated p-value
0.5763
Critical value
7.815
Decision: Fail to Reject H0
Fail to reject the null hypothesis at alpha = 0.05.
Category contributions
Use Chi-square when:
Formula
χ² = Σ (O - E)² / E
Decision rule
Reject H0 if χ² > χ²critical
Insight
Per-category contribution list
Observed: [20, 30, 25, 25], Expected: [25, 25, 25, 25]
Chi-square statistic
2.0000
Degrees of freedom
3
The calculator applies the chi-square goodness-of-fit formula to each category, sums contributions, and compares the total against the critical threshold for your selected significance level.
χ² = Σ (Observed - Expected)² / ExpectedDegrees of freedom are computed as number of categories minus one (df = k - 1). The result is then used for hypothesis testing with your selected alpha level.
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