Chi-Square Goodness-of-Fit
χ² = Σ(O−E)²/E. Test if observed frequencies match expected.
Result
χ²
1.0000
df = 3; rough p ≈ 0.6065.
- Categories4
- Observed50, 55, 45, 50
- Expected50, 50, 50, 50
- χ²1.000000
- df3
- Critical χ² (α=0.05)7.81
- Reject H₀?✗ No
Step-by-step
- χ² = Σ (O − E)² / E.
- Compute term-by-term, sum.
- Compare to χ² critical at df = 3.
How to use this calculator
- Enter observed counts + expected counts.
About this calculator
Chi-square goodness-of-fit test: do observed counts match expected? χ² = Σ(O−E)²/E. Larger = bigger discrepancy. Compare to χ² distribution at df = (categories − 1). Common use: testing if data follows hypothesized distribution (uniform, normal, Poisson). Sample size requirement: each expected ≥ 5 for good approximation. Source: Pearson (1900); NIST Engineering Statistics Handbook.
Frequently asked
Goodness-of-fit: 1 categorical variable vs. expected. Independence: 2 categorical variables tested for relationship.
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