Chi-square goodness-of-fit calculator
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Result
χ²4.32
Degrees of freedom3
p-value0.2289
Critical value7.815
Decisiondo not reject H₀
Step-by-step solution
Contributions (O − E)²/E
(18 − 25)²/25 = 1.96
(22 − 25)²/25 = 0.36
(30 − 25)²/25 = 1
(30 − 25)²/25 = 1
Sum
χ² = 4.32, df = k − 1 = 3
Decision
p = P(χ²(3) ≥ 4.32) = 0.2289
Critical value (α = 0.05): χ²crit = 7.815
χ² = 4.32 ≤ 7.815 → do not reject H₀: the difference can be explained by chance.
Key formulas
- Test statistic
- χ² = Σ(O − E)²/E
- Goodness of fit
- E = n·p, df = k − 1 − (estimated parameters)
- Independence
- E = row total × column total / grand total, df = (r − 1)(c − 1)
- Critical values (α = 0.05)
- df 1: 3.841, 2: 5.991, 3: 7.815, 4: 9.488
- Decision
- reject H0 if χ² > χ²crit
Practise Chi-square tests
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.
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