How to Calculate Chi-Square Test
What is Chi-Square Test?
The chi-square (χ²) test compares observed counts to expected counts to determine whether a categorical distribution differs from what is expected. Common uses: genetics ratios, goodness of fit, independence testing.
Step-by-Step Guide
- 1χ² = Σ (O − E)² / E
- 2O = observed · E = expected
- 3df = categories − 1 (goodness of fit)
- 4Large χ² → observed differs significantly from expected
Worked Examples
Input
Observed: 50, 30, 20 · Expected: 40, 35, 25
Result
χ² = 5.05 · df=2 · critical value 5.99 at p<0.05
χ² < critical → fail to reject H₀
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