📊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.
- 1χ² = Σ (O − E)² / E
- 2O = observed · E = expected
- 3df = categories − 1 (goodness of fit)
- 4Large χ² → observed differs significantly from expected
Observed: 50, 30, 20 · Expected: 40, 35, 25=χ² = 5.05 · df=2 · critical value 5.99 at p<0.05χ² < critical → fail to reject H₀
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Fun Fact
Karl Pearson developed the chi-square test in 1900 — making it one of the oldest still-used statistical tests.
References
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