16.2.3—Chi-squared test in genetics

The chi-squared statistic compares observed and expected counts: χ² = Σ((O−E)²/E). A large value indicates a larger discrepancy, but significance is judged using degrees of freedom and a chosen probability threshold.

State the null hypothesis → calculate expected counts → compute each contribution → sum χ² → find degrees of freedom → compare with a critical value or p-value → accept or reject the null.

Random sampling alone can move counts away from the exact ratio. The test quantifies whether the deviation is compatible with chance under the assumed genetic model.

If χ² is below the critical value, there is insufficient evidence to reject the expected ratio; this does not prove the ratio is true.

Failing to reject the null is not proof of no biological difference. Check sample size, expected-count assumptions and whether the model itself is appropriate.