Testing Genetic Ratios with Chi-squared
Observed offspring counts can match a predicted ratio exactly by chance, so chi-squared measures whether the gap is bigger than chance would give. The test hands back a decision, not a proof.
What a learner can do afterwards
- Calculates expected counts from a predicted ratio and a total.
- Works out the chi-squared value and compares it with the critical value at the right degrees of freedom.
- States what accepting or rejecting the null hypothesis means for the cross.
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Real offspring counts can match a predicted ratio exactly by chance, so you still need a referee. The chi-squared goodness of fit test covers one cross and one set of counts. It asks one question: is the gap between observed and predicted counts bigger than chance would deal. The predicted Mendelian ratio, such as 3:1 or 9:3:3:1, is the null hypothesis you test.
Start by turning the ratio into expected counts. Multiply the total offspring by each ratio fraction. With 160 offspring and a 3:1 ratio, expect one quarter recessive, which is 40, and three quarters dominant, which is 120. With a 9:3:3:1 ratio the shares of 16 are 9, 3, 3 and 1.
Next build the statistic. For each class, square the gap, divide by the expected, then add up. Say a class shows 110 against 100 expected: that class contributes 1. Compare the total with the critical value at the right degrees of freedom, which is categories minus one. Past the critical value, reject the ratio; below it, keep the ratio as plausible but unproved.
Read the verdict like a judge, not a prover. A large statistic with a tiny p value rejects the predicted ratio, since chance would rarely deal such a gap. A small statistic keeps the ratio as plausible, but never proves it true. The test hands back a decision, not a proof.
Expected counts come from the ratio, chi-squared sums each scaled squared gap, and the verdict is a decision.
Two readings written for this topic. Videos by Khan Academy on YouTube; viewing follows platform terms.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.