Testing Genetic Ratios with Chi-squared
Observed offspring counts never match a predicted ratio exactly, 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.
1 · Read
Real offspring counts never land exactly on a predicted ratio, so you need a referee. The chi-squared goodness of fit test is that referee for one cross with one set of counts. It asks a single question: is the gap between your observed and predicted counts bigger than chance alone 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 fractions are ninths style shares of sixteen: 9 of 16, 3 of 16, 3 of 16 and 1 of 16.
Next build the statistic. For each class, square the gap between observed and expected, divide by the expected, then add the results up. Say a class shows 110 against 100 expected: the gap is 10, squared is 100, divided by 100 is 1. Compare the total with the critical value at the right degrees of freedom, which is categories minus one: a two class 3:1 test runs on one, and a four class 9:3:3:1 test runs on three.
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 for this sample size, 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.
2 · Watch
Take it off screen
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.