--- title: "Testing Genetic Ratios with Chi-squared" description: "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." canonical: https://lightmysky.com/learn/science/testing-genetic-ratios-with-chi-squared-mt_YCO6jijrNQ source: https://lightmysky.com/learn/science/testing-genetic-ratios-with-chi-squared-mt_YCO6jijrNQ.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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. Subject: Science · Area: Genetics & Evolution · Ages 17 to 18 Page: https://lightmysky.com/learn/science/testing-genetic-ratios-with-chi-squared-mt_YCO6jijrNQ ## Ready when they can - 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. ## Lesson: Testing ratios with chi-squared 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. **Tip.** 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. **Recap.** Expected counts come from the ratio, chi-squared sums each scaled squared gap, and the verdict is a decision. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Dihybrid Crosses and the 9:3:3:1 Ratio](https://lightmysky.com/learn/science/dihybrid-crosses-and-the-9-3-3-1-ratio-mt_9IlVo04Dbt) ## Opens up - [The Hardy-Weinberg Principle and Allele Frequencies](https://lightmysky.com/learn/science/the-hardy-weinberg-principle-and-allele-frequencies-mt_eJjwZ2qVAE) - [Linkage, Recombination Frequency and Genetic Maps](https://lightmysky.com/learn/science/linkage-recombination-frequency-and-genetic-maps-mt_xBjZXt3TVn)