AGRI10051 Chap.8 Chi-Square Testing of Genetic Hypotheses in the Practicals
Chi-Square Testing of Genetic Hypotheses in the Practicals
Use chi-square to ask whether genetic counts depart from a stated model by more than sampling variation would plausibly explain. The chapter walks from expected ratios and counts through contributions, degrees of freedom and decision language, with a full return to biological assumptions. You will learn why ‘fail to reject’ is useful but never proves the model true.
What this chapter covers
- 01
Chi-square asks whether deviations are larger than sampling predicts: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 02
Model before statistic: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 03
Write the genetic model in words before symbols: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 04
The model bundle: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 05
Directional alternatives: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 06
Use a limited conclusion: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 07
Scale every probability by the same total N: use the chapter explanation to connect mechanism, model, evidence and limitation.
- 08
Expected-count adequacy: use the chapter explanation to connect mechanism, model, evidence and limitation.
Chi-square asks whether deviations are larger than sampling predicts
- +1EX 8.1 Test a 3:1 segregation model Question. A selfed heterozygous plant produces 118 dominant and 42 recessive progeny. Test a 3:1 phenotype expectation at the 5% threshold.
- +2N = 160, so expected counts are 120 dominant and 40 recessive. Contributions are (118−120)²/120 = 4/120 = 0.0333 and (42−40)²/40 = 4/40 = 0.1000. Thus χ² = 0.1333 .
- +3With two fixed classes, df = 2−1 = 1 . This statistic is far below the usual 5% critical value for df 1, so we fail to reject the 3:1 null. The modest deviation is compatible with sampling under the model.
- +4This does not prove the cross assumptions true; it says these counts provide no strong evidence against them.
Key terms
- null hypothesis
- The stated genetic model under which differences between observed and expected counts are attributed to sampling variation.
- fail to reject
- This chapter expands that sequence and uses cautious decision language: reject or fail to reject , rather than treating a non-significant result as proof that the model is true.
- Model solution
- A key chapter term that must be defined in relation to the stated genetic model and evidence.
- Observed evidence
- In Chi-Square Testing of Genetic Hypotheses in the Practicals, this is made explicit so a reader can trace the conclusion back through the chapter’s mechanism, working and evidence.
- Biological interpretation
- In Chi-Square Testing of Genetic Hypotheses in the Practicals, this is made explicit so a reader can trace the conclusion back through the chapter’s mechanism, working and evidence.
- Limitation
- In Chi-Square Testing of Genetic Hypotheses in the Practicals, this is made explicit so a reader can trace the conclusion back through the chapter’s mechanism, working and evidence.
- Validation
- In Chi-Square Testing of Genetic Hypotheses in the Practicals, this is made explicit so a reader can trace the conclusion back through the chapter’s mechanism, working and evidence.
Chi-Square Testing of Genetic Hypotheses in the Practicals FAQ
What is the central reasoning task in Chi-Square Testing of Genetic Hypotheses in the Practicals?
Use chi-square to ask whether genetic counts depart from a stated model by more than sampling variation would plausibly explain. The chapter walks from expected ratios and counts through contributions, degrees of freedom and decision language, with a full return to biological assumptions. You will learn why ‘fail to reject’ is useful but never proves the model true.
Which mistake should I actively check for?
A ratio is not expected counts For 140 offspring and a 3:1 model, expected counts are 105 and 35. Chi-square workflow Model before statistic Chi-square does not discover a ratio. The largest contribution locates mismatch but is not permission to delete a class; investigate scoring, viability, entry and genotype grouping. Never replace one with the other while filling a table.
It need not specify one replacement mechanism unless the experiment compares explicit alternatives. Rejecting the ratio does not identify which assumption failed. Below a critical value, fail to reject the null at that threshold; do not say it is proved or accepted.
How much working should a genetics answer show?
EX 8.1 Test a 3:1 segregation model Question. A selfed heterozygous plant produces 118 dominant and 42 recessive progeny. Test a 3:1 phenotype expectation at the 5% threshold. N = 160, so expected counts are 120 dominant and 40 recessive. Contributions are (118−120)²/120 = 4/120 = 0.0333 and (42−40)²/40 = 4/40 = 0.1000. Thus χ² = 0.1333 . With two fixed classes, df = 2−1 = 1 .
This statistic is far below the usual 5% critical value for df 1, so we fail to reject the 3:1 null. The modest deviation is compatible with sampling under the model. This does not prove the cross assumptions true; it says these counts provide no strong evidence against them.
How should I revise this chapter?
Rebuild one diagram or cross without notes, solve the worked example with changed labels and numbers, then explain the conclusion aloud. Record the first incorrect line as a model, representation, operation or interpretation error. Return two days later and repeat a fresh problem so delayed reconstruction, rather than immediate recognition, is doing the work.
Exam move
Study Chi-Square Testing of Genetic Hypotheses in the Practicals as a decision sequence. Start with these navigation points: Chi-square asks whether deviations are larger than sampling predicts; Model before statistic; Write the genetic model in words before symbols; The model bundle; Directional alternatives. For each, write the biological mechanism, the model assumptions, a predicted observation and one limitation.
Cover the chapter answer and reconstruct its symbols and arithmetic. Change one premise—phase, dominance, sample size, environment or population—and predict which lines must change before recalculating. Use the glossary for active recall, not copying: define each term, contrast it with its nearest neighbour and give one observation that discriminates them.
Finish with a timed explanation that shows setup, working and a qualified conclusion. Revisit the first error after a delay and solve a new version rather than memorising the displayed numbers.
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