Safety, privacy and evidence boundary
Use fictional organisms, coins/cards, and published-style datasets. Do not require personal family histories, ancestry testing, fertility information, medical pedigrees, or personal genetic data. Trait inheritance never ranks human worth.
Explicit science instruction
A chi-square goodness-of-fit statistic summarizes how far observed category counts differ from expected counts relative to the expected counts. One form is Σ(O−E)²/E. Larger values mean greater discrepancy, but interpretation depends on degrees of freedom and a reference distribution.
The test does not measure biological importance, prove a model, or identify the cause of mismatch. Expected counts should be based on a specified model, and categories/observations should satisfy the test's assumptions.
Worked example with reasoning
A 3:1 model predicts 75 and 25 among 100 offspring. Observed counts are 70 and 30. χ² = (70−75)²/75 + (30−25)²/25 ≈ 0.33 + 1 = 1.33. The statistic quantifies discrepancy; judging whether it is unusual requires the appropriate reference threshold.
Guided question
Why can't a small chi-square value prove the genetic model is true?
Independent work
- Calculate expected counts for a 3:1 model with n=160.
- Compute χ² for an observed 115:45 result.
- State the degrees of freedom for two categories.
- List two assumptions.
- Explain what the test cannot identify.
Investigation / Data Lab
Fictional pedigree constraint analysis
Question: Which inheritance model is most consistent with a supplied fictional pedigree, and what remains ambiguous?
- Use only the supplied anonymous/fictitious pedigree. Do not substitute family medical history.
- Test autosomal dominant, autosomal recessive, and one sex-linked model against the same relationships.
- Mark which genotypes are forced, possible, or excluded under each model.
- Choose the best-supported model and list at least two assumptions such as penetrance or complete reporting.
- Identify one additional observation that would discriminate between the remaining models.
Evidence standard: submit the annotated pedigree/model table, not a diagnosis or inference about real relatives.
Misconception check
A p-value is not the probability that the hypothesis is true, and “not significant” is not proof of no difference.
Formative understanding check
What happens to χ² when observed counts move farther from fixed expected counts?
Worked response
It generally increases because squared deviations grow.
Open-book formative practice only; not an official mastery attempt or grade.
Mentor evidence conference
Ask Archaemenes to challenge your probability, evidence classification, model assumptions, and limitations. The mentor does not infer personal genetics or provide protected assessment answers.
Open ArchaemenesTeacher guidance
Foundation: use a calculation table with O, E, O−E, and contribution. Core: compute and interpret without causal overclaiming. Extended: compare statistical detectability with biological effect size and sample size.
Preserve learning evidence
Keep models, calculations, corrections, and limitations in the matching Week 21 evidence field.
Return to evidence workspace