Chi-squared test in genetics
BiologyΒ· 12 min read
1. Core Principles of Chi-squared Test for Geneticsβ β ββββ± 3 min
The chi-squared test is the only statistical method CIE expects you to use to check if offspring phenotypic counts from a genetic cross match a predicted Mendelian ratio. It quantifies whether differences between your real experimental counts and theoretical expected counts are caused by random chance, or a real violation of the inheritance model (e.g. linkage, epistasis).
Chi-squared ($\chi^2$) goodness of fit test
A non-parametric statistical test used to assess whether there is a statistically significant difference between observed categorical data counts and counts predicted by a theoretical genetic model.
Example:
Testing if 87 tall and 33 short pea plant offspring match an expected 3:1 monohybrid ratio
Test your baseline understanding of test eligibility
Which of the following datasets is appropriate for a chi-squared test?
A) Difference in average height between two plant groups
B) Difference between observed and expected counts of purple vs white flower offspring
C) Correlation between leaf size and sunlight exposure
D) Rate of enzyme reaction at different temperatures
Reveal answer
B βChi-squared only applies to discrete, categorical count data, not continuous measurements or correlation analysis.
2. Step-by-Step Calculation Workflowβ β β βββ± 4 min
State a clear null hypothesis that no significant difference exists between observed and expected phenotypic counts
Record all observed counts from your genetic cross experiment
Calculate expected counts for each phenotypic class using your predicted Mendelian ratio, ensuring total expected counts equal total observed counts
Compute the term for each class, square it, divide by the expected value for that class
Sum all resulting values to get your final statistic
A monohybrid cross of two heterozygous pea plants for flower colour produces 24 purple and 6 white offspring. Test against an expected 3:1 ratio.
- 1
Step 1: Total offspring = 24 + 6 = 30. Null hypothesis: No significant difference between observed counts and 3:1 expected ratio.
- 2
Step 2: Expected counts: 3/4 * 30 = 22.5 purple, 1/4 * 30 = 7.5 white.
- 3$(24 - 22.5)^2 / 22.5 = 2.25 / 22.5 = 0.1$
- 4$(6 - 7.5)^2 / 7.5 = 2.25 / 7.5 = 0.3$
- 5Sum = 0.1 + 0.3 = 0.4, so $\chi^2 = 0.4$
Exam tip:
CIE awards 1 dedicated mark for ensuring your total expected counts exactly match total observed counts, do not skip this verification step.
3. Degrees of Freedom and Hypothesis Conclusionβ β β βββ± 3 min
Degrees of freedom (df) for a chi-squared test in genetics is calculated as the number of phenotypic classes minus 1. For a standard 3:1 monohybrid ratio, df = 2 - 1 = 1. For a 9:3:3:1 dihybrid ratio, df = 4 - 1 = 3. CIE almost always uses the standard 5% (0.05) significance level as the threshold for conclusions.
Critical value
The pre-determined threshold value for a given degrees of freedom at the 5% significance level. If your calculated is lower than the critical value, you accept the null hypothesis; if higher, you reject it.
4. Validity Rules for Chi-squared in Geneticsβ β β β ββ± 2 min
All data must be raw counts of individuals in phenotypic classes, not percentages or ratios
No expected count for any phenotypic class can be less than 5. If this happens, combine adjacent classes
The data points must be independent: no individual organism can be counted in more than one class
The sample size should ideally be greater than 20 total offspring to reduce random error
Check your validity knowledge
You have 4 phenotypic classes, one of which has an expected count of 3. What should you do?
A) Proceed with the test anyway
B) Merge that class with the next smallest phenotypic class
C) Discard that data point
D) Use a different significance level
Reveal answer
B βCombining adjacent classes to ensure all expected values are >5 is the standard accepted correction for chi-squared tests.
5. Common Pitfalls
Wrong move:
Using percentages or ratios directly instead of raw counts in the chi-squared formula
Why:
The test is sensitive to absolute sample size, percentages will give an artificially low or incorrect chi-squared value
Correct move:
Always convert all values back to raw individual counts before calculation
Wrong move:
Calculating degrees of freedom as total number of offspring minus 1
Why:
Degrees of freedom only refers to the number of independent phenotypic classes, not sample size
Correct move:
Use df = number of phenotypic categories - 1, no exceptions for genetic crosses
Wrong move:
Comparing chi-squared value to the wrong critical value for their df
Why:
CIE provides a standard table, using df=1 critical value 3.84 for all monohybrid tests, df=3 critical value 7.82 for dihybrid 9:3:3:1 tests
Correct move:
Explicitly state your df value first, then pull the matching 0.05 critical value
Wrong move:
Writing a conclusion that says 'the ratio is 3:1' instead of 'data is consistent with 3:1 ratio'
Why:
You can never prove a genetic model is 100% correct, only that the data does not contradict it
Correct move:
Frame conclusions to refer to acceptance or rejection of the null hypothesis, not absolute proof of the inheritance ratio
Wrong move:
Using chi-squared test for continuous variation data like seed mass
Why:
Chi-squared is only designed for discrete categorical count data
Correct move:
Use a t-test for continuous data comparisons of means
6. Quick Reference Cheatsheet
Step | Action for CIE Exams | Typical Mark Allocation |
|---|---|---|
1 | State null hypothesis clearly | 1 mark |
2 | Calculate expected counts matching total observed | 1 mark |
3 | Compute sum of | 2 marks |
4 | State degrees of freedom = classes - 1 | 1 mark |
5 | Compare to 0.05 critical value | 1 mark |
6 | Write valid conclusion referencing null hypothesis | 1 mark |
When this came up on past exams
AI-estimated based on syllabus patterns β cross-check with official past papers for accuracy. Use only as revision-focus signals.
- 2023 Β· Paper 4
Dihybrid cross chi-squared calculation
- 2022 Β· Paper 3
Practical chi-squared hypothesis test
- 2021 Β· Paper 2
Null hypothesis definition for chi-squared
What's Next
Mastering the chi-squared test is a critical skill for both A2 theory papers and practical assessment questions in CIE 9700, as it is regularly paired with dihybrid inheritance, epistasis, and autosomal linkage scenarios. Understanding how non-Mendelian ratios produce chi-squared values above the critical threshold will help you explain why observed offspring counts deviate from expected 9:3:3:1 ratios in cross questions. This skill also transfers directly to population genetics topics where you test for Hardy-Weinberg equilibrium using similar goodness of fit logic. Practice full chi-squared responses to ensure you hit every mark scheme point to avoid losing easy marks in extended answer sections.