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D3.2.21 (HL)—Chi-squared test

The chi-squared test compares observed and expected genetic results to judge whether differences could be due to chance in inheritance problems.

Syllabus
First assessment 2025
Objective
D3.2.21
Level
HL

Exam analysis

Chance of appearing2%of analysed past papers
Latest appearanceNovember 2021
Most common paperPaper1
Typical marks1–2

Recent exam appearances

November 2021Paper1 ["HL"] · TZ035[ 1 ]D3.2.21 (HL)—Chi-squared test
November 2019Paper2 ["HL"] · TZ02(c)[ 2 ]D3.2.21 (HL)—Chi-squared test
Practice this objective

Coverage 2019–2021 · Updated 16 Jul 2026

Use Chi-Squared to Test a Dihybrid Ratio

HL only

A chi-squared goodness-of-fit test asks whether differences between observed and expected dihybrid counts are larger than expected from chance sampling.

χ2=Σ((O−E)2/E),whereOiseachobservedcountandEisitsexpectedcount.χ2hasnounit;degreesoffreedom=numberofcategories−1.χ² = Σ((O − E)² / E), where O is each observed count and E is its expected count. χ² has no unit; degrees of freedom = number of categories − 1.

State H₀: observed counts fit the stated Mendelian ratio; H₁: they do not. Convert the ratio to expected counts, calculate and sum each contribution, then compare χ² with the critical value at p = 0.05.

In local Question Bank record 10900, a four-category 1:1:1:1 model gives E = 575 in each category and df = 3. The supplied χ² = 1002.6 exceeds the p = 0.05 critical value 7.815, so reject H₀: the observed ratio differs significantly from expectation.

Failing to reject H₀ does not prove the model; rejecting it does not by itself identify linkage or another cause. Check assumptions, expected counts and experimental design.

Chi-squared test

HL only

Assessment in practice

1–2 marks
How it is assessed

This objective is assessed through structured response.

What earns marks

Build the answer around this relationship: Chi-squared compares observed counts with expected counts.

Representative question

Question 1

[Maximum number: 2]

The chi-squared value was calculated as shown. Deduce, with reasons, whether the observed ratio differed significantly from the expected Mendelian ratio.

c2=Σ( Observed − Expected )2 Expected =1002.6c^{2}=\Sigma \frac{(\text { Observed }- \text { Expected })^{2}}{\text { Expected }}=1002.6
Probability
Degrees of freedom0.9950.9750.200.100.050.0250.020.010.0050.0020.001
10.000040.0011.6422.7063.8415.0245.4126.6357.8799.55010.828
20.0100.0513.2194.6055.9917.3787.8249.21010.59712.42913.816
30.0720.2164.6426.2517.8159.3489.83711.34512.83814.79616.266
40.2070.4845.9897.7799.48811.14311.66813.27714.86016.92418.467
50.4120.8317.2899.23611.07012.83313.38815.08616.75018.90720.515
60.6761.2378.55810.64512.59214.44915.03316.81218.54820.79122.458
70.9891.6909.80312.01714.06716.01316.62218.47520.27822.60124.322

Retrieve the HL Inheritance Route

HL only

HL D3.2 is secure when chromosome behaviour explains the ratios: segregation and independent assortment produce unlinked dihybrid expectations, gene loci explain linkage, recombinants reveal crossing over, and chi-squared decides whether observed counts fit the expected model.

  • homologous chromosomes separate and random bivalent orientation assort unlinked genes
  • unlinked autosomal genes can produce 9:3:3:1 or 1:1:1:1 ratios
  • linked genes give more parental types and fewer recombinants after crossing over
  • observed counts are compared with expected ratios using df and p = 0.05

Solve HL Linkage and Chi-Squared Questions

HL only

HL inheritance transfer is about deciding whether the expected ratio should be Mendelian or linked, then testing the evidence. Start from meiosis and gene location, predict gametes or ratios, identify parental and recombinant classes, and use chi-squared when observed counts need a statistical conclusion.

  • Explain segregation and independent assortment from meiosis before using dihybrid ratios.
  • Use gene loci, linkage, crossing over, and recombinant frequency to interpret offspring classes.
  • Apply chi-squared with observed/expected values, degrees of freedom, p = 0.05, and a null-hypothesis conclusion.

Concept essentials

  • Chi-squared compares observed counts with expected counts.
  • Expected values must come from a stated genetic hypothesis or ratio.
  • A larger chi-squared value means a poorer fit to the expected ratio.