Test observed offspring counts against expected Mendelian ratios in real time. Use it for monohybrid, dihybrid, trihybrid, test cross, and incomplete dominance data. The tool reports χ², degrees of freedom, p-value, expected counts, and the phenotype class that contributes most to deviation.
Choose a ratio preset, enter your observed offspring counts, and watch the statistical test update instantly without a submit button.
Load a common cross, then edit the phenotype labels, observed counts, or expected ratio values.
Monohybrid F₂
Use this for flower colour, seed shape, or any single-gene complete dominance cross.
Enter the real counts from your cross. Use whole offspring counts, not percentages.
Enter the theoretical ratio from your genetic hypothesis, such as 3:1 or 9:3:3:1.
Live result
Do not reject H₀. The deviations fit normal sampling variation for this ratio.
χ²
0.053
df
1
p-value
0.817
The contribution column shows which phenotype class drives the χ² statistic.
| Class | Observed | Ratio | Expected | O − E | χ² contribution |
|---|---|---|---|---|---|
| Dominant phenotype | 76 | 3 | 75 | 1 | 0.013 |
| Recessive phenotype | 24 | 1 | 25 | -1 | 0.040 |
Null hypothesis: The observed offspring counts follow the expected Mendelian ratio.
Alternative hypothesis: The counts deviate more than expected from random sampling.
Largest contribution: Recessive phenotype adds 0.040 to χ².
Longer bars identify the classes where observed counts diverge most from the expected ratio.
A Mendelian ratio chi-square test compares observed offspring counts with a ratio predicted by a genetic model. Gregor Mendel published his pea hybridisation work in 1866, long before biologists connected chromosomes, meiosis, and genes. Karl Pearson later introduced the chi-square test in 1900, giving geneticists a formal way to ask whether count data fit an expectation.
The test uses the formula (O − E)2 / E for each phenotype class. O means observed count, while E means expected count. The calculator adds those class contributions into one χ² statistic and converts it into a p-value using the chi-square distribution.
In a monohybrid Aa × Aa cross, meiosis separates A and a alleles into gametes. Random fertilisation then creates a 3:1 phenotype ratio under complete dominance. OpenStax summarises the same segregation and independent assortment logic in its genetics chapter on inheritance laws. Read the OpenStax inheritance overview.
Select a preset such as 3:1, 1:1, 1:2:1, 9:3:3:1, or 27:9:9:9:3:3:3:1.
Type the counted offspring number for each phenotype class. Use raw counts rather than percentages.
Review the expected counts that the calculator derives from the ratio and total offspring number.
Compare the p-value with α. Do not reject the ratio when p is greater than or equal to α.
For genotype notation, use uppercase letters for dominant alleles and lowercase letters for recessive alleles. Examples include Aa, AaBb, and AaBbCc. For phenotype labels, use clear class names such as A_B_, A_bb, aaB_, and aabb.
A 3:1 ratio fits a single-gene F2 cross when one allele shows complete dominance. A 1:2:1 ratio fits genotype counts or incomplete dominance, because the heterozygote forms its own class. A 1:1 ratio fits a monohybrid test cross such as Aa × aa.
Dihybrid ratios add a second locus. AaBb × AaBb produces 9:3:3:1 when both genes assort independently and each gene shows complete dominance. AaBb × aabb produces 1:1:1:1 when the heterozygous parent makes AB, Ab, aB, and ab gametes at equal frequency.
Trihybrid F2 data often use 27:9:9:9:3:3:3:1. That ratio contains eight phenotype classes and a rare triple-recessive class at 1/64 of the total. Small samples can miss that class by chance, so trihybrid chi-square tests need more offspring than monohybrid tests.
| Cross type | Example | Expected ratio | Classes |
|---|---|---|---|
| Monohybrid F₂ | Aa × Aa | 3:1 | Dominant and recessive phenotypes |
| Test cross | Aa × aa | 1:1 | Two phenotype classes |
| Dihybrid F₂ | AaBb × AaBb | 9:3:3:1 | Four phenotype classes |
| Trihybrid F₂ | AaBbCc × AaBbCc | 27:9:9:9:3:3:3:1 | Eight phenotype classes |
A class counts 76 dominant offspring and 24 recessive offspring from Aa × Aa. The total equals 100. A 3:1 ratio predicts 75 dominant and 25 recessive offspring.
χ² = (76 − 75)2 / 75 + (24 − 25)2 / 25 = 0.053. With 1 degree of freedom, p is about 0.82. The observed counts fit the expected 3:1 ratio at α = 0.05.
A dihybrid F2 cross gives 315 A_B_, 108 A_bb, 101 aaB_, and 32 aabb offspring. The total equals 556. A 9:3:3:1 ratio predicts 312.75, 104.25, 104.25, and 34.75 offspring.
The class contributions sum to χ² ≈ 0.47. With 3 degrees of freedom, p is about 0.93. These counts support independent assortment for the two loci under this simple model.
Biology students use chi-square tests to decide whether real offspring counts support a proposed cross. The method also helps breeders compare observed seed, coat, or flower phenotypes with a planned inheritance model. A rejected ratio can guide the next experiment, especially when two genes may show linkage or epistasis.
Molecular genetics gives those classical ratios a physical basis. Bhattacharyya, Smith, Ellis, Hedley, and Martin showed in 1990 that Mendel’s wrinkled pea seed phenotype traces to a transposon-like insertion in a gene encoding starch-branching enzyme. That discovery connected a visible 3:1 trait with starch biosynthesis in the developing seed. View the PubMed record.
For teaching statistics, the same workflow matches the general chi-square goodness-of-fit framework. OpenStax Statistics describes how observed and expected categorical counts drive the χ² statistic. Review the OpenStax goodness-of-fit method.
A chi-square test does not prove that a genetic model works. It only measures whether your observed counts deviate more than expected under that model. A non-significant result can still hide weak linkage, incomplete penetrance, or phenotype scoring error.
Expected counts below 5 weaken the chi-square approximation. This problem appears often in trihybrid crosses, rare phenotypes, and small classroom data sets. Combine classes only when biological logic supports that choice.
This calculator supports education and research planning. It does not provide clinical genetic advice, diagnostic interpretation, or professional breeding certification.
Use these tools before or after a chi-square test to connect the genetic cross with the statistical result.