What is the chi-square test in genetics?

The chi-square goodness-of-fit test compares observed phenotype counts from a genetics experiment to expected counts derived from a Mendelian ratio. A small chi-square value means the data fit the expected ratio well; a large value suggests deviation that may be statistically significant.

How are degrees of freedom calculated?

Degrees of freedom equal the number of phenotype classes minus one. A two-class ratio (e.g., 3:1) has 1 degree of freedom; a four-class ratio (e.g., 9:3:3:1) has 3 degrees of freedom.

What p-value is considered significant?

The conventional threshold is α = 0.05. A p-value below 0.05 means you reject the null hypothesis that the data match the expected Mendelian ratio. A p-value above 0.05 means you fail to reject it — the deviation could be due to chance alone.

What is the minimum expected count per class?

For the chi-square approximation to be reliable, each expected count should be at least 5. If any class has fewer than 5 expected observations, the result is noted as potentially unreliable and you should collect more data.

Can I enter a custom ratio?

Yes. Select "Custom" from the ratio dropdown, then type your ratio values separated by colons (e.g., 2:1:1 or 1:3:3:1). The tool parses the values and distributes expected counts proportionally.

Why might my cross deviate from the expected ratio?

Possible reasons include small sample size (chance variation), linked genes, lethal alleles, incomplete penetrance, epistasis, or experimental error. A significant chi-square result warrants further investigation but does not by itself identify the cause.

Chi Square Genetics

Enter observed phenotype counts and choose a Mendelian ratio to calculate chi-square, p-value, and whether your cross results match predictions.

Cross Setup

Expected Mendelian Ratio

Observed Counts

Critical Values at α = 0.05

df	χ² critical	Common ratio
1	3.841	3:1, 1:1, 2:1
2	5.991	1:2:1
3	7.815	9:3:3:1, 1:1:1:1, 3:1:3:1
4	9.488	Custom 5-class

Enter observed counts and click Calculate Chi-Square to see results.

χ² Statistic

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Degrees of Freedom

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p-value

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Observed vs. Expected Breakdown

Class	Observed (O)	Expected (E)	(O−E)²/E
Total

Interpretation

Summary

The chi-square goodness-of-fit test is the standard statistical method for evaluating whether observed phenotype counts from a genetics cross match the expected Mendelian ratios. You select a ratio (such as 3:1 for a monohybrid dominant cross or 9:3:3:1 for a dihybrid cross), enter your observed counts, and the calculator computes expected counts, the chi-square statistic, degrees of freedom, and the p-value. A p-value below 0.05 indicates a statistically significant departure from the predicted Mendelian ratio.

How it works

Select a Mendelian ratio preset or enter a custom ratio for your cross.
Enter the observed count for each phenotype class.
The tool calculates expected counts based on the total and the chosen ratio.
Chi-square (χ²) is computed as the sum of (observed − expected)² / expected across all classes.
Degrees of freedom equal the number of phenotype classes minus one.
The p-value is derived from the chi-square distribution to determine statistical significance.

Use cases

Analyze monohybrid cross results against the 3:1 dominant-to-recessive ratio.
Test dihybrid cross data against the 9:3:3:1 ratio.
Evaluate codominance or incomplete dominance crosses using the 1:2:1 ratio.
Verify testcross results against the expected 1:1 ratio.
Assess lab or classroom genetics experiment data for significant deviation.
Determine whether observed F2 phenotype counts support Mendelian inheritance.
Check for linkage or other non-Mendelian effects in experimental crosses.
Quickly calculate chi-square for any custom phenotype ratio.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu