Chi-Square Goodness of Fit (Genetics)

In genetics, a chi-square goodness of fit test tells you whether the offspring counts from a breeding experiment match what Mendel's laws predict — or whether the difference is too large to be explained by random chance. Enter your observed phenotype counts (up to four phenotypes) and select an expected Mendelian ratio (such as 3:1, 1:1, 1:2:1, or 9:3:3:1) to get the chi-square value (χ²), p-value, and a clear hypothesis test result. Secondary outputs include degrees of freedom, critical value, and total observed count.

Number of offspring showing the first phenotype

Number of offspring showing the second phenotype

Third phenotype count for 3:1 or 1:2:1 ratios

Fourth phenotype count for 9:3:3:1 ratios

First number in custom ratio

Second number in custom ratio

Third number in custom ratio (0 if not used)

Fourth number in custom ratio (0 if not used)

Results

Chi-Square Value (χ²)

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Degrees of Freedom

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P-value

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Critical Value

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Hypothesis Test Result

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Total Observed

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Results Table

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Frequently Asked Questions

What is a chi-square goodness of fit test in genetics?

A chi-square goodness of fit test determines whether observed genetic ratios from crosses significantly differ from expected Mendelian ratios. It helps geneticists validate inheritance patterns and hypotheses.

How do I interpret the p-value in genetic chi-square tests?

If p-value < 0.05 (or your chosen significance level), reject the null hypothesis - your observed data significantly differs from expected ratios. If p-value ≥ 0.05, fail to reject the null hypothesis - your data supports the expected Mendelian ratio.

What does degrees of freedom mean in chi-square genetics tests?

Degrees of freedom equals the number of phenotype categories minus one (n-1). For a 3:1 ratio, df = 1; for 1:2:1 ratio, df = 2; for 9:3:3:1 ratio, df = 3.

When should I use different Mendelian ratios?

Use 3:1 for monohybrid crosses with complete dominance, 1:1 for test crosses, 1:2:1 for incomplete dominance or codominance, and 9:3:3:1 for dihybrid crosses involving two traits.

What assumptions must be met for chi-square tests in genetics?

Key assumptions include: independent observations, expected frequency of at least 5 in each category, random sampling, and that the data represents actual counts (not percentages or proportions).

How do I calculate expected frequencies for genetic crosses?

Multiply the total number of offspring by the proportion for each phenotype in the expected ratio. For example, with 160 total offspring and a 3:1 ratio: expected dominant = 160 × (3/4) = 120, expected recessive = 160 × (1/4) = 40.

What if my chi-square value is very high?

A very high chi-square value indicates large deviations from expected ratios, suggesting the observed data doesn't fit the hypothesized Mendelian pattern. This might indicate linkage, epistasis, or other genetic factors affecting inheritance.

Can I use this test for more than 4 phenotype categories?

While this calculator handles up to 4 categories (sufficient for most Mendelian ratios), chi-square tests can theoretically handle any number of categories. For complex genetic analyses, consult specialized statistical software.