Chi-Square Goodness-of-Fit Calculator

Test if observed experimental counts differ significantly from theoretical expected counts (e.g. Mendelian ratios 3:1 or 9:3:3:1).

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Category Data

Input Observed and Expected counts. Leave rows empty to exclude categories.

Category Name
Observed (O)
Expected (E)

Test Results

Chi-Square (χ2) 1.333
Degrees of Freedom (df) 1
p-value 0.248
Stat. Significance Not Significant (p > 0.05)
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Alpha Threshold

By standard scientific convention, α = 0.05 is used. If p > 0.05, observed variations do not differ significantly from Mendelian predictions.

Chi-Square Critical Value Distribution Table (α = 0.05)

Degrees of Freedom (df) Categories (k) Critical Value (α = 0.05) Critical Value (α = 0.01)
1 2 (Monohybrid 3:1) 3.841 6.635
2 3 (Incomplete Dom 1:2:1) 5.991 9.210
3 4 (Dihybrid 9:3:3:1) 7.815 11.345
7 8 (Trihybrid 27:9:9...) 14.067 18.475

Calculation Methodology & Biological Principles

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Chi-Square Test Equation

χ² = Σ [ (O - E)² / E ]

Sum the squared differences between observed (O) and expected (E) counts divided by E.

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Biological Hypothesis Testing

Null hypothesis (H0): Observed counts do not differ from expected Mendelian ratios. Rejection (p ≤ 0.05) signals genetic linkage, differential lethality, or selection.

Frequently Asked Questions

What is a Chi-Square Goodness-of-Fit test in genetics?

The Chi-Square (χ²) goodness-of-fit test compares observed experimental genotype or phenotype counts against theoretical ratios predicted by Mendelian inheritance (e.g. 3:1 monohybrid or 9:3:3:1 dihybrid ratio) to determine if variations are statistically significant or due to chance.

How do you calculate degrees of freedom (df)?

Degrees of freedom equal the number of distinct categorical outcomes minus one: df = k - 1. For a monohybrid cross with 2 phenotype categories, df = 2 - 1 = 1.

What does p-value <= 0.05 mean in genetic experiments?

A p-value <= 0.05 indicates statistical significance, leading us to reject the null hypothesis. It implies that observed counts deviate significantly from expected Mendelian ratios, suggesting phenomena such as gene linkage, lethal alleles, or natural selection.

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