0.48
1
3.841
-3.361
100
75
25
0
0
0.12
0.36
0
0
0.48
1
3.841
-3.361
100
75
25
0
0
0.12
0.36
0
0
The Chi-Square Goodness of Fit Calculator tests whether observed offspring ratios in a genetic cross match the expected Mendelian ratios. This statistical test is essential in genetics for determining whether deviations from expected ratios are due to random chance or indicate that the genetic model is incorrect.
Enter observed counts for two phenotype classes and the expected ratio (e.g., 3:1 for a monohybrid cross), and the calculator will compute the chi-square statistic and compare it to the critical value.
The chi-square statistic is calculated as:
χ² = Σ ((Observed − Expected)² / Expected)
For each class, compute the squared difference between observed and expected values, divide by expected, and sum across all classes. The expected values are calculated from the total sample size and the predicted ratio. The result is compared to the critical value from the chi-square distribution table at α = 0.05 with (k−1) degrees of freedom, where k is the number of classes.
If χ² is less than the critical value, the data are consistent with the expected ratio (fail to reject H₀).
Inputs
Results
χ² = 0.48, which is less than the critical value of 3.841 (df=1, α=0.05). The deviation is not significant, so the data are consistent with a 3:1 ratio.
Inputs
Results
χ² = 16.67, far exceeding the critical value of 3.841. The 50:50 split significantly deviates from the expected 3:1, suggesting the genetic model may be wrong (e.g., possible 1:1 test cross ratio).
If χ² exceeds the critical value (3.841 for 1 degree of freedom at α=0.05), the observed data significantly deviate from the expected ratio. This means the probability of getting such extreme deviations by chance alone is less than 5%. You reject the null hypothesis and conclude the data do not fit the proposed genetic model.
Each expected class should have at least 5 individuals for the chi-square approximation to be valid. Ideally, aim for a total sample size of at least 50-100. With very small samples, even large deviations may not be statistically significant, and the chi-square approximation becomes unreliable.
Yes. You can test any expected ratio: 1:1 for a test cross, 9:3:3:1 for a dihybrid (use four categories), 1:2:1 for incomplete dominance, or any other predicted ratio. Just ensure you enter the correct expected ratio values for your genetic hypothesis. For more than 2 classes, the degrees of freedom increase accordingly.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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