Chi-Square Goodness-of-Fit Calculator (Genetic Ratios)
Enter observed counts and the expected ratio to test the fit.
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Chi-Square Goodness-of-Fit Calculator (Genetic Ratios) by TheCalcTools
How the Chi-Square Goodness-of-Fit Calculator (Genetic Ratios) works
Expected counts are the total multiplied by each ratio share. Chi-square adds (observed − expected)² ÷ expected over all categories; larger values mean a worse fit.
The p-value is the chance of a deviation this large if the ratio were true, from the chi-square distribution with (categories − 1) degrees of freedom. Expected counts should be at least 5 in each category for the test to be reliable.
The formula
Worked example
Using the default values shown in the calculator:
| Observed counts | 315, 108, 101, 32 |
|---|---|
| Expected ratio (same order) | 9, 3, 3, 1 |
- Mendel’s pea data 315 : 108 : 101 : 32 against 9 : 3 : 3 : 1 gives χ² = 0.470 with 3 df.
- p = 0.925: Fits the expected ratio (p ≥ 0.05).
Result:
| Chi-square value | 0.4700 |
|---|---|
| Degrees of freedom | 3 |
| p-value | 0.9254 |
| Conclusion at the 5% level | Fits the expected ratio (p ≥ 0.05) |
| Total observed | 556 |
Frequently asked questions
Does a high p-value prove the ratio?
No. It only means the data are consistent with it. A low p-value suggests the model (for example independent assortment) does not fit.
Sources and further reading
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