How to use (3 steps)
- Select a ratio preset (3:1, etc.) or enter a custom ratio.
- Enter observed counts for each category (use an example to start quickly).
- Results (χ², p-value, expected counts, charts) appear; with auto update on, they refresh as you type.
Results are guides. Check contributions and charts together.
Inputs (ratio & observed counts)
Results (χ² & p-value)
χ²
—
df
—
p-value
—
α (guide)
—
—
Observed vs expected (table & charts)
Observed
Expected
| Category | Observed | Expected | O−E | Contribution | Pearson residual | Ratio |
|---|
Observed vs expected
Contribution
How it’s calculated
- From total N and ratio r, compute expected counts (Ei = N · ri / Σr).
- Compute χ² = Σ (Observed − Expected)² / Expected.
- Degrees of freedom df = number of categories − 1 (assuming the ratio is fixed).
- The p-value is the upper-tail probability of the χ² distribution (P(Χ² ≥ χ²)).
- (Optional) For df=1 (2 categories), you can apply Yates continuity correction (guide).
“Guide” on this page is not a definitive judgement. Review assumptions (e.g., how categories are grouped) as needed.
FAQ
What if expected counts are small?
Small expected counts can make the χ² approximation rough. This page shows a warning (guide).
Does p<0.05 mean it does not fit?
It is a common guideline, but interpretation depends on context. We show it as a reference only.
What should I enter for category names?
Anything is fine (e.g., dominant/recessive, AA/Aa/aa). It works even if blank.
Does the share URL include data?
You can choose to include or exclude it. Data stays in your browser and is not sent.
Where are observed data sent?
All calculations run in your browser. Inputs are not sent anywhere.
Related tools
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