Result
Enter values and select Calculate.
Formula and methodology
Goodness of fit sums (O−E)²/E with df = k−1. Independence calculates expected cells from row and column totals with df = (r−1)(c−1). Right-tail p-values use the regularized upper incomplete gamma function Q(df/2, χ²/2).
Worked example
Observed 10, 20, 30 against expected 15, 15, 30 gives χ² = 3.333333, df = 2, and p ≈ 0.188876.
Assumptions and interpretation
- Datasets and results stay in this browser and are not sent to analytics.
- This educational tool performs mathematical computation; it does not establish causation, choose a study design, or validate scientific conclusions.
- Check assumptions, sampling methods, and context before interpreting an inferential result.
- Keep full precision for decisions; displayed values are rounded for readability.