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Updated 2026-03-07 UTC
Chi‑Square (χ²) Test Guide — Goodness‑of‑Fit and Independence — GetCalcMaster
Chi-square test workflow and formulas: χ² = Σ(O−E)²/E, degrees of freedom for goodness-of-fit and contingency tables, and links to χ² critical values.
Chi-square (χ²) tests compare observed counts to expected counts. They’re used for goodness‑of‑fit (one categorical variable) and independence/homogeneity (contingency tables).
Important: Educational. Ensure observations are independent and expected counts are adequate for χ² approximations.
What this calculator is
The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- One core statistic: χ² = Σ(O−E)²/E
- Clear df rules for common cases
- Links to χ² critical values table
- Highlights expected count assumptions
Formula
χ² = Σ (O - E)^2 / E
df (contingency table) = (r-1)(c-1)
df (goodness-of-fit) = k - 1 - (# estimated parameters)Quick examples
If expected counts are very small, χ² approximations can be poor—consider exact tests.χ² tests are about counts, not percentages (compute expectations using totals).
How to use it (quick steps)
- Write down observed counts O for each category/cell.
- Compute expected counts E under H₀.
- Compute χ² = Σ (O−E)²/E.
- Compute df (goodness-of-fit: k−1−params; contingency: (r−1)(c−1)).
- Get a p-value from the χ² distribution or compare to critical values.
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FAQ
Is this calculator official?
No. GetCalcMaster provides educational estimates and learning tools. Always verify against official definitions, documents, or professional advice.
Do you store my inputs on the server?
No. Calculations run locally in your browser. Optional remember/restore features (if enabled) use local browser storage.
Tip: For reproducible work, save your inputs and reasoning in Notebook.