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Chi-Square Goodness of Fit — result sheet
Tests counts against expected counts with the Pearson chi-square statistic.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: χ² = Σ(O−E)²/E; df = categories − 1.
Sums squared standardized residuals across categories. Larger values signal worse fit at df = categories − 1.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Observed counts — Comma-separated, same count as expected.
- Expected counts — Comma-separated, every value positive.
Worked example
| Input | Value |
|---|---|
| Observed counts | 10, 20, 30 |
| Expected counts | 15, 15, 30 |
χ² = 3.3333 with df = 2.
Assumptions and limits
- Independent counts with matching observed/expected categories.
- Every expected count positive (5+ preferred); at least 2 categories.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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