Chi-Square Goodness-of-Fit Test
Chi-Square Goodness-of-Fit Test with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent category counts and a specified null model. This is goodness of fit, not a contingency-table independence test. Sparse expected counts may need an exact method. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Observed counts: 20, 30
- Expected counts: 25, 25
- Parameters fitted from these data: 0
Observed20,30 and expected25,25 give χ²=2 and df1.
Frequently asked questions
How do I use this calculator?
Enter observed counts, expected counts, parameters fitted from these data. The result updates automatically. Use Reset to restore the example values.
What method does it use?
χ²=Σ(O−E)²/E; df=categories−1−fitted parameters; p is the χ² upper tail.. Independent category counts and a specified null model. This is goodness of fit, not a contingency-table independence test. Sparse expected counts may need an exact method. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.