Statistics

Chi-Square GOF Calculator

Calculate chi-square goodness-of-fit statistic from observed vs expected counts.

Last validated: 2026-02-14

Chi-Square GOF Calculator tests whether observed categorical counts fit an expected distribution. It is useful for quality checks, survey analysis, and model validation. The tool computes chi-square statistic and significance output from count tables. Use it to identify meaningful distribution mismatch.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Chi-Square GOF Inputs

Result

Chi-square: 2.000000

df: 3

How to use this tool

Enter observed counts and expected counts/proportions.
Run the test to compute chi-square and p-value.
Interpret significance with awareness of sample-size assumptions.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Observed: 30, 25, 20, 25
Expected: 25, 25, 25, 25
Chi square: 2.0
Df: 3

Expected Outputs

Chi square: 2
Df: 3

Interpretation

Chi square is 2.0. Use this as a decision input, not as a standalone conclusion.
Df is 3. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

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