How does the Chi-Square Test work?

χ² = Σ (O − E)² / E Then: O = observed · E = expected Then: df = categories − 1 (goodness of fit) Then: Large χ² → observed differs significantly from expected.

Can you give an example of how to use the Chi-Square Test?

Example: Input Observed: 50, 30, 20 · Expected: 40, 35, 25 gives a result of χ² = 5.05 · df=2 · critical value 5.99 at p<0.05 (χ² < critical → fail to reject H₀).

Is the Chi-Square Test free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Chi-Square Test?

Our Chi-Square Test uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Chi-Square Test

📊Chi-square Test

Observed values (comma separated)

Expected values (comma separated)

The chi-square (χ²) test compares observed counts to expected counts to determine whether a categorical distribution differs from what is expected. Common uses: genetics ratios, goodness of fit, independence testing.

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Did You Know?

Karl Pearson developed the chi-square test in 1900 — making it one of the oldest still-used statistical tests.

References

›Chi-squared test — Wikipedia

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Chi-Square Test

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📊Chi-square Test