Test statistical independence between categorical variables. Calculate chi-square statistics, expected frequencies, and determine significance with confidence.
Contingency Table
Enter observed frequencies in the table below
Observed Frequencies
Test Results
χ²
Chi-Square Statistic
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df
Degrees of Freedom
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χ²₀
Critical Value
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✓
Test Conclusion
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ΣChi-Square Formula
χ² = Σ[(O - E)² / E]
Where O = Observed frequency, E = Expected frequency
Expected Frequencies
Calculated under the assumption of independence
Step-by-Step Calculations
Cell-by-cell contribution to chi-square statistic
Maintained by ToolexeLast updated October 14, 2026
