Chi-Square Test of Independence Calculator
Pearson’s chi-square test of independence checks whether two categorical variables are associated in a 2×2 table by comparing observed and expected cell counts.
How to use this calculator
- Enter four nonnegative integer counts using the row/column definitions consistently.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by chi square independence calculator
χ² = Σ((observed − expected)² ÷ expected); df = 1 for a 2×2 table.
- χ² = Σ((observed − expected)² ÷ expected); df = 1 for a 2×2 table.
- The p-value is asymptotic. Small expected counts, dependence between observations or complex survey design may call for other methods.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
A table has observed counts 40, 10, 20 and 30 across its four cells.
Expected counts are computed from row and column totals, then the Pearson statistic and asymptotic tail probability are returned.
The result summarizes evidence of association in the supplied table.
Understanding the result
Pearson’s chi-square test of independence checks whether two categorical variables are associated in a 2×2 table by comparing observed and expected cell counts.
The p-value is asymptotic. Small expected counts, dependence between observations or complex survey design may call for other methods.
Important notes
The p-value is asymptotic. Small expected counts, dependence between observations or complex survey design may call for other methods.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Does association imply causation?
No. A contingency-table test does not establish a causal relationship.
What if expected cell counts are small?
Review assumptions and consider an exact method such as Fisher’s exact test.
How should I interpret this result?
The p-value is asymptotic. Small expected counts, dependence between observations or complex survey design may call for other methods.
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Related explanations
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.