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Chi-square test calculator (test of independence)

Tests whether two categorical variables are associated. Enter the observed counts in a contingency table; get χ², df, p, expected counts and Cramér’s V.

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Your data

Enter the observed frequency (count) for each combination. Edit the category labels and variable names to match your data; add rows or columns as needed.

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When to use this

Use the chi-square test of independence when each case falls into one category on each of two categorical variables — pass/fail by teaching format, diagnosis by treatment arm, preference by country — and you want to know whether the two classifications are related. The test compares the observed counts with the counts expected if the variables were independent; a large χ² means the pattern in your table is unlikely under independence. Cramér’s V then expresses the strength of the association on a 0–1 scale, which matters because with large samples even trivial associations become “significant”.

Key assumptions

  • Each observation is independent and appears in exactly one cell (no repeated measures).
  • The data are counts (frequencies), not percentages, proportions or means.
  • Expected counts are at least 5 in (about 80% of) cells — the calculator warns when this fails.
  • Categories are mutually exclusive and exhaustive.

Common mistakes

  • Entering percentages instead of raw counts — the test is only valid on frequencies.
  • Using chi-square on paired/repeated categorical data (use McNemar’s test instead).
  • Ignoring the low-expected-count warning; for small 2×2 tables use Fisher’s exact test.
  • Reporting p without Cramér’s V, so readers cannot judge the strength of the association.

Frequently asked questions

What if my expected counts are below 5?
The χ² distribution is an approximation that becomes unreliable with small expected counts. For a 2×2 table, switch to Fisher’s exact test; for larger tables, consider combining sparse categories or collecting more data. This calculator flags the affected cells.
How do I interpret Cramér’s V?
V ranges from 0 (no association) to 1 (perfect association). For tables where the smaller dimension is 2, common benchmarks are .10 small, .30 medium, .50 large. Always report it alongside χ² and p.
Can I use this for a 3×4 (or larger) table?
Yes — add rows and columns as needed; the test handles any r×c table. The degrees of freedom are (rows − 1) × (columns − 1).

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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