Chi-Square Independence Test
Paste a contingency table (rows separated by newlines, columns by commas/spaces). Get χ² statistic, degrees of freedom, p-value, and effect size (Cramer's V for tables larger than 2×2).
Contingency table
One row per line. Numbers separated by commas or spaces.
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Result
Expected vs observed
What this test does (and doesn't) do
The chi-square test of independence answers one question: "are these two categorical variables associated?" It does NOT tell you how strong the association is, in what direction, or whether the relationship is causal. Always report effect size (we compute Cramer's V) along with the p-value.
Assumptions
- All expected cell counts should be ≥ 5. If not, use Fisher's exact test instead (we don't implement it; see R's
fisher.test). - Observations are independent.
- Sample is random (or at least representative).
Who uses it
- Market researchers checking if two survey variables are related.
- Biology students testing Mendelian ratios (goodness-of-fit version).
- A/B testers checking if conversion rates differ across segments.