Chi-Square Independence Calculator

About this calculator

A Pearson chi-square test of independence checks whether two categorical variables in a contingency table are statistically associated or independent, by comparing the observed cell counts against the counts you'd expect if there were truly no relationship (expected counts derived from the row and column totals). The test statistic χ² = Σ(observed − expected)²/expected grows larger the more the actual data deviates from that independence assumption, and is compared against a chi-square distribution to get a p-value; Cramér's V then scales that association to a 0-1 effect size that, unlike the p-value, doesn't grow automatically with sample size.

This calculator takes the four cell counts of a 2×2 table and returns the χ² statistic, its p-value, and Cramér's V. Researchers analyzing survey or experimental data with categorical outcomes, market researchers testing whether a campaign response differs by segment, and statistics students working through hypothesis-testing coursework use it to determine whether an observed association between two binary variables — like treatment group and outcome, or gender and preference — is likely real or could plausibly be due to chance.