Chi-Square Calculator

A Chi-Square test on a 2x2 contingency table tells you whether two categorical variables are genuinely associated or merely appear linked by chance. The question comes up often: a market researcher might ask whether a new ad campaign (variable 1) shifts customer purchase intent (variable 2), while a clinical team might test whether a treatment outperforms a placebo on a particular patient outcome.

Computation runs on the formula Σ((Observed - Expected)² / Expected). For every cell, the expected frequency comes from (Row Total × Column Total) / Grand Total, representing what you would see if the two variables had no relationship at all. Summing the standardized gaps between observed and expected counts produces the χ² statistic, which in turn yields a p-value, the probability of seeing an association this strong purely by chance when no real relationship exists.

Treat statistical significance and effect size as separate questions, because a small p-value signals only that the association is unlikely to be random, never that it is large or practically meaningful. The test also rests on having enough data in each cell. When more than 20% of cells carry expected counts below 5, the test's assumptions break down and the resulting p-values can no longer be trusted.