Chi-Square Test Calculator (2×2)
Test whether two categorical variables are associated — independence test for 2×2 contingency tables.
The chi-square test of independence asks whether the row variable (group) and column variable (outcome) are related. A small p-value means the groups differ in their outcome distribution. For 2×2 tables with small counts (<5 expected), use Fisher's exact test instead; phi (φ) gives the effect size the p-value omits.
Formula
About Chi-Square Test Calculator (2×2)
The chi-square test of independence asks whether two categorical variables are associated — does treatment group affect outcome, does channel affect conversion, does segment affect churn? This calculator runs the test on a 2×2 contingency table, returning the χ² statistic, the p-value, and the phi effect size that the p-value alone leaves out. It's the standard tool for analyzing categorical experiment results and survey cross-tabs, with built-in guidance on when small expected counts mean you should switch to Fisher's exact test instead.
How to use Chi-Square Test Calculator (2×2)
- 1Enter your values into Chi-Square Test Calculator (2×2) — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
- 2The result recomputes live using the formula shown on the page; there is no button to press.
- 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.
Why use Chi-Square Test Calculator (2×2)?
- ✓Computes Chi-Square Test instantly in your browser — no sign-up, no upload, no server round-trip.
- ✓100% free and unlimited, with the exact formula shown: χ² = N(ad-bc)² / [(a+b)(c+d)(a+c)(b+d)].
- ✓Runs entirely client-side, so every value you enter stays private on your device.
- ✓Live recompute as you type, with a worked example and authoritative references for trust.
Frequently asked questions
What does the chi-square test of independence tell me?+
Whether the distribution of outcomes differs across groups more than chance would produce. A significant result (small p-value) means the two categorical variables are associated — knowing the group tells you something about the likely outcome. It does NOT tell you the size or direction of the effect, which is why you should also report phi or the rate difference.
When should I use Fisher's exact test instead?+
When any expected cell count is small (the common rule is below 5). Chi-square relies on a large-sample approximation that breaks down with sparse tables, overstating significance. Fisher's exact test computes the probability directly without that approximation, so it's the correct choice for small samples — most stats software offers it alongside chi-square.
What is the phi coefficient?+
Phi (φ = √(χ²/N)) is the effect size for a 2×2 table — essentially a correlation coefficient for two binary variables, ranging 0 (no association) to 1 (perfect). It complements the p-value: with large samples a trivial association can be 'significant', so phi tells you whether the association is also meaningfully strong, not just statistically detectable.
Chi-square vs the two-proportion z-test for 2×2 data?+
They're mathematically equivalent for a 2×2 table — the χ² statistic equals the square of the z-statistic, and the p-values match. Use the z-test when you're comparing two conversion rates and want a directional difference and confidence interval; use chi-square when framing it as an independence/association question or extending to larger tables.
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