Chi-Square Calculator
Free chi-square test calculator.
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What is Chi-Square Calculator?
The chi-square (χ²) test is a cornerstone of categorical data analysis. It compares the counts you observed against the counts you would expect under a null hypothesis, and converts the mismatch into a single statistic with a known distribution — so you can state, with a p-value, whether the difference is likely real or just sampling noise.
Key Benefits
- Decide with numbers whether survey answers, A/B variants, or defect counts genuinely differ
- Skip statistical tables — exact p-values are computed instantly from the incomplete gamma function
- Find the drivers, not just the verdict — standardized residuals show which cells deviate most
- Gauge practical significance with Cramér's V, not just statistical significance
- Keep sensitive data local — every computation runs in your browser with zero uploads
Common Use Cases
- •Testing whether a die, roulette, or random generator is fair (goodness of fit)
- •Checking Mendelian inheritance ratios such as 9:3:3:1 from breeding counts
- •Analyzing survey cross-tabs: is satisfaction independent of subscription plan?
- •Comparing conversion rates across traffic sources with a contingency table
- •Validating that defect counts are evenly distributed across production shifts
How to Use the Chi-Square Calculator
- Pick the test type: Choose goodness-of-fit to compare counts against an expected ratio, or independence to analyze a contingency table of two categorical variables.
- Enter your counts: For goodness of fit, paste observed counts and optionally expected ratios like 9 3 3 1. For independence, paste the table with one row per group, columns separated by spaces.
- Set the significance level: Pick α = 0.01, 0.05, or 0.10. The critical value and the accept/reject verdict update instantly as you type.
- Read the result: Check χ², df, and the p-value against α, then scan the residual table — values beyond ±2 mark the categories or cells that deviate most from expectation.
Key Features
- Goodness-of-fit with uniform or custom expected ratios (e.g. a 9:3:3:1 Mendelian split)
- Independence test for any r×c contingency table with totals computed automatically
- Exact p-values via the regularized incomplete gamma function — no lookup tables
- Cell-by-cell expected counts and standardized residuals that show which cells drive the result
- Cramér's V effect size plus the critical value at α = 0.01 / 0.05 / 0.10
- Warns when expected counts drop below 5, where the chi-square approximation weakens
Frequently Asked Questions
What is the difference between goodness-of-fit and the independence test?
Goodness-of-fit compares one set of observed counts against a theoretical distribution (like uniform or a 9:3:3:1 ratio). The independence test works on a two-way contingency table and asks whether two categorical variables are related — for example, whether device type and conversion outcome are associated.
When should I not use a chi-square test?
When any expected count is below 5 (or below 1 in some texts) the chi-square approximation becomes unreliable. This tool warns you when that happens — merge sparse categories, collect more data, or switch to an exact test such as Fisher’s exact test for 2×2 tables.
What does Cramér's V tell me?
The p-value only says whether an association exists; Cramér's V measures how strong it is, ranging from 0 (no association) to 1 (perfect). As a rough guide for tables larger than 2×2: 0.1 is weak, 0.3 is moderate, and 0.5 is strong.
How are the degrees of freedom calculated?
For goodness-of-fit, df = k − 1 where k is the number of categories. For an r×c contingency table, df = (r − 1)(c − 1). The df determines the shape of the chi-square distribution used for the p-value.