About Chi-Square Tester

Test chi-square statistics for categorical data. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.

Use Cases

• Test whether two categorical variables are independent (e.g., gender vs product preference)
• Verify that survey response distributions match expected demographics
• Analyze A/B test results with categorical outcomes (clicked, not clicked)
• Check whether dice or random number generators are producing fair outcomes

Tips

• Enter your contingency table directly (rows = categories, columns = groups) — the tool computes expected frequencies and the chi-square statistic automatically
• Check degrees of freedom in the output: (rows-1) * (columns-1). The critical value depends on both df and your significance level
• Use the goodness-of-fit mode (one variable) when testing whether observed frequencies match an expected distribution, not independence between two variables

Fun Facts

• The chi-square test was developed by Karl Pearson in 1900 and published in the Philosophical Magazine. It was one of the first formal statistical significance tests — predating t-tests, ANOVA, and most of modern statistics.
• The chi-square distribution has an interesting property: it is the distribution of the sum of k squared standard normal variables. This mathematical fact links it directly to the normal distribution and underlies its widespread use.
• In genetics, chi-square tests were used by early Mendelian geneticists to verify that observed inheritance ratios (3:1 for dominant traits) matched Mendel's predicted ratios — connecting statistics to biology before either field was fully formalized.

FAQ

When should I use chi-square vs a t-test?

Chi-square is for categorical data (counts in categories). T-tests are for continuous numerical data (means). If your outcome variable is 'clicked vs did not click' use chi-square; if it is 'time on page in seconds' use a t-test.

What is the minimum sample size for chi-square?

Each expected cell count should be at least 5. If any cell has expected count < 5, use Fisher's Exact Test instead. Very small samples make chi-square unreliable.

What does a p-value of 0.03 mean in a chi-square test?

There is a 3% probability of observing a chi-square statistic this large (or larger) if the two variables are truly independent. Below the conventional 5% threshold, we reject the null hypothesis of independence.