Chi-square test
Pearson's chi-square goodness-of-fit or contingency-table test of independence. Get the statistic, degrees of freedom and p-value. Runs in your browser, nothing is uploaded.
About this tool
The chi-square test checks whether observed category counts differ from what you'd expect under a null hypothesis. This tool runs both common variants of Pearson's χ² and reports the statistic, degrees of freedom, and the p-value.
Goodness-of-fit
Compare a single row of observed counts against an expected distribution.
Leave the expected box blank for an equal-frequency (uniform) null — e.g. testing
whether a die is fair. Or supply expected counts or ratios (like 9 3 3 1 for
a Mendelian cross); ratios are automatically rescaled to the observed total.
Degrees of freedom = k − 1, where k is the number of categories.
Contingency table (test of independence)
Pick contingency and paste an r × c table of observed counts — one row per line, cells separated by spaces, commas, or tabs. The test asks whether the row and column variables are independent. Expected counts are row-total × column-total ÷ grand-total, degrees of freedom = (r − 1)(c − 1), and the tool also reports Cramér's V as an effect-size measure (0 = no association, 1 = perfect association). For a 2×2 table you can enable Yates' continuity correction, which shrinks each |O−E| by 0.5 before squaring for a more conservative statistic.
Reading the result
A small p-value (conventionally p < 0.05) means the observed counts are unlikely under the null, so you reject it. The tool flags any cell whose expected count is below 5, where the chi-square approximation becomes unreliable.
Privacy
Everything runs in your browser via WebAssembly — your data is never uploaded. Also available from the gizza CLI and in chat (which return the values as structured JSON).
FAQ
Can I enter expected ratios instead of exact counts?
Yes. In goodness-of-fit mode the expected box accepts either counts or ratios —
whatever you type is rescaled so it sums to the observed total, so 9 3 3 1
works directly for a Mendelian 9:3:3:1 cross. The only requirements are that
every expected value is positive and that the number of expected values matches
the number of observed categories.
Why is Yates' continuity correction being ignored for my table?
Yates' correction only makes sense for a 2×2 contingency table, so the tool applies it there and silently skips it for anything larger (a 3×4 table gets the plain Pearson statistic even with the box ticked). It also has no effect in goodness-of-fit mode.
What does the "expected count below 5" warning mean?
The chi-square p-value is an approximation that breaks down when expected cell counts are small. The tool counts how many cells have an expected value under 5 and flags them; if any are flagged, treat the p-value as rough — for small 2×2 tables consider Fisher's exact test instead.
How do I format a contingency table?
One row per line, with cells separated by spaces, commas, or tabs. Every row must have the same number of columns, and the table needs at least 2 rows and 2 columns; counts must be non-negative and can't all be zero.
Developer & Automation Access
Run it from the terminal
Same engine as this page, headless — via the gizza CLI:
gizza tool chi-square-test 'mode=goodness-of-fit'New to the CLI? Get gizza →
Open it by URL
Pre-fill and auto-run this tool with query parameters — the names match the API/CLI:
https://gizza.ai/tools/chi-square-test/?mode=goodness-of-fit&observed=Goodness-of-fit%3A%2016%2015%2019%2017%2011%2013%20%20%20%C2%B7%20%20%20Contingency%3A%20one%20row%20per%20line&expected=e.g.%209%203%203%201&yates=trueMachine-readable descriptor: tool.json — title + parameters JSON Schema for agents.