Chi-Square Independence Test
Paste a contingency table (rows separated by newlines, columns by commas/spaces). Get χ² statistic, degrees of freedom, p-value, and effect size (Cramer's V for tables larger than 2×2).
Contingency table
One row per line. Numbers separated by commas or spaces.
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Result
Expected vs observed
What this test does (and doesn't) do
The chi-square test of independence answers one question: "are these two categorical variables associated?" It does NOT tell you how strong the association is, in what direction, or whether the relationship is causal. Always report effect size (we compute Cramer's V) along with the p-value.
Assumptions
- All expected cell counts should be ≥ 5. If not, use Fisher's exact test instead (we don't implement it; see R's
fisher.test). - Observations are independent.
- Sample is random (or at least representative).
Who uses it
- Market researchers checking if two survey variables are related.
- Biology students testing Mendelian ratios (goodness-of-fit version).
- A/B testers checking if conversion rates differ across segments.
Frequently asked questions
How do I use Chi-Square Independence Test step by step without mistakes?
Follow the order given in the usage section: Run a chi-square test of independence on a contingency table. Get χ² statistic, degrees of freedom, p-value, and effect-size (phi / Cramer's V). The step-by-step part matters less than the unit check that sits inside it. Confirm every unit matches the thing you are actually trying to measure before you press calculate - that single check catches more wrong answers than any other habit, and it costs about ten seconds.
What are the common mistakes when using Chi-Square Independence Test?
Most common mistakes come down to four habits: entering 20 when the field expects 0.2 because the field is a percentage; leaving a field blank and accepting the default without checking what it stands for; changing one input and reading a result that was calculated before the change; and quoting the output as an exact figure when the page describes it as a reference estimate. Press calculate again after any edit, and treat the number as a reference point rather than a final answer.
How do I read the result from Chi-Square Independence Test?
Read the final figure first, then come back to this section for the conditions behind it: Run a chi-square test of independence on a contingency table. Get χ² statistic, degrees of freedom, p-value, and effect-size (phi / Cramer's V). Keep two things apart: the number itself, which comes from the values you typed, and the assumptions it depends on, which decide whether that number is meaningful. The page sets out what a higher or lower result means for your case, so check that direction as well as the magnitude.
Can I act on the Chi-Square Independence Test result directly?
Treat it as one reference sheet before you decide, rather than as the answer itself: Run a chi-square test of independence on a contingency table. Get χ² statistic, degrees of freedom, p-value, and effect-size (phi / Cramer's V). The output describes a magnitude under the conditions you entered. It does not include what it actually costs to act, what might change while you act, or how the other side behaves. Before you commit, compare the result against reality and note which assumptions do not hold where you are.
What inputs does Chi-Square Independence Test need?
The inputs for this tool sit in the form area of the page - fill them in one at a time as prompted. Before you start, check that each one uses the unit you actually measured: mismatched units are the most common source of a wrong answer here.
What should I check before I run Chi-Square Independence Test?
Three checks pay for themselves. First, confirm the question you need answered is really inside the scope of this tool rather than a neighbouring one. Second, confirm that the figures you have are drawn from the same source and the same period - mixing monthly and annual numbers, or two different definitions of the same quantity, quietly distorts the result. Third, keep the key inputs written down, so that later you can tell which set of numbers produced a figure you are about to quote.
Who is Chi-Square Independence Test for, and who should not use it?
It suits people who already have concrete numbers and want a quick sense of scale - drafting a budget, aligning on a figure with a colleague, or sanity-checking an estimate before a meeting. It is not for people who need an exact value they can promise to a third party, and it is not for people who have not yet agreed what each input means. Spending a few minutes settling the definitions first is far cheaper than re-running the numbers afterwards.