Chi-Square Test Calculator
Run a chi-square test of independence from a contingency table and interpret the association between categorical variables.
Formula / method
χ² = Σ (O−E)²/E.
How to use
Use data from the same population, sample or study definition and keep paired observations aligned.
Understanding a chi-square test
The chi-square test of independence asks whether two categorical variables show evidence of association. The statistic compares observed cell counts with the counts expected under independence.
Expected counts matter
Very small expected cell counts can make the usual chi-square approximation unreliable. The calculator reports the smallest expected count as a diagnostic; sparse tables may require a different method.
What this calculator answers
The Chi-Square Test Calculator uses the requested values to calculate the requested result. The core method is χ² = Σ (O−E)²/E.. This makes the assumptions visible so you can check whether the inputs match your situation.
How to get a useful result
Use data from the same population, sample or study definition and keep paired observations aligned.
How to interpret it
Statistical output describes the entered sample/model. It does not by itself prove causation, practical significance or that model assumptions are satisfied.
Before relying on the number
Recheck unusual inputs, confirm units and compare the result with any official quote, statement, specification or rule that applies to the real decision. Small changes in rates, time periods or measurements can materially change some results.