Chi-Square Test of Independence

Tap a term to see what it means, or .

Calculate

Example: 50 patients got treatment A and 50 got B. With A, 30 improved and 20 didn't; with B, 18 improved and 32 didn't. Does improvement depend on the treatment? Change the values to work out your own case.

Observed frequencies O_ij One table row at a time: values separated by spaces or commas, rows by semicolons.

Step by step

What each term means

Chi-Square Statistic (χ²): Measures how far the observed table is from the one expected if the two variables were independent. The larger it is, the stronger the evidence of an association.
Double Sum (Σᵢ,ⱼ): Adds over every cell of the table: each row i and each column j. With r rows and c columns, the test has (r − 1)(c − 1) degrees of freedom.
Squared Difference ((Oᵢⱼ − Eᵢⱼ)²): The gap between the observed count in the cell and the expected one, squared so that deviations up and down don't cancel out.
Expected Frequency (Eᵢⱼ): The count the cell would have if the variables were independent: row total × column total ÷ grand total. Dividing by it puts each difference in proportion to the size of the cell.

When to use it, assumptions and alternatives: the chi-square test of independence in the statistical tests catalog.