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Chi-Square Test of IndependenceStatLens

Choose a dataset:

Paste data (CSV with two categorical columns):

Open a CSV, TSV, or JSON file:

Enter Observed Counts

Rows Columns

Row variable: Column variable:

Test Results

χ²	—
df	—
p-value	—

Observed Counts

Expected Counts

Chi-Square Test of Independence

Test whether two categorical variables are associated. The null hypothesis is fixed — H₀ says the variables are independent (not related) — so there is nothing to edit and no confidence interval. The test compares the counts you observe with the counts expected under independence: χ² = Σ(O−E)²/E, with df = (rows − 1)(columns − 1), and the p-value is the right tail.

Load raw data from the Datasets, Edit Data, or Open File/URL tab, then choose a Row variable and Column variable to cross-tabulate.
Or use the Enter Table tab to type observed counts directly — set the number of rows and columns, fill in the table, and click Load.
Click Compute to run the test. (This is the only inference page with a Compute button; the others update automatically.)
Read the results: the χ² statistic, degrees of freedom, and p-value, plus the observed and expected count tables. Every expected count should be at least 5 for the approximation to hold.

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