Chi-Square Independence Test
Test association between row and column categories.
How the chi-square independence test works
A chi-square independence test asks whether two categorical variables are associated in a contingency table. Expected counts under independence equal each row total times each column total divided by the grand total. The calculator compares every observed cell with that expectation, sums squared standardized differences, and reports degrees of freedom from rows minus one times columns minus one.
The default two-by-two table has rows 20, 30 and 30, 20. All row and column totals are 50, so every expected cell under independence is 25. Four deviations of magnitude five each contribute one, giving the verified chi-square statistic 4 with one degree of freedom. The output shows the expected table directly.
Reading chi-square independence test results privately
Rows and columns must represent mutually exclusive categories, and observations must be independent. Small expected counts can make the chi-square approximation unreliable; exact methods may be preferable for sparse two-by-two tables. The statistic shows evidence of association but not direction, effect size, or causation. Percentage tables should be converted back to counts. This chi-square independence test calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
How are expected counts calculated?
For each cell, multiply its row total by its column total and divide by the grand total.
How is this different from goodness of fit?
Independence uses a two-dimensional contingency table; goodness of fit compares one observed category distribution with specified expectations.
Is the chi-square independence test private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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