Work out chi square test of independence instantly with clear inputs, formula shown and shareable results.
The test of independence compares each cell with the count expected if the row and column variables were unrelated: row total times column total over the grand total. Degrees of freedom are (rows − 1)(columns − 1).
Expected count
Eᵢⱼ = (row total × column total) / grand total
Degrees of freedom
df = (r − 1)(c − 1)
χ² ≈ 4.0 on 2 df, giving p ≈ 0.135 — not enough evidence of association.
It rescales χ² to a 0-to-1 effect size, so large samples with trivial associations are not mistaken for strong ones.