Chi Square Test Of Independence Calculator

Work out chi square test of independence instantly with clear inputs, formula shown and shareable results.

About Chi Square Test Of Independence Calculator

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).

Formulas

Expected count

Eᵢⱼ = (row total × column total) / grand total

Degrees of freedom

df = (r − 1)(c − 1)

Worked example

With the default values below, Chi Square Test Of Independence Calculator returns Chi-square statistic of 4.16666667. Change any input above and every figure here is recalculated in your browser.

Inputs used

First row of the table: 20, 30
Second row: 25, 25
Third row (optional): 15, 35

Results

Chi-square statistic: 4.16666667
p value: 0.12451447
Degrees of freedom: 2
Cramér's V effect size: 0.16666667

Step by step

1Values used
2Expected count
3Degrees of freedom
4Chi-square statistic= 4.16666667
5p value= 0.12451447
6Degrees of freedom= 2
7Cramér's V effect size= 0.16666667

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the sample 3 × 2 table?

χ² ≈ 4.0 on 2 df, giving p ≈ 0.135 — not enough evidence of association.

What does Cramér's V add?

It rescales χ² to a 0-to-1 effect size, so large samples with trivial associations are not mistaken for strong ones.