2 × 2 Chi-Square Test
Test independence in a two-by-two count table without continuity correction.
Your numbers
Chi-square statistic
The chi-square approximation can be unreliable with small expected counts. No Yates correction is applied.
Scenario comparison
Up to three snapshots in this tab. Loading one replaces the current inputs.
Formula
χ²=N(ad−bc)²/((a+b)(c+d)(a+c)(b+d)); df=1
Test independence in a two-by-two count table without continuity correction.
Worked example
- Row 1, column 1 count
- 10
- Row 1, column 2 count
- 20
- Row 2, column 1 count
- 30
- Row 2, column 2 count
- 40
- Chi-square statistic
- 0.793650793651
- Degrees of freedom
- 1
- p-value
- 0.372998483613
- Smallest expected count
- 12
Scope and limitations
The chi-square approximation can be unreliable with small expected counts. No Yates correction is applied.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: f41d8fc00392 · Example checked: