How to use the chi-square for a 2×2 table calculator
Test independence in a 2×2 contingency table. Enter a, b, c, d in the fields above; the chi-square χ², p-value (1 df), significant at 5%? are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a — a
- b — b
- c — c
- d — d
Worked example
With a = 30, b = 20, c = 15, d = 35, the calculator gives chi-square χ² ≈ 9.090909; p-value (1 df) ≈ 0.00256897; significant at 5%? ≈ Yes.
Frequently asked questions
What is the formula for the chi-square for a 2×2 table calculation?
Chi-square χ² = (a+b+c+d) × (a × d-b × c)^2 / ((a+b) × (c+d) × (a+c) × (b+d)). p-value (1 df) = 2 × (1-ncdf(√([Chi-square χ²]))). Significant at 5%? = [p-value (1 df)]<0.05?"Yes":"No". Here a is a, b is b, c is c, d is d.
What inputs do I need for the chi-square for a 2×2 table calculator?
You need a, b, c, d. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.