A chi-square test answers questions like “is recovery related to treatment group?”.
How to use the Chi-Square Test Calculator
- Group 1, outcome yes (a)
- Group 1, outcome no (b)
- Group 2, outcome yes (c)
- Group 2, outcome no (d)
Results update as you type, and every field accepts the units shown in its menu.
How it works
The shortcut formula for 2×2 tables compares observed counts with those expected under independence; df = 1.
Inputs explained
| Field | What to enter |
|---|---|
| Group 1, outcome yes (a) | A number |
| Group 1, outcome no (b) | A number |
| Group 2, outcome yes (c) | A number |
| Group 2, outcome no (d) | A number |
What each result means
- Total = [Group 1, outcome yes (a)] + [Group 1, outcome no (b)] + [Group 2, outcome yes (c)] + [Group 2, outcome no (d)]
- Chi-square (χ²) = [Total]×([Group 1, outcome yes (a)]×[Group 2, outcome no (d)] – [Group 1, outcome no (b)]×[Group 2, outcome yes (c)])^2÷(([Group 1, outcome yes (a)] + [Group 1, outcome no (b)])×([Group 2, outcome yes (c)] + [Group 2, outcome no (d)])×([Group 1, outcome yes (a)] + [Group 2, outcome yes (c)])×([Group 1, outcome no (b)] + [Group 2, outcome no (d)]))
- p-value = 1 – chicdf([Chi-square (χ²)], 1)
- Phi coefficient = ([Group 1, outcome yes (a)]×[Group 2, outcome no (d)] – [Group 1, outcome no (b)]×[Group 2, outcome yes (c)])÷sqrt(([Group 1, outcome yes (a)] + [Group 1, outcome no (b)])×([Group 2, outcome yes (c)] + [Group 2, outcome no (d)])×([Group 1, outcome yes (a)] + [Group 2, outcome yes (c)])×([Group 1, outcome no (b)] + [Group 2, outcome no (d)]))
Example values
How the main result changes when Group 1, outcome yes changes and everything else stays at the example values above:
| Group 1, outcome yes (a) | p-value |
|---|---|
| 15 | 7.4740e-5 |
| 22.5 | 0.0027 |
| 30 | 0.0285 |
| 37.5 | 0.1368 |
| 45 | 0.3842 |
| 60 | 0.8617 |
Formula
χ² = n(ad − bc)² ÷ ((a + b)(c + d)(a + c)(b + d))Worked example
Inputs — Group 1, outcome yes (a): 30; Group 1, outcome no (b): 70; Group 2, outcome yes (c): 45; Group 2, outcome no (d): 55.
Results — Total = 200; Chi-square (χ²) = 4.8; p-value = 0.02846; Phi coefficient = -0.1549.
Frequently asked questions
When should I use Fisher’s exact test instead?
When any expected count is below 5.
Does chi-square show direction?
No; check the proportions or the sign of phi.
What formula does the Chi-Square Test Calculator use?
χ² = n(ad − bc)² ÷ ((a + b)(c + d)(a + c)(b + d)).