What this calculator does
Degrees of freedom works out works out degrees of freedom for a one-sample, two-sample or chi-square test. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formula1-sample: df=n−1. 2-sample (equal var): df=n₁+n₂−2. Welch: df=(s₁²/n₁+s₂²/n₂)²÷[(s₁²/n₁)²/(n₁−1)+(s₂²/n₂)²/(n₂−1)]. Chi-square: df=(rows−1)(cols−1)
The inputs explained
| Field | What to enter |
|---|---|
| Sample size n₁ | A number. Starts at 15. |
| Sample size n₂ (0 if one-sample) | A number. Starts at 12. |
| Std deviation s₁ (for Welch) | A number. Starts at 2.1. |
| Std deviation s₂ (for Welch) | A number. Starts at 3.4. |
| Rows (for chi-square, 0 to skip) | A number. Starts at 3. |
| Columns (for chi-square, 0 to skip) | A number. Starts at 4. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with sample size n₁
Every other input is held at the calculator’s starting values while sample size n₁ varies. Select any row to load that scenario into the calculator.