Degrees of Freedom Calculator
Find degrees of freedom for t-tests, chi-square independence and one-way ANOVA.
Formula
One sample: n−1; pooled: n+k−2; χ²: (n−1)(k−1); ANOVA: k−1, n−k, n−1; Welch uses variance-weighted df.
Degrees of freedom ≈ (30)-1
How to use
- Choose the test or ANOVA component.
- Set n and k: sample sizes; rows/columns for χ²; total/group count for ANOVA.
- Enter sample variances only for Welch and read df.
Examples
- 30 observations in 3 ANOVA groups give within-group df=27.
Frequently asked questions
What are n and k?
For one sample use n only; for two samples they are the two sample sizes.
Can df be fractional?
Yes, Welch uses (v₁/n+v₂/k)²/[(v₁/n)²/(n−1)+(v₂/k)²/(k−1)].
What assumptions apply?
Pooled t needs equal variances; Welch needs positive sample variances. ANOVA requires n>k. This does not run the test.
Sources
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