How this calculator works
An F statistic compares two variance estimates. The variance-test mode preserves group order rather than placing the larger variance on top; select the corresponding alternative. The classical variance test assumes independent normal populations. ANOVA and overall regression tests use an upper tail and require their own error assumptions. Regression R-squared mode assumes an intercept and k predictors. Nested-model mode compares residual SSE for a full fit with K coefficients against a restricted fit excluding J coefficients on the same observations; it also inverts that relationship. Both models must use the same response and error assumptions.
Formula
Variance test: F = s1²/s2², df = (n1 - 1, n2 - 1). ANOVA: F = [SSbetween/(g - 1)]/[SSwithin/(n - g)]. Regression: F = (R²/k)/[(1 - R²)/(n - k - 1)]. Nested models: F = [(SSErestricted - SSEfull)/J]/[SSEfull/(n - K)].
Worked example
Variances 4 and 1 from samples of 11 each give F = 4 with df (10,10). With regression R squared 0.5, one predictor and n = 18, F = 16 with df (1,16).
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Frequently asked questions
Should the larger variance always be first?
No. This tool preserves your group order, which is essential for one-sided hypotheses.
Why is ANOVA right-tailed?
A large between-group to within-group ratio supplies evidence against equal means.
Does this test tolerate non-normal variances well?
The classical two-variance F test is sensitive to non-normality. Consider robust alternatives when its assumptions fail.