F-Test Calculator (Equality of Variances)
Test whether two samples have the same variance — the F-test, with the warning about how badly it behaves when the data is not normal.
F is the ratio of the two sample variances, larger over smaller, compared against the F distribution on (n₁−1, n₂−1) degrees of freedom.
How the f-test calculator (equality of variances) works
F is the ratio of the two sample variances, larger over smaller, compared against the F distribution on (n₁−1, n₂−1) degrees of freedom.
It is notoriously sensitive to non-normality: heavy tails make it reject far too often, which is why using it as a preliminary screen before a t-test is bad practice. Levene's test is far more robust, and Welch's t-test removes the need for the question entirely.
Formula: F = s₁² / s₂², df = (n₁ − 1, n₂ − 1)
Worked examples
| Inputs | F statistic | Note |
|---|---|---|
| SDs of 12 and 8 | 2.25 | F = 2.25, p = 0.039 |
| Equal spread | 1 | F = 1, p = 1 |
| A large difference | 16 | F = 16 — strongly significant |
FAQFrequently asked questions
What does the F-test test?
Whether two samples come from populations with the same variance.
Why is it criticised?
Because it assumes normality strictly. With heavy-tailed data it rejects far more often than its stated 5%, so a "significant" result may say more about the tails than the variances.
Should I run it before a t-test?
No. A preliminary test inflates the overall error rate, and the fix — Welch's t-test — costs nothing. Just use Welch.
What is a more robust alternative?
Levene's test, or Brown-Forsythe, which use absolute deviations from the mean or median and are far less sensitive to shape.
Is this the same F as in ANOVA?
The same distribution, a different application. ANOVA compares between-group and within-group variance to test means; this compares two sample variances directly.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.