F-Test Calculator (Two Variances)
Test whether two samples have equal variances with the F-test — get the variance ratio F, degrees of freedom and a two-tailed p-value.
How it works
F = s²_larger ÷ s²_smaller · df = (n_larger − 1, n_smaller − 1) · two-tailed p = 2·P(F > F_obs)
The F-test checks whether two samples could plausibly share the same population variance. It takes the ratio of the two sample variances — larger over smaller so the statistic is at least 1 — and compares it to the F distribution. It is most often used as a preliminary check before choosing between a pooled and a Welch t-test, but it is quite sensitive to departures from normality.
Worked example
Sample 1 has variance about 4.6 and sample 2 about 82.6. F = 82.6 ÷ 4.6 ≈ 17.9 on (6, 6) degrees of freedom; the two-tailed p is roughly 0.003, so the variances differ significantly and a pooled t-test would be inappropriate.
Sources: F-test — Wikipedia
Frequently asked questions
Why divide the larger variance by the smaller one?
It forces F ≥ 1 so you always work in the upper tail of the F distribution, which is what standard tables and this calculator report. The two-tailed p-value is then twice that upper-tail probability.
What does a significant F-test tell me?
It suggests the two groups do not share a common variance. In that case prefer Welch’s t-test (which does not assume equal variances) over the pooled two-sample t-test.
Is the F-test robust to non-normal data?
Not very. Unlike the t-test, the F-test for variances is quite sensitive to non-normality. Levene’s or Bartlett’s test is often preferred when normality is doubtful.
Related calculators
For education — confirm the test assumptions (independence, sample size, roughly normal data) before drawing conclusions from a p-value.