F-Test Calculator
Compare two sample variances with the F statistic.
F-Test Formula
The basic F statistic is the ratio of two variances: F = s₁² / s₂². This tool places the larger variance on top so the displayed F value is at least 1.
What It Tells You
An F statistic is commonly used when comparing variability or as part of broader statistical tests such as ANOVA and regression.
Understanding an F-Test
An F-test compares two variances by forming a ratio. It is often used when checking whether two samples show similar variability.
F-Test Example
If one sample variance is 25 and another is 16, the variance ratio is 1.5625 before comparing it with the appropriate F distribution.
Interpretation Notes
The result depends on sample sizes and degrees of freedom. Extreme variance ratios can indicate evidence that variability differs between groups.
Frequently Asked Questions
Can F be negative?
No. Variance ratios are nonnegative.
Does F = 1 mean equal sample variances?
Yes, the observed variances are equal.
Is the F-test sensitive to non-normal data?
Yes, strong departures from normality can affect it.
Methodology, Assumptions and Interpretation
An F-test for two variances uses the ratio of sample variances. It is sensitive to departures from normality, so robust alternatives may be preferable for skewed or heavy-tailed data; the numerator/denominator order also affects the reported statistic.