🧮 F-statistic Calculator
Compare the variability of two samples with an F-test. Enter each sample’s standard deviation and size to get the F-statistic and degrees of freedom.
What This Calculator Does
The F-statistic (or F-ratio) compares the variances of two independent samples to test whether they come from populations with equal variability. It’s also the core test statistic used inside ANOVA.
The Formula
The F-statistic is calculated by dividing the larger sample variance by the smaller one, so the result is always 1 or greater:
- F = larger variance ÷ smaller variance = (larger SD)² ÷ (smaller SD)²
- The numerator degrees of freedom is (n − 1) for whichever sample has the larger variance; the denominator degrees of freedom is (n − 1) for the other sample.
A larger F value suggests a bigger difference in variability between the two samples. To determine statistical significance, compare the F-statistic to a critical value from an F-distribution table using the reported degrees of freedom. This tool is for general educational and analytical use.