F-distribution
The F-distribution is the right-skewed sampling distribution of a ratio of two independent variance estimates, indexed by numerator and denominator degrees of freedom, supplying critical values for the F-test and ANOVA.
What it is
See it move
Line A's sample variance is 36 from 13 units, giving 12 degrees of freedom. Line B's sample variance is 9 from 9 units, giving 8 degrees of freedom. The F statistic is F = 36 ÷ 9 = 4.00, with 12 numerator and 8 denominator degrees of freedom, checked against the right-skewed F-distribution to decide whether the two lines' variability genuinely differs.
The formula
Variables
- Sample variance of the first group
- Sample variance of the second group
Gives the F statistic used to test whether two independent samples come from populations with equal variance, referenced against the F-distribution with (n1 − 1) and (n2 − 1) degrees of freedom.
Check yourself
Quality analysts compare the variability of delivery times from two suppliers. Supplier X's delivery times have a sample variance of 25 days² from a sample of 10 deliveries. Supplier Y's delivery times have a sample variance of 5 days² from a sample of 7 deliveries. What is the F statistic for testing equality of variances, computed as Supplier X's variance over Supplier Y's?