# In an ANOVA, what does F=1 mean?

Mar 5, 2016

When using a F-test to compare variances, a value of $F = 1$ implies that the two variances are equal.

#### Explanation:

An F-test is used to test if the variances of two populations are equal. The statistic we define to test this is the ratio of the two variances:

$F = {s}_{1}^{2} / {s}_{2}^{2}$

Where ${s}_{1}$ and ${s}_{2}$ are the sample variances. The further this value deviates from 1, the more likely that the underlying variances are actually different. The F-distribution is used to quantify this likelihood for differing sample sizes and the confidence or significance we would like the answer to hold.

A value of $F = 1$ means that no matter what significance level we use for the test, we will conclude that the two variances are equal.