A Statistical F-Test can be used to compare two variances, s1 and s2, by dividing them. The result is always a positive number (because variances are always positive). The equation for comparing two variances with the f-test is:
F = s21 / s22
How to compare two variance with the statistical F-Test
Step 1: If you are given standard deviations, go to Step 2. If you are given variances to compare, go to Step 3.
Step 2: Square both standard deviations to get the variances. For example, if σ1 = 9.6 and σ2 = 10.9, then the variances (s1 and s2) would be 9.62 = 92.16 and 10.92 = 118.81.
Step 3:Take the largest variance, and divide it by the smallest variance. For example, if your two variances were s1 = 2.5 and s2 = 9.4, divide 9.4 / 2.5 = 3.76.
Why? Placing the largest variance on top will force the F-test into a right tailed test, which is much easier to calculate than a left-tailed test.
Step 4:Look the critical value you calculated in Step 3 in the f-table. Note that there are several f-tables, so you’ll need to locate the right table for your alpha level. Unsure how to read an f-table? Read this article, which also includes a short article on how to read the f-table.