Hypothesis Testing > F Test to Compare Two Variances
What is an F Test to Compare Two Variances?
A Statistical F Test uses an F Statistic 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
F Test to compare two variances by hand: Steps
These are the general steps to follow. Scroll down for a specific example (watch the video underneath the steps).
Step 3:Take the largest variance, and divide it by the smallest variance to get the f-value. 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:Find your degrees of freedom. Degrees of freedom is your sample size minus 1. As you have two samples (variance 1 and variance 2), you’ll have two degrees of freedom: one for the numerator and one for the denominator.
Step 5:Look the f-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 What is an f-table?.
Step 4:Compare your calculated value (Step 3) with the table f-value in Step 5. If the f-table value is smaller than the calculated value, you can reject the null hypothesis.
F Test to Compare Two Variances in Excel
If you have Excel on your computer, you can use it to run an F Test to Compare Two Variances. If you have to do the calculations by hand, you can use Excel to check your work. Check out this short video:
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