The **F Test** is used to test whether or not the variances of two populations are equal.

The null hypothesis of the F test states that two populations have equal variances, while the alternative hypothesis states that two populations do *not* have equal variances.

**H _{0}** (null hypothesis): σ

_{1}

^{2}= σ

_{2}

^{2}

**H _{A}** (alternative hypothesis): σ

_{1}

^{2}≠ σ

_{2}

^{2}

This tutorial explains how to perform the F Test in Excel.

**F Test in Excel**

Suppose we have the following dataset that shows the scores on a particular test for two classes:

To compare the variances of these two groups, we choose to perform the F test. To perform the F test, click on the **Data Analysis** option in the top right corner of the *Data* tab.

**Note:** If you don’t see the Data Analysis option, you need to first ** load the Data Analysis Toolpak**.

Once you click the Data Analysis option, a new window will appear. Click on *F-Test Two-Sample for Variances* and then click *OK.*

In the *Variable 1 Range* box, select the range A2:A11.

In the *Variable 2 Range* box, select the range B2:B11.

In the *Output Range* box, select the location where you’d like the results of the F Test to appear. I chose cell D2. Then click *OK*.

The results of the F Test appear:

**How to Interpret the Results of the F Test**

The results of the F Test show that the mean test score for variable 1 (Class A) is 86.6 and the mean test score for variable 2 (Class B) is 80.9. However, for this test we’re only interested in comparing the variances of the two classes.

We see that the variance of test scores for variable 1 (Class A) is **70.93333 **and the variance of test scores for variable 2 (Class B) is **65.43333**. Although these two variances are different, the F test tells us whether or not this difference is *statistically significant* by comparing the F test statistic with the F critical value.

We see that the F test statistic is **1.084055**, which is found by dividing the variance of class A by the variance of class B (70.93333 / 65.43333 = 1.084055). We also see that the F critical value is **3.178893**.

Since the F test statistic (1.084055) is less than the F critical value (3.178893), we fail to reject the null hypothesis. This means we do not have sufficient evidence to say that the variances of these two groups are significantly different.

**Note:** If instead the F test statistic was *greater* than the F critical value, we would reject the null hypothesis and conclude that the difference in variances between the two groups was significantly different.