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.
H0 (null hypothesis): σ12 = σ22
HA (alternative hypothesis): σ12 ≠ σ22
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.