An **F-test **is used to test whether two population variances are equal.

The null and alternative hypotheses for the test are as follows:

**H**σ_{0}:_{1}^{2}= σ_{2}^{2}(the population variances are equal)**H**σ_{A}:_{1}^{2}≠ σ_{2}^{2}(the population variances are*not*equal)

The F-test is typically used to answer one of the following questions:

**1.** Do two samples come from populations with equal variances?

**2.** Does a new treatment or process reduce the variability of some current treatment or process?

The easiest way to perform an F-test in SAS is to use the **PROC TTEST** statement, which is used for performing t-tests but also performs an F-test by default.

The following example shows how to perform an F-test in SAS in practice.

**Example: F-Test in SAS**

Suppose we have the following dataset in SAS that contains information about the points scored by various basketball players on two different teams:

/*create dataset*/ data my_data; input team $ points; datalines; A 18 A 19 A 22 A 25 A 27 A 28 A 41 A 45 A 51 A 55 B 14 B 15 B 15 B 17 B 18 B 22 B 25 B 25 B 27 B 34 ; run; /*view dataset*/ proc print data=my_data;

Suppose we would like to perform an F-test to determine if the variance in points scored is equal between the two teams.

We can use the following syntax to do so:

**/*perform F-test for equal variances*/
proc ttest data=my_data;
class team;
var points;
run;**

The last table in the output titled **Equality of Variances** contains the F-test results.

From this table we can see:

- The F-Test statistic is
**4.39**. - The corresponding p-value is
**0.0383**.

Since this p-value is less than .05, we reject the null hypothesis of the F-test.

This means we have sufficient evidence to say that the variance in points scored by the two teams is *not* equal.

**Note**: If you perform a two sample t-test to determine if the mean points values are equal between the two teams, you would use the p-value for the row called **Satterthwaite** in the output since you cannot assume that the population variances are equal between the two groups.

**Additional Resources**

The following tutorials explain how to perform other common tasks in SAS:

How to Perform a One Sample t-Test in SAS

How to Perform a Two Sample t-Test in SAS

How to Perform a Paired Samples t-Test in SAS