# How to Perform an F-Test in SAS

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

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

• H0: σ12 = σ22 (the population variances are equal)
• HA: σ12 ≠ σ22 (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.