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Hypothesis Tests |

In the Two-Sample Test for Variances task, you can test whether two variables have different variances, or, if you have a single variable that contains values for two groups, you can determine whether the variance differs between the groups.

The data set analyzed in this example, Gpa, contains test scores for 224 students. The data include the students' grade point averages (the variable gpa), high school scores in mathematics, science, and English (the variables hsm, hss, and hse, respectively), and SAT math and verbal scores (the variables satm and satv, respectively).

Suppose that you want to examine the difference in grade point averages between males and females. You can use the two-sample test for variances to test whether the variance of the grade point average differs between males and females.

- Select
**Tools****Sample Data**... - Select GPA.
- Click
**OK**to create the sample data set in your Sasuser directory. - Select
**File****Open By SAS Name**... - Select Sasuser from the list of
**Libraries**. - Select Gpa from the list of members.
- Click
**OK**to bring the Gpa data set into the data table.

- Select
**Statistics****Hypothesis Tests****Two-Sample Test for Variances**... - Ensure that
**One variable**is selected in the box labeled**Groups are in**. - Select the variable gpa as the Dependent variable.
- Select the variable sex as the Group variable.

If your data are arranged so that the values for both groups are
contained in two variables, you can define the two groups
by checking the **Two variables** selection in the box
labeled **Groups are in**.

The null hypothesis for the test is that the two variances are equal (or, equivalently, that their ratio is equal to 1). You can specify the type of alternative hypothesis. The three choices are that Variance 1 is not equal to, is greater than, or is less than Variance 2. In Figure 8.14, the alternative hypothesis states that the two variances are not equal, which is the two-sided alternative hypothesis.

- Click on the
**Plots**button. - Select
**Box-&-whisker plot**. - Click
**OK**.

Figure 8.15 displays the Plots dialog with **
Box-&-whisker plot** selected. Note that the plot is constructed to
have a mean of zero.

Click **OK** in the Two-Sample Test for Variances dialog
to perform the hypothesis test.

The "Sample Statistics" table displays the variance of the variable
gpa for both females (0.6509) and males (0.5311).
The "Hypothesis Test" table displays the test statistics: the
*F* value is 1.23
and the resulting *p*-value is 0.3222. Thus, the data give no
evidence for rejecting the hypothesis of equal variances.

Figure 8.17 displays the box-and-whisker plot. Observations that fall beyond the whiskers are identified with a square symbol.

The box-and-whisker plot displays the amount of spread and the range for the two variables. The two groups do not appear to be appreciably different.

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