### Example 4.13 Performing a Sign Test Using Paired Data

This example demonstrates a sign test for paired data, which is a specific application of the tests for location discussed in Example 4.12.

The instructor from Example 4.4 is now interested in performing a sign test for the pairs of test scores in his college course. The following statements request basic statistical measures and tests for location:

```title 'Test Scores for a College Course';
ods select BasicMeasures TestsForLocation;
proc univariate data=Score;
var ScoreChange;
run;
```

The ODS SELECT statement restricts the output to the BasicMeasures and TestsForLocation tables; see the section ODS Table Names. The instructor is not willing to assume that the `ScoreChange` variable is normal or even symmetric, so he decides to examine the sign test. The large -value (0.7744) of the sign test provides insufficient evidence of a difference in test score medians.

Output 4.13.1: Sign Test for ScoreChange

 Test Scores for a College Course

The UNIVARIATE Procedure
Variable: ScoreChange (Change in Test Scores)

Basic Statistical Measures
Location Variability
Mean -3.08333 Std Deviation 13.33797
Median -3.00000 Variance 177.90152
Mode -5.00000 Range 51.00000
Interquartile Range 10.50000

 Note: The mode displayed is the smallest of 2 modes with a count of 2.

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t -0.80079 Pr > |t| 0.4402
Sign M -1 Pr >= |M| 0.7744
Signed Rank S -8.5 Pr >= |S| 0.5278

A sample program for this example, uniex03.sas, is available in the SAS Sample Library for Base SAS software.