# CHAPTER 3Comparing Two Related Samples: The Wilcoxon Signed Rank and the Sign Test

## 3.1 Objectives

In this chapter, you will learn the following items:

- How to compute the Wilcoxon signed rank test.
- How to perform the Wilcoxon signed rank test using SPSS
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- How to construct a median confidence interval based on the Wilcoxon signed rank test for matched pairs.
- How to compute the sign test.
- How to perform the sign test using SPSS.

## 3.2 Introduction

Imagine that you give an attitude test to a small group of people. After you deliver some type of treatment, say, a daily vitamin C supplement for several weeks, you give that same group of people another attitude test. Finally, you compare the two measures of attitude to see if there is any type of difference between the two sets of scores.

The two sets of test scores in the previous scenario are related or paired. This is because each person was tested twice. In other words, each test score in one group of scores has another test score counterpart. The Wilcoxon signed rank test and the sign test are nonparametric statistical procedures for comparing two samples that are paired or related. The parametric equivalent to these tests goes by names such as the Student's *t*-test, *t*-test for matched pairs, *t*-test for paired samples, or *t*-test for dependent samples.

In this chapter, we will describe how to perform and interpret a Wilcoxon signed rank test and a sign test, using both small samples and large samples. In addition, we demonstrate ...