# CHAPTER 4Comparing Two Unrelated Samples: The Mann−Whitney U-Test and the Kolmogorov−Smirnov Two-Sample Test

## 4.1 Objectives

In this chapter, you will learn the following items:

- How to perform the Mann−Whitney
*U-*test.
- How to construct a median confidence interval based on the difference between two independent samples.
- How to perform the Kolmogorov−Smirnov two-sample test.
- How to perform the Mann−Whitney
*U-*test and the Kolmogorov−Smirnov two-sample test using SPSS^{®}.

## 4.2 Introduction

Suppose a teacher wants to know if his first-period's early class time has been reducing student performance. To test his idea, he compares the final exam scores of students in his first-period class with those in his fourth-period class. In this example, each score from one class period is independent, or unrelated, to the other class period.

The Mann−Whitney *U-*test and the Kolmogorov−Smirnov two-sample test are nonparametric statistical procedures for comparing two samples that are independent, or not related. The parametric equivalent to these tests is the *t*-test for independent samples.

In this chapter, we will describe how to perform and interpret a Mann−Whitney *U-*test and a Kolmogorov−Smirnov two-sample test. We will demonstrate both small samples and large samples for each test. We will also explain how to perform the procedure using SPSS. Finally, we offer varied examples of these nonparametric statistics from the literature.

## 4.3 Computing the Mann−Whitney *U**-*Test Statistic

The Mann−Whitney ...