### Introduction

In Section 45.1 we look at the sign test and the Wilcoxon signed-rank test. Each of these is a one-sample test which is used for hypotheses about the location (or “average” of some sort) of a single distribution. When we looked at
$t$
-tests in
**
HELM booklet
**
41 we saw how hypotheses concerning the mean of a single normal distribution could be tested using a one-sample
$t$
-test and the means of two normal populations could be compared using a two-sample
$t$
-test. In the same way we can have a two-sample nonparametric test to compare the locations of two distributions when we are unwilling to assume that the distribution is normal or belongs to some other particular type. In this Section we will look at one such test, the Wilcoxon rank-sum test.

#### Prerequisites

- be familiar with the general ideas and terms of significance tests
- be familiar with the ideas of a nonparametric test and rank-based tests as explained in Section 45.1
- be familiar with $t$ -tests
- be familiar with the general ideas of continuous distributions

#### Learning Outcomes

- decide when a Wilcoxon rank-sum test may be used
- use and interpret the results of a Wilcoxon rank-sum test

#### Contents

1 The Wilcoxon rank-sum test1.1 General comments about the Wilcoxon rank-sum test

1.2 Critical values for the Wilcoxon signed-rank test

1.3 Critical Values for the Wilcoxon Rank-Sum Test (5% Two-tail Values)

1.4 Critical Values for the Wilcoxon Rank-Sum Test (1% Two-tail Values)