Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 14

Nonparametric Tests

The focus of this chapter is the development of some commonly used nonparametric procedures. The topics covered are:

• The one-sample and two-sample sign test
• The Mann-Whitney (Wilcoxon) W test for two samples
• Run tests: runs above and below the median and the Wald-Wolfowitz run test
• Spearman rank correlation

Learning Outcomes:

After studying this chapter, the reader will be able to

• Use a nonparametric method for testing hypotheses about a location parameter when the sample is drawn from one population.
• Use a nonparametric method for testing hypotheses about location parameters when samples are drawn from two populations.
• Perform a nonparametric test of whether or not the sample at hand is a random sample.
• Investigate whether or not there is some association between two variables.

14.1 Introduction

In Chapter 9 we discussed various statistical tests based on the assumption that the samples involved are drawn from normal populations. There are many situations in which we know little about the shape of the population distribution from which the samples are drawn, and in such cases the assumption of normality may be hazardous. There is a class of statistical tests that are valid for samples from continuous population distributions of any shape. These are called nonparametric tests, and they are based on order statistics. In this chapter we consider several of the simplest and most widely used of these tests. Throughout this chapter we assume that the ...