# CHAPTER 1Nonparametric Statistics: An Introduction

## 1.1 Objectives

In this chapter, you will learn the following items:

- The difference between parametric and nonparametric statistics.
- How to rank data.
- How to determine counts of observations.

## 1.2 Introduction

If you are using this book, it is possible that you have taken some type of introductory statistics class in the past. Most likely, your class began with a discussion about probability and later focused on particular methods of dealing with populations and samples. Correlations, *z*-scores, and *t*-tests were just some of the tools you might have used to describe populations and/or make inferences about a population using a simple random sample.

Many of the tests in a traditional, introductory statistics text are based on samples that follow certain assumptions called parameters. Such tests are called *parametric tests*. Specifically, parametric assumptions include samples that

- are randomly drawn from a normally distributed population,
- consist of independent observations, except for paired values,
- consist of values on an interval or ratio measurement scale,
- have respective populations of approximately equal variances,
- are adequately large,* and
- approximately resemble a normal distribution.

If any of your samples breaks one of these rules, you violate the assumptions of a parametric test. You do have some options, however.

You might change the nature of your study so that your data meet the needed parameters. For instance, if ...