Nonparametric Statistics: A Step-by-Step Approach, 2nd Edition

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 ...