CONTENTS

PREFACE

PURPOSE OF THIS BOOK

INTENDED AUDIENCE

SPECIAL FEATURES OF THIS BOOK

A NOTE TO THE STUDENT

1: NONPARAMETRIC STATISTICS: AN INTRODUCTION

1.1 OBJECTIVES

1.2 INTRODUCTION

1.3 THE NONPARAMETRIC STATISTICAL PROCEDURES PRESENTED IN THIS BOOK

1.4 RANKING DATA

1.5 RANKING DATA WITH TIED VALUES

1.6 COUNTS OF OBSERVATIONS

1.7 SUMMARY

1.8 PRACTICE QUESTIONS

1.9 SOLUTIONS TO PRACTICE QUESTIONS

2: TESTING DATA FOR NORMALITY

2.1 OBJECTIVES

2.2 INTRODUCTION

2.3 DESCRIBING DATA AND THE NORMAL DISTRIBUTION

2.4 COMPUTING AND TESTING KURTOSIS AND SKEWNESS FOR SAMPLE NORMALITY

2.5 THE KOLMOGOROV–SMIRNOV ONE-SAMPLE TEST

2.6 SUMMARY

2.7 PRACTICE QUESTIONS

2.8 SOLUTIONS TO PRACTICE QUESTIONS

3: COMPARING TWO RELATED SAMPLES: THE WILCOXON SIGNED RANKS TEST

3.1 OBJECTIVES

3.2 INTRODUCTION

3.3 COMPUTING THE WILCOXON SIGNED RANKS TEST STATISTIC

3.4 EXAMPLES FROM THE LITERATURE

3.5 SUMMARY

3.6 PRACTICE QUESTIONS

3.7 SOLUTIONS TO PRACTICE QUESTIONS

4: COMPARING TWO UNRELATED SAMPLES: THE MANN–WHITNEY U-TEST

4.1 OBJECTIVES

4.2 INTRODUCTION

4.3 COMPUTING THE MANN–WHITNEY U-TEST STATISTIC

4.4 EXAMPLES FROM THE LITERATURE

4.5 SUMMARY

4.6 PRACTICE QUESTIONS

4.7 SOLUTIONS TO PRACTICE QUESTIONS

5: COMPARING MORE THAN TWO RELATED SAMPLES: THE FRIEDMAN TEST

5.1 OBJECTIVES

5.2 INTRODUCTION

5.3 COMPUTING THE FRIEDMAN TEST STATISTIC

5.4 EXAMPLES FROM THE LITERATURE

5.5 SUMMARY

5.6 PRACTICE QUESTIONS

5.7 SOLUTIONS TO PRACTICE QUESTIONS

6: COMPARING MORE THAN TWO UNRELATED SAMPLES: THE KRUSKAL–WALLIS H-TEST

6.1 OBJECTIVES

6.2 INTRODUCTION

6.3 COMPUTING THE KRUSKAL–WALLIS H-TEST STATISTIC

6.4 EXAMPLES FROM THE LITERATURE

6.5 SUMMARY

6.6 PRACTICE QUESTIONS

6.7 SOLUTIONS TO PRACTICE QUESTIONS

7: COMPARING VARIABLES OF ORDINAL OR DICHOTOMOUS SCALES: SPEARMAN RANK-ORDER, POINT-BISERIAL, AND BISERIAL CORRELATIONS

7.1 OBJECTIVES

7.2 INTRODUCTION

7.3 THE CORRELATION COEFFICIENT

7.4 COMPUTING THE SPEARMAN RANK-ORDER CORRELATION COEFFICIENT

7.5 COMPUTING THE POINT-BISERIAL AND BISERIAL CORRELATION COEFFICIENTS

7.6 EXAMPLES FROM THE LITERATURE

7.7 SUMMARY

7.8 PRACTICE QUESTIONS

7.9 SOLUTIONS TO PRACTICE QUESTIONS

8: TESTS FOR NOMINAL SCALE DATA: CHI-SQUARE AND FISHER EXACT TEST

8.1 OBJECTIVES

8.2 INTRODUCTION

8.3 THE CHI-SQUARE GOODNESS-OF-FIT TEST

8.4 THE CHI-SQUARE TEST FOR INDEPENDENCE

8.5 THE FISHER EXACT TEST

8.6 EXAMPLES FROM THE LITERATURE

8.7 SUMMARY

8.8 PRACTICE QUESTIONS

8.9 SOLUTIONS TO PRACTICE QUESTIONS

9: TEST FOR RANDOMNESS: THE RUNS TEST

9.1 OBJECTIVES

9.2 INTRODUCTION

9.3 THE RUNS TEST FOR RANDOMNESS

9.4 EXAMPLES FROM THE LITERATURE

9.5 SUMMARY

9.6 PRACTICE QUESTIONS

9.7 SOLUTIONS TO PRACTICE QUESTIONS

APPENDIX A: SPSS AT A GLANCE

A.1 INTRODUCTION

A.2 OPENING SPSS

A.3 INPUTTING DATA

A.4 ANALYZING DATA

A.5 THE SPSS OUTPUT

APPENDIX B: TABLES OF CRITICAL VALUES

BIBLIOGRAPHY

INDEX

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Library of Congress Cataloging-in-Publication Data:

Corder, Gregory W., 1972-

Nonparametric statistics for non-statisticians: a step-by-step approach/Gregory W. Corder, Dale I. Foreman.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-45461-9 (cloth)

1. Nonparametric statistics. I. Foreman, Dale I. II. Title.

QA278.8.C67 2009

519.5-dc22

2008049903

PREFACE

The social and behavioral sciences need the ability to use nonparametric statistics in research. Many studies in these areas involve data that are classified on the nominal or ordinal scale. At times, interval data from these fields lack parameters for classification as normal. Nonparametric statistics is a useful tool for analyzing such data.

PURPOSE OF THIS BOOK

This book is intended to provide a conceptual and procedural approach to nonparametric statistics. It is written in such a manner as to enable someone who does not have an extensive mathematical background to work through the process necessary to conduct the given statistical tests presented. In addition, the outcome includes a discussion of the final decision for each statistical test. Each chapter takes the reader through an example from the beginning hypotheses, through the statistical calculations, to the final decision vis-a-vis the hypothesis taken into account. The examples are then followed by a detailed, step-by-step analysis by using the computer program, SPSS®. Finally, research literature is identified that uses the respective nonparametric statistical tests.

INTENDED AUDIENCE

Although not limited as such, this book is written for graduate and undergraduate students in social science programs. As stated earlier, it is targeted at the student who does not have an especially strong mathematical background and can be used effectively by students with both strong and weak mathematical backgrounds.

SPECIAL FEATURES OF THIS BOOK

There are currently few books available that provide a practical and applied approach to teaching nonparametric statistics. Many books take a more theoretical approach to the instructional process that can leave students disconnected and frustrated, in need of supplementary material to give them the ability to apply the statistics taught.

It is hoped that this book will provide students with a concrete approach to performing the nonparametric statistical procedures, along with their application and interpretation. We chose these particular nonparametric procedures since they represent a breadth of the typical analyses found in social science research. It is our hope that students will confidently learn the content presented with the promise of future successful applications.

In addition, each statistical test includes a section that explains how to use the computer program, SPSS. However, the organization of the book provides effective instruction of the nonparametric statistical procedures for those individuals with or without the software. Therefore, instructors (and students) can focus on learning the tests with a calculator, SPSS, or both.

A NOTE TO THE STUDENT

We have written this book with you in mind. Each of us has had a great deal of experience working with students just like you. It has been our experience that most people outside of the fields of mathematics or hard sciences struggle with and/or are intimidated by statistics. Moreover, we have found that when statistical procedures are explicitly communicated in a step-by-step manner, almost anyone can use them.

This book begins with a brief introduction (Chapter 1) and is followed with an explanation of how to perform the crucial step of checking your data for normality (Chapter 2). The chapters that follow (Chapters 3-9) highlight several nonparametric statistical procedures. Each of the chapters focuses on a particular type of variable and/or sample condition.

Chapters 3-9 have a similar organization. They each explain the statistical methods included in the respective chapters. At least one sample problem is included for each test using a step-by-step approach. (In some cases, we provide additional sample problems when procedures differ between large and small samples.) Then, those same sample problems are demonstrated by using the statistical software package, SPSS. Whether or not your instructor incorporates SPSS, this section will give you the opportunity to learn how to use the program. Toward the end of each chapter, we identify examples of the tests in published research. Finally, we present sample problems with solutions.

As you seek to learn nonparametric statistics, we strongly encourage you to work through the sample problems. Then, using the sample problems as a reference, work through the problems at the end of the chapters and additional data sets provided.

GREGORY W. CORDER

DALE 1. FOREMAN

1

NONPARAMETRIC 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 for 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 apopulation using a simple random sample.

Many of the tests in a traditional, introductory statistics class 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,¹ 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 to adhere to the rules. If you are using an ordinal or nominal measurement scale, you might redesign your study to use an interval or ratio scale. (See Box 1.1 for a description of measurement scales.) Also, you may try to seek additional participants to enlarge your sample sizes. Unfortunately, there are times when one or neither of these changes is appropriate or even possible.

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

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Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

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Lesen Sie weiter in der vollständigen Ausgabe!