a. To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs, in equal numbers, to receive either 4 or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. What type of design is this, and what type of statistic is needed to analyze the data?b. Dr. Bill Board designs a 2 X 2 between-subjects factorial design, where Factor A is word frequency (low or high) and Factor B is category cues (no cues or cues). Assume that the data are interval. What type of statistic is needed to analyze the data?

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STATISTICS

Eleventh Edition

Robert S. Witte

Emeritus, San Jose State University

John S. Witte

University of California, San Francisco

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Abidha Sulaiman

M.C. Escher’s Spirals © The M.C. Escher Company

– The Netherlands

This book was set in 10/11 Times LT Std by SPi Global and printed and bound by Lightning Source Inc. The

cover was printed by Lightning Source Inc.

Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding for

more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our

company is built on a foundation of principles that include responsibility to the communities we serve and

where we live and work. In 2008, we launched a Corporate Citizenship Initiative, a global effort to address

the environmental, social, economic, and ethical challenges we face in our business. Among the issues we are

addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and

among our vendors, and community and charitable support. For more information, please visit our website:

www.wiley.com/go/citizenship.

Copyright © 2017, 2010, 2007 John Wiley & Sons, Inc. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by

any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission

of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923 (Web site: www.copyright.com). Requests to

the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc.,

111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, or online at: www.wiley.

com/go/permissions.

Evaluation copies are provided to qualified academics and professionals for review purposes only, for use

in their courses during the next academic year. These copies are licensed and may not be sold or transferred

to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return

instructions and a free of charge return shipping label are available at: www.wiley.com/go/returnlabel. If you

have chosen to adopt this textbook for use in your course, please accept this book as your complimentary

desk copy. Outside of the United States, please contact your local sales representative.

ISBN: 978-1-119-25451-5(PBK)

ISBN: 978-1-119-25445-4(EVALC)

Library of Congress Cataloging-in-Publication Data

Names: Witte, Robert S. | Witte, John S.

Title: Statistics / Robert S. Witte, Emeritus, San Jose State University,

John S. Witte, University of California, San Francisco.

Description: Eleventh edition. | Hoboken, NJ: John Wiley & Sons, Inc.,

[2017] | Includes index.

Identifiers: LCCN 2016036766 (print) | LCCN 2016038418 (ebook) | ISBN

9781119254515 (pbk.) | ISBN 9781119299165 (epub)

Subjects: LCSH: Statistics.

Classification: LCC QA276.12 .W57 2017 (print) | LCC QA276.12 (ebook) | DDC

519.5—dc23

LC record available at https://lccn.loc.gov/2016036766

The inside back cover will contain printing identification and country of origin if omitted from this page.

In addition, if the ISBN on the back cover differs from the ISBN on this page, the one on the back cover

is correct.

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To Doris

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Preface

TO THE READER

Students often approach statistics with great apprehension. For many, it is a required

course to be taken only under the most favorable circumstances, such as during a quarter or semester when carrying a light course load; for others, it is as distasteful as a visit

to a credit counselor—to be postponed as long as possible, with the vague hope that

mounting debts might miraculously disappear. Much of this apprehension doubtless

rests on the widespread fear of mathematics and mathematically related areas.

This book is written to help you overcome any fear about statistics. Unnecessary

quantitative considerations have been eliminated. When not obscured by mathematical

treatments better reserved for more advanced books, some of the beauty of statistics, as

well as its everyday usefulness, becomes more apparent.

You could go through life quite successfully without ever learning statistics. Having

learned some statistics, however, you will be less likely to flinch and change the topic

when numbers enter a discussion; you will be more skeptical of conclusions based on

loose or erroneous interpretations of sets of numbers; you might even be more inclined

to initiate a statistical analysis of some problem within your special area of interest.

TO THE INSTRUCTOR

Largely because they panic at the prospect of any math beyond long division, many

students view the introductory statistics class as cruel and unjust punishment. A halfdozen years of experimentation, first with assorted handouts and then with an extensive

set of lecture notes distributed as a second text, convinced us that a book could be written for these students. Representing the culmination of this effort, the present book

provides a simple overview of descriptive and inferential statistics for mathematically

unsophisticated students in the behavioral sciences, social sciences, health sciences,

and education.

PEDAGOGICAL FEATURES

• Basic concepts and procedures are explained in plain English, and a special effort

has been made to clarify such perennially mystifying topics as the standard deviation, normal curve applications, hypothesis tests, degrees of freedom, and analysis of variance. For example, the standard deviation is more than a formula; it

roughly reflects the average amount by which individual observations deviate

from their mean.

• Unnecessary math, computational busy work, and subtle technical distinctions

are avoided without sacrificing either accuracy or realism. Small batches of data

define most computational tasks. Single examples permeate entire chapters or

even several related chapters, serving as handy frames of reference for new concepts and procedures.

iv

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P R E FA C E

v

• Each chapter begins with a preview and ends with a summary, lists of important

terms and key equations, and review questions.

• Key statements appear in bold type, and step-by-step summaries of important

procedures, such as solving normal curve problems, appear in boxes.

• Important definitions and reminders about key points appear in page margins.

• Scattered throughout the book are examples of computer outputs for three of the

most prevalent programs: Minitab, SPSS, and SAS. These outputs can be either

ignored or expanded without disrupting the continuity of the text.

• Questions are introduced within chapters, often section by section, as Progress

Checks. They are designed to minimize the cumulative confusion reported by

many students for some chapters and by some students for most chapters. Each

chapter ends with Review Questions.

• Questions have been selected to appeal to student interests: for example, probability calculations, based on design flaws, that re-create the chillingly high likelihood of the Challenger shuttle catastrophe (8.18, page 165); a t test analysis of

global temperatures to evaluate a possible greenhouse effect (13.7, page 244);

and a chi-square test of the survival rates of cabin and steerage passengers aboard

the Titanic (19.14, page 384).

• Appendix B supplies answers to questions marked with asterisks. Other appendices provide a practical math review complete with self-diagnostic tests, a glossary of important terms, and tables for important statistical distributions.

INSTRUCTIONAL AIDS

An electronic version of an instructor’s manual accompanies the text. The instructor’s

manual supplies answers omitted in the text (for about one-third of all questions), as well

as sets of multiple-choice test items for each chapter, and a chapter-by-chapter commentary

that reflects the authors’ teaching experiences with this material. Instructors can access

this material in the Instructor Companion Site at http://www.wiley.com/college/witte.

An electronic version of a student workbook, prepared by Beverly Dretzke of the

University of Minnesota, also accompanies the text. Self-paced and self-correcting, the

workbook contains problems, discussions, exercises, and tests that supplement the text.

Students can access this material in the Student Companion Site at http://www.wiley.

com/college/witte.

CHANGES IN THIS EDITION

• Update discussion of polling and random digit dialing in Section 8.4

• A new Section 14.11 on the “file drawer effect,” whereby nonsignificant statistical findings are never published and the importance of replication.

• Updated numerical examples.

• New examples and questions throughout the book.

• Computer outputs and website have been updated.

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vi

P R E FA C E

USING THE BOOK

The book contains more material than is covered in most one-quarter or one-semester

courses. Various chapters can be omitted without interrupting the main development.

Typically, during a one-semester course we cover the entire book except for analysis of

variance (Chapters 16, 17, and 18) and tests of ranked data (Chapter 20). An instructor

who wishes to emphasize inferential statistics could skim some of the earlier chapters,

particularly Normal Distributions and Standard Scores (z) (Chapter 5), and Regression

(Chapter 7), while an instructor who desires a more applied emphasis could omit Populations, Samples, and Probability (Chapter 8) and More about Hypothesis Testing

(Chapter 11).

ACKNOWLEDGMENTS

The authors wish to acknowledge their immediate family: Doris, Steve, Faith, Mike,

Sharon, Andrea, Phil, Katie, Keegan, Camy, Brittany, Brent, Kristen, Scott, Joe, John,

Jack, Carson, Sam, Margaret, Gretchen, Carrigan, Kedrick, and Alika. The first author

also wishes to acknowledge his brothers and sisters: Henry, the late Lila, J. Stuart, A.

Gerhart, and Etz; deceased parents: Henry and Emma; and all friends and relatives,

past and present, including Arthur, Betty, Bob, Cal, David, Dick, Ellen, George, Grace,

Harold, Helen, John, Joyce, Kayo, Kit, Mary, Paul, Ralph, Ruth, Shirley, and Suzanne.

Numerous helpful comments were made by those who reviewed the current and

previous editions of this book: John W. Collins, Jr., Seton Hall University; Jelani Mandara, Northwestern University; L. E. Banderet, Northeastern University; S. Natasha

Beretvas, University of Texas at Austin; Patricia M. Berretty, Fordham University;

David Coursey, Florida State University; Shelia Kennison, Oklahoma State University; Melanie Kercher, Sam Houston State University; Jennifer H. Nolan, Loyola

Marymount University; and Jonathan C. Pettibone, University of Alabama in Huntsville; Kevin Sumrall, Montgomery College; Sky Chafin, Grossmont College; Christine

Ferri, Richard Stockton College of NJ; Ann Barich, Lewis University.

Special thanks to Carson Witte who proofread the entire manuscript twice.

Excellent editorial support was supplied by the people at John Wiley & Sons, Inc.,

most notably Abidha Sulaiman and Gladys Soto.

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Contents

PREFACE

iv

ACKNOWLEDGMENTS

1

INTRODUCTION

vi

1

1.1

WHY STUDY STATISTICS? 2

1.2

WHAT IS STATISTICS? 2

1.3

MORE ABOUT INFERENTIAL STATISTICS

1.4

THREE TYPES OF DATA 6

1.5

LEVELS OF MEASUREMENT 7

1.6

TYPES OF VARIABLES 11

1.7

HOW TO USE THIS BOOK 15

Summary 16

Important Terms 17

Review Questions 17

3

PART 1 Descriptive Statistics: Organizing

and Summarizing Data 21

2

DESCRIBING DATA WITH TABLES AND GRAPHS

TABLES (FREQUENCY DISTRIBUTIONS)

2.1

2.2

2.3

2.4

2.5

2.6

2.7

22

23

FREQUENCY DISTRIBUTIONS FOR QUANTITATIVE DATA 23

GUIDELINES 24

OUTLIERS 27

RELATIVE FREQUENCY DISTRIBUTIONS 28

CUMULATIVE FREQUENCY DISTRIBUTIONS 30

FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA

INTERPRETING DISTRIBUTIONS CONSTRUCTED BY OTHERS 32

GRAPHS

31

33

2.8

GRAPHS FOR QUANTITATIVE DATA 33

2.9

TYPICAL SHAPES 37

2.10 A GRAPH FOR QUALITATIVE (NOMINAL) DATA

2.11 MISLEADING GRAPHS 40

2.12 DOING IT YOURSELF 41

Summary 42

Important Terms 43

Review Questions 43

39

vii

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viii

CONTENTS

3

DESCRIBING DATA WITH AVERAGES

47

3.1

MODE 48

3.2

MEDIAN 49

3.3

MEAN 51

3.4

WHICH AVERAGE? 53

3.5

AVERAGES FOR QUALITATIVE AND RANKED DATA

Summary 56

Important Terms 57

Key Equation 57

Review Questions 57

4

DESCRIBING VARIABILITY

55

60

4.1

INTUITIVE APPROACH 61

4.2

RANGE 62

4.3

VARIANCE 63

4.4

STANDARD DEVIATION 64

4.5

DETAILS: STANDARD DEVIATION 67

4.6

DEGREES OF FREEDOM (df ) 75

4.7

INTERQUARTILE RANGE (IQR) 76

4.8

MEASURES OF VARIABILITY FOR QUALITATIVE AND RANKED DATA

Summary 78

Important Terms 79

Key Equations 79

Review Questions 79

5

NORMAL DISTRIBUTIONS AND STANDARD (z) SCORES

5.1

THE NORMAL CURVE 83

5.2

z SCORES 86

5.3

STANDARD NORMAL CURVE 87

5.4

SOLVING NORMAL CURVE PROBLEMS

5.5

FINDING PROPORTIONS 90

5.6

FINDING SCORES 95

5.7

MORE ABOUT z SCORES 100

Summary 103

Important Terms 103

Key Equations 103

Review Questions 103

6

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82

89

DESCRIBING RELATIONSHIPS: CORRELATION

6.1

6.2

6.3

6.4

6.5

6.6

78

107

AN INTUITIVE APPROACH 108

SCATTERPLOTS 109

A CORRELATION COEFFICIENT FOR QUANTITATIVE DATA: r

DETAILS: COMPUTATION FORMULA FOR r 117

OUTLIERS AGAIN 118

OTHER TYPES OF CORRELATION COEFFICIENTS 119

113

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CONTENTS

ix

6.7

COMPUTER OUTPUT 120

Summary 123

Important Terms and Symbols 124

Key Equations 124

Review Questions 124

7

REGRESSION

126

7.1

TWO ROUGH PREDICTIONS 127

7.2

A REGRESSION LINE 128

7.3

LEAST SQUARES REGRESSION LINE 130

7.4

STANDARD ERROR OF ESTIMATE, sy |x 133

7.5

ASSUMPTIONS 135

7.6

INTERPRETATION OF r 2 136

7.7

MULTIPLE REGRESSION EQUATIONS 141

7.8

REGRESSION TOWARD THE MEAN 141

Summary 143

Important Terms 144

Key Equations 144

Review Questions 144

PART 2 Inferential Statistics: Generalizing

Beyond Data 147

8

POPULATIONS, SAMPLES, AND PROBABILITY

POPULATIONS AND SAMPLES

8.1

8.2

8.3

8.4

8.5

8.6

149

POPULATIONS 149

SAMPLES 150

RANDOM SAMPLING 151

TABLES OF RANDOM NUMBERS 151

RANDOM ASSIGNMENT OF SUBJECTS

SURVEYS OR EXPERIMENTS? 154

PROBABILITY

153

155

8.7

DEFINITION 155

8.8

ADDITION RULE 156

8.9

MULTIPLICATION RULE 157

8.10 PROBABILITY AND STATISTICS

Summary 162

Important Terms 163

Key Equations 163

Review Questions 163

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148

161

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x

CONTENTS

9

SAMPLING DISTRIBUTION OF THE MEAN

168

9.1

WHAT IS A SAMPLING DISTRIBUTION? 169

9.2

CREATING A SAMPLING DISTRIBUTION FROM SCRATCH

9.3

SOME IMPORTANT SYMBOLS 173

9.4

MEAN OF ALL SAMPLE MEANS (μ ) 173

X

9.5

STANDARD ERROR OF THE MEAN (σ ) 174

X

9.6

SHAPE OF THE SAMPLING DISTRIBUTION 176

9.7

OTHER SAMPLING DISTRIBUTIONS 178

Summary 178

Important Terms 179

Key Equations 179

Review Questions 179

10

INTRODUCTION TO HYPOTHESIS TESTING: THE z TEST

170

182

10.1 TESTING A HYPOTHESIS ABOUT SAT SCORES 183

10.2 z TEST FOR A POPULATION MEAN 185

10.3 STEP-BY-STEP PROCEDURE 186

10.4 STATEMENT OF THE RESEARCH PROBLEM 187

10.5 NULL HYPOTHESIS (H0) 188

10.6 ALTERNATIVE HYPOTHESIS (H1) 188

10.7 DECISION RULE 189

10.8 CALCULATIONS 190

10.9 DECISION 190

10.10 INTERPRETATION 191

Summary 191

Important Terms 192

Key Equations 192

Review Questions 193

11

MORE ABOUT HYPOTHESIS TESTING

195

11.1 WHY HYPOTHESIS TESTS? 196

11.2 STRONG OR WEAK DECISIONS 197

11.3 ONE-TAILED AND TWO-TAILED TESTS 199

11.4 CHOOSING A LEVEL OF SIGNIFICANCE ( ) 202

11.5 TESTING A HYPOTHESIS ABOUT VITAMIN C 203

11.6 FOUR POSSIBLE OUTCOMES 204

11.7 IF H0 REALLY IS TRUE 206

11.8 IF H0 REALLY IS FALSE BECAUSE OF A LARGE EFFECT 207

11.9 IF H0 REALLY IS FALSE BECAUSE OF A SMALL EFFECT 209

11.10 INFLUENCE OF SAMPLE SIZE 211

11.11 POWER AND SAMPLE SIZE 213

Summary 216

Important Terms 217

Review Questions 218

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CONTENTS

12

xi

ESTIMATION (CONFIDENCE INTERVALS)

221

12.1 POINT ESTIMATE FOR μ 222

12.2 CONFIDENCE INTERVAL (CI) FOR μ 222

12.3 INTERPRETATION OF A CONFIDENCE INTERVAL 226

12.4 LEVEL OF CONFIDENCE 226

12.5 EFFECT OF SAMPLE SIZE 227

12.6 HYPOTHESIS TESTS OR CONFIDENCE INTERVALS? 228

12.7 CONFIDENCE INTERVAL FOR POPULATION PERCENT 228

Summary 230

Important Terms 230

Key Equation 230

Review Questions 231

13

t TEST FOR ONE SAMPLE

233

13.1 GAS MILEAGE INVESTIGATION 234

13.2 SAMPLING DISTRIBUTION OF t 234

13.3 t TEST 237

13.4 COMMON THEME OF HYPOTHESIS TESTS 238

13.5 REMINDER ABOUT DEGREES OF FREEDOM 238

13.6 DETAILS: ESTIMATING THE STANDARD ERROR (s X )

13.7 DETAILS: CALCULATIONS FOR THE t TEST 239

13.8 CONFIDENCE INTERVALS FOR BASED ON t 241

13.9 ASSUMPTIONS 242

Summary 242

Important Terms 243

Key Equations 243

Review Questions 243

14

t TEST FOR TWO INDEPENDENT SAMPLES

238

245

14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

EPO EXPERIMENT 246

STATISTICAL HYPOTHESES 247

SAMPLING DISTRIBUTION OF X1 – X 2 248

t TEST 250

DETAILS: CALCULATIONS FOR THE t TEST 252

p-VALUES 255

STATISTICALLY SIGNIFICANT RESULTS 258

ESTIMATING EFFECT SIZE: POINT ESTIMATES AND CONFIDENCE

INTERVALS 259

14.9 ESTIMATING EFFECT SIZE: COHEN’S d 262

14.10 META-ANALYSIS 264

14.11 IMPORTANCE OF REPLICATION 264

14.12 REPORTS IN THE LITERATURE 265

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xii

CONTENTS

14.13 ASSUMPTIONS 266

14.14 COMPUTER OUTPUT 267

Summary 268

Important Terms 268

Key Equations 269

Review Questions 269

15

t TEST FOR TWO RELATED SAMPLES (REPEATED MEASURES)

15.1 EPO EXPERIMENT WITH REPEATED MEASURES 274

15.2 STATISTICAL HYPOTHESES 277

15.3 SAMPLING DISTRIBUTION OF D 277

15.4 t TEST 278

15.5 DETAILS: CALCULATIONS FOR THE t TEST 279

15.6 ESTIMATING EFFECT SIZE 281

15.7 ASSUMPTIONS 283

15.8 OVERVIEW: THREE t TESTS FOR POPULATION MEANS 283

15.9 t TEST FOR THE POPULATION CORRELATION COEFFICIENT, ρ

Summary 287

Important Terms 288

Key Equations 288

Review Questions 288

16

ANALYSIS OF VARIANCE (ONE FACTOR)

273

285

292

16.1

TESTING A HYPOTHESIS ABOUT SLEEP DEPRIVATION

AND AGGRESSION 293

16.2 TWO SOURCES OF VARIABILITY 294

16.3 F TEST 296

16.4 DETAILS: VARIANCE ESTIMATES 299

16.5 DETAILS: MEAN SQUARES (MS ) AND THE F RATIO 304

16.6 TABLE FOR THE F DISTRIBUTION 305

16.7 ANOVA SUMMARY TABLES 307

16.8 F TEST IS NONDIRECTIONAL 308

16.9 ESTIMATING EFFECT SIZE 308

16.10 MULTIPLE COMPARISONS 311

16.11 OVERVIEW: FLOW CHART FOR ANOVA 315

16.12 REPORTS IN THE LITERATURE 315

16.13 ASSUMPTIONS 316

16.14 COMPUTER OUTPUT 316

Summary 317

Important Terms 318

Key Equations 318

Review Questions 319

17

ANALYSIS OF VARIANCE (REPEATED MEASURES)

17.1

17.2

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322

SLEEP DEPRIVATION EXPERIMENT WITH REPEATED MEASURES

F TEST 324

323

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CONTENTS

xi i i

17.3 TWO COMPLICATIONS 325

17.4 DETAILS: VARIANCE ESTIMATES 326

17.5 DETAILS: MEAN SQUARE (MS ) AND THE F RATIO

17.6 TABLE FOR F DISTRIBUTION 331

17.7 ANOVA SUMMARY TABLES 331

17.8 ESTIMATING EFFECT SIZE 333

17.9 MULTIPLE COMPARISONS 333

17.10 REPORTS IN THE LITERATURE 335

17.11 ASSUMPTIONS 336

Summary 336

Important Terms 336

Key Equations 337

Review Questions 337

18

ANALYSIS OF VARIANCE (TWO FACTORS)

329

339

18.1 A TWO-FACTOR EXPERIMENT: RESPONSIBILITY IN CROWDS

18.2 THREE F TESTS 342

18.3 INTERACTION 344

18.4 DETAILS: VARIANCE ESTIMATES 347

18.5 DETAILS: MEAN SQUARES (MS ) AND F RATIOS 351

18.6 TABLE FOR THE F DISTRIBUTI …

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