Novo Nordisk Ex. 2095, P. 1
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`R. Romano
`1/21/2021
`Forrest, Ph.D.
`Ex 2095
`
`

`

`Witte11e_fm.indd 16
`
`11/18/2016 8:18:14 PM
`
`Novo Nordisk Ex. 2095, P. 2
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`S T A T I S T I C S
`
`Eleventh Edition
`
`Robert S. Witte
`Emeritus, San Jose State University
`John S. Witte
`University of California, San Francisco
`
`Witte11e_fm.indd 1
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 3
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`VP AND EDITORIAL DIRECTOR
`EDITORIAL DIRECTOR
`EDITORIAL ASSISTANT
`EDITORIAL MANAGER
`CONTENT MANAGEMENT DIRECTOR
`CONTENT MANAGER
`SENIOR CONTENT SPECIALIST
`PRODUCTION EDITOR
`COVER PHOTO CREDIT
`
`George Hoffman
`Veronica Visentin
`Ethan Lipson
`Gladys Soto
`Lisa Wojcik
`Nichole Urban
`Nicole Repasky
`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 un-
`der 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 Clear-
`ance 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.
`
`Witte11e_fm.indd 2
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 4
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`To Doris
`
`Witte11e_fm.indd 3
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 5
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`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 quar-
`ter 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 INSTRUCTO R
`
`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 half-
`dozen 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 writ-
`ten 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.
`
`PEDAGOGI CAL FEATU RES
`
`• 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 devi-
`ation, normal curve applications, hypothesis tests, degrees of freedom, and anal-
`ysis 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 con-
`cepts and procedures.
`
`iv
`
`Witte11e_fm.indd 4
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 6
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`PREFACE
`
`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, proba-
`bility calculations, based on design flaws, that re-create the chillingly high likeli-
`hood 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 appendi-
`ces provide a practical math review complete with self-diagnostic tests, a glos-
`sary 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 THI S EDI TI ON
`
`• Update discussion of polling and random digit dialing in Section 8.4
`• A new Section 14.11 on the “file drawer effect,” whereby nonsignificant statisti-
`cal 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.
`
`Witte11e_fm.indd 5
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 7
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`vi
`
`PREFACE
`
`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 Pop-
`ulations, 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 Man-
`dara, 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 Univer-
`sity; Melanie Kercher, Sam Houston State University; Jennifer H. Nolan, Loyola
`Marymount University; and Jonathan C. Pettibone, University of Alabama in Hunts-
`ville; 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.
`
`Witte11e_fm.indd 6
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 8
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`Contents
`
`PREFACE
`
`iv
`
`ACKNOWLEDGMENTS vi
`
`1
`
`INTRODUCTION 1
`1.1 WHY STUDY STATISTICS? 2
`1.2 WHAT IS STATISTICS? 2
`1.3 MORE ABOUT INFERENTIAL STATISTICS 3
`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
`
`2
`
`PART 1 Descriptive Statistics: Organizing
`and Summarizing Data 21
` DESCRIBING DATA WITH TABLES AND GRAPHS 22
`TABLES (FREQUENCY DISTRIBUTIONS) 23
`2.1
`FREQUENCY DISTRIBUTIONS FOR QUANTITATIVE DATA 23
`2.2
`GUIDELINES 24
`2.3
`OUTLIERS 27
`2.4
`RELATIVE FREQUENCY DISTRIBUTIONS 28
`2.5
`CUMULATIVE FREQUENCY DISTRIBUTIONS 30
`2.6
`FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA 31
`2.7
`INTERPRETING DISTRIBUTIONS CONSTRUCTED BY OTHERS 32
`
`
`
`GRAPHS 33
`2.8
`GRAPHS FOR QUANTITATIVE DATA 33
`2.9
`TYPICAL SHAPES 37
`2.10 A GRAPH FOR QUALITATIVE (NOMINAL) DATA 39
`2.11 MISLEADING GRAPHS 40
`2.12 DOING IT YOURSELF 41
`Summary 42
`Important Terms 43
`Review Questions 43
`
`vii
`
`Witte11e_fm.indd 7
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 9
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`viii
`
`CONTENTS
`
`3
`
`4
`
`5
`
`6
`
`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 55
`Summary 56
`Important Terms 57
`Key Equation 57
`Review Questions 57
`
`DESCRIBING VARIABILITY 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
`DEGREES OF FREEDOM (df ) 75
`4.6
`4.7
`INTERQUARTILE RANGE (IQR) 76
`4.8 MEASURES OF VARIABILITY FOR QUALITATIVE AND RANKED DATA 78
`Summary 78
`Important Terms 79
`Key Equations 79
`Review Questions 79
`
`NORMAL DISTRIBUTIONS AND STANDARD (z) SCORES 82
`5.1
`THE NORMAL CURVE 83
`z SCORES 86
`5.2
`5.3
`STANDARD NORMAL CURVE 87
`5.4
`SOLVING NORMAL CURVE PROBLEMS 89
`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
`
`DESCRIBING RELATIONSHIPS: CORRELATION 107
`6.1
`AN INTUITIVE APPROACH 108
`6.2
`SCATTERPLOTS 109
`A CORRELATION COEFFICIENT FOR QUANTITATIVE DATA: r 113
`6.3
`DETAILS: COMPUTATION FORMULA FOR r 117
`6.4
`6.5
`OUTLIERS AGAIN 118
`6.6
`OTHER TYPES OF CORRELATION COEFFICIENTS 119
`
`Witte11e_fm.indd 8
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 10
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`CONTENTS
`
`ix
`
`COMPUTER OUTPUT 120
`6.7
`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
`STANDARD ERROR OF ESTIMATE, sy |x 133
`7.4
`7.5
`ASSUMPTIONS 135
`INTERPRETATION OF r 2 136
`7.6
`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
`POPULATIONS, SAMPLES, AND PROBABILITY 148
`
`8
`
`POPULATIONS AND SAMPLES 149
`8.1
`POPULATIONS 149
`8.2
`SAMPLES 150
`8.3
`RANDOM SAMPLING 151
`8.4
`TABLES OF RANDOM NUMBERS 151
`8.5
`RANDOM ASSIGNMENT OF SUBJECTS 153
`8.6
`SURVEYS OR EXPERIMENTS? 154
`
`
`
`PROBABILITY 155
`8.7
`DEFINITION 155
`8.8
`ADDITION RULE 156
`8.9 MULTIPLICATION RULE 157
`8.10 PROBABILITY AND STATISTICS 161
`Summary 162
`Important Terms 163
`Key Equations 163
`Review Questions 163
`
`Witte11e_fm.indd 9
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 11
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`x
`
`CONTENTS
`
`9
`
`10
`
`SAMPLING DISTRIBUTION OF THE MEAN 168
`9.1 WHAT IS A SAMPLING DISTRIBUTION? 169
`9.2
`CREATING A SAMPLING DISTRIBUTION FROM SCRATCH 170
`9.3
`SOME IMPORTANT SYMBOLS 173
`9.4 MEAN OF ALL SAMPLE MEANS (μ
`X) 173
`STANDARD ERROR OF THE MEAN (σ
`9.5
`X) 174
`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
`
`INTRODUCTION TO HYPOTHESIS TESTING: THE z TEST 182
`10.1 TESTING A HYPOTHESIS ABOUT SAT SCORES 183
`z TEST FOR A POPULATION MEAN 185
`10.2
`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
`IF H0 REALLY IS TRUE 206
`11.7
`IF H0 REALLY IS FALSE BECAUSE OF A LARGE EFFECT 207
`11.8
`IF H0 REALLY IS FALSE BECAUSE OF A SMALL EFFECT 209
`11.9
`11.10 INFLUENCE OF SAMPLE SIZE 211
`11.11 POWER AND SAMPLE SIZE 213
`Summary 216
`Important Terms 217
`Review Questions 218
`
`Witte11e_fm.indd 10
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 12
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`CONTENTS
`
`xi
`
`12 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
`
`14
`
`t TEST FOR ONE SAMPLE 233
`13.1 GAS MILEAGE INVESTIGATION 234
`13.2 SAMPLING DISTRIBUTION OF t 234
`t TEST 237
`13.3
`13.4 COMMON THEME OF HYPOTHESIS TESTS 238
`13.5 REMINDER ABOUT DEGREES OF FREEDOM 238
`13.6 DETAILS: ESTIMATING THE STANDARD ERROR ( Xs ) 238
`13.7 DETAILS: CALCULATIONS FOR THE t TEST 239
`13.8 CONFIDENCE INTERVALS FOR 𝜇 BASED ON t 241
`13.9 ASSUMPTIONS 242
`Summary 242
`Important Terms 243
`Key Equations 243
`Review Questions 243
`
`2 248
`
`t TEST FOR TWO INDEPENDENT SAMPLES 245
`14.1 EPO EXPERIMENT 246
`14.2 STATISTICAL HYPOTHESES 247
`1 – X
`14.3 SAMPLING DISTRIBUTION OF X
`t TEST 250
`14.4
`14.5 DETAILS: CALCULATIONS FOR THE t TEST 252
`14.6 p-VALUES 255
`14.7 STATISTICALLY SIGNIFICANT RESULTS 258
`14.8 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
`
`Witte11e_fm.indd 11
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 13
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`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) 273
`15.1 EPO EXPERIMENT WITH REPEATED MEASURES 274
`15.2 STATISTICAL HYPOTHESES 277
`15.3 SAMPLING DISTRIBUTION OF D 277
`t TEST 278
`15.4
`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
`t TEST FOR THE POPULATION CORRELATION COEFFICIENT, ρ 285
`15.9
`Summary 287
`Important Terms 288
`Key Equations 288
`Review Questions 288
`
`16 ANALYSIS OF VARIANCE (ONE FACTOR) 292
`16.1 TESTING A HYPOTHESIS ABOUT SLEEP DEPRIVATION
`AND AGGRESSION 293
`16.2 TWO SOURCES OF VARIABILITY 294
`F TEST 296
`16.3
`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
`F TEST IS NONDIRECTIONAL 308
`16.8
`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) 322
`17.1 SLEEP DEPRIVATION EXPERIMENT WITH REPEATED MEASURES 323
`F TEST 324
`17.2
`
`Witte11e_fm.indd 12
`
`11/18/2016 8:18:13 PM
`
`Novo Nordisk Ex. 2095, P. 14
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`CONTENTS
`
`xiii
`
`17.3 TWO COMPLICATIONS 325
`17.4 DETAILS: VARIANCE ESTIMATES 326
`17.5 DETAILS: MEAN SQUARE (MS ) AND THE F RATIO 329
`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) 339
`18.1 A TWO-FACTOR EXPERIMENT: RESPONSIBILITY IN CROWDS 340
`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 DISTRIBUTION 353
`18.7 ESTIMATING EFFECT SIZE 353
`18.8 MULTIPLE COMPARISONS 354
`18.9 SIMPLE EFFECTS 355
`18.10 OVERVIEW: FLOW CHART FOR TWO-FACTOR ANOVA 358
`18.11 REPORTS IN THE LITERATURE 358
`18.12 ASSUMPTIONS 360
`18.13 OTHER TYPES OF ANOVA 360
`Summary 360
`Important Terms 361
`Key Equations 361
`Review Questions 361
`
`19 CHI-SQUARE ( χ 2) TEST FOR QUALITATIVE (NOMINAL) DATA 365
`ONE-VARIABLE χ 2 TEST 366
`
`19.1 SURVEY OF BLOOD TYPES 366
`19.2 STATISTICAL HYPOTHESES 366
`19.3 DETAILS: CALCULATING χ 2 367
`19.4 TABLE FOR THE χ 2 DISTRIBUTION 369
`χ 2 TEST 370
`19.5
`TWO-VARIABLE χ2 TEST 372
`19.6 LOST LETTER STUDY 372
`19.7 STATISTICAL HYPOTHESES 373
`19.8 DETAILS: CALCULATING χ 2 373
`
`
`
`Witte11e_fm.indd 13
`
`11/18/2016 8:18:14 PM
`
`Novo Nordisk Ex. 2095, P. 15
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`xiv
`
`CONTENTS
`
`19.9 TABLE FOR THE χ 2 DISTRIBUTION 376
`19.10 χ 2 TEST 376
`19.11 ESTIMATING EFFECT SIZE 377
`19.12 ODDS RATIOS 378
`19.13 REPORTS IN THE LITERATURE 380
`19.14 SOME PRECAUTIONS 380
`19.15 COMPUTER OUTPUT 381
`Summary 382
`Important Terms 382
`Key Equations 382
`Review Questions 382
`
`20 TESTS FOR RANKED (ORDINAL) DATA 386
`20.1 USE ONLY WHEN APPROPRIATE 387
`20.2 A NOTE ON TERMINOLOGY 387
`20.3 MANN–WHITNEY U TEST (TWO INDEPENDENT SAMPLES) 387
`20.4 WILCOXON T TEST (TWO RELATED SAMPLES) 392
`20.5 KRUSKAL–WALLIS H TEST
`(THREE OR MORE INDEPENDENT SAMPLES) 396
`20.6 GENERAL COMMENT: TIES 400
`Summary 400
`Important Terms 400
`Review Questions 400
`
`21 POSTSCRIPT: WHICH TEST? 403
`21.1 DESCRIPTIVE OR INFERENTIAL STATISTICS? 404
`21.2 HYPOTHESIS TESTS OR CONFIDENCE INTERVALS? 404
`21.3 QUANTITATIVE OR QUALITATIVE DATA? 404
`21.4 DISTINGUISHING BETWEEN THE TWO TYPES OF DATA 406
`21.5 ONE, TWO, OR MORE GROUPS? 407
`21.6 CONCLUDING COMMENTS 408
`Review Questions 408
`
`APPENDICES 411
`A MATH REVIEW 411
`B ANSWERS TO SELECTED QUESTIONS 419
`C TABLES 457
`D GLOSSARY 471
`
`INDEX 477
`
`Witte11e_fm.indd 14
`
`11/18/2016 8:18:14 PM
`
`Novo Nordisk Ex. 2095, P. 16
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`S T A T I S T I C S
`
`Eleventh Edition
`
`Witte11e_fm.indd 15
`
`11/18/2016 8:18:14 PM
`
`Novo Nordisk Ex. 2095, P. 17
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`CHAPTER
`
`11
`
`More about Hypothesis Testing
`
`11.1 WHY HYPOTHESIS TESTS?
`11.2
`STRONG OR WEAK DECISIONS
`11.3
`ONE-TAILED AND TWO-TAILED TESTS
`CHOOSING A LEVEL OF SIGNIFICANCE (𝜶)
`11.4
`11.5
`TESTING A HYPOTHESIS ABOUT VITAMIN C
`11.6
`FOUR POSSIBLE OUTCOMES
`IF H0 REALLY IS TRUE
`11.7
`IF H0 REALLY IS FALSE BECAUSE OF A LARGE EFFECT
`11.8
`IF H0 REALLY IS FALSE BECAUSE OF A SMALL EFFECT
`11.9
`11.10
`INFLUENCE OF SAMPLE SIZE
`11.11 POWER AND SAMPLE SIZE
`Summary / Important Terms / Review Questions
`
`Preview
`
`Based on the notion of everything that could possibly happen just by chance—in other
`words, based on the concept of a sampling distribution—hypothesis tests permit
`us to draw conclusions that go beyond a limited set of actual observations. This
`chapter describes why rejecting the null hypothesis is stronger than retaining the null
`hypothesis and why a one-tailed test is more likely than a two-tailed test to detect a
`false null hypothesis.
`We speculate about how the hypothesis test fares if we assume, in turn, that the
`null hypothesis is true and then that it is false. The two types of incorrect decisions—
`rejecting a true null hypothesis (a false alarm) or retaining a false null hypothesis
`(a miss)—can be controlled by our selection of the level of significance and of the
`sample size.
`
`Witte11e_c11.indd 195
`
`11/18/2016 6:12:16 PM
`
`195
`
`Novo Nordisk Ex. 2095, P. 18
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`196
`
`MORE ABOUT HYPOTHESIS TESTING
`
`11.1 WHY HYPOTHESIS TE ST S?
`There is a crucial link between hypothesis tests and the need of investigators, whether
`pollsters or researchers, to generalize beyond existing data. If the 100 freshmen in
`the SAT example of the previous chapter had been not a sample but a census of the
`entire freshman class, there wouldn’t have been any need to generalize beyond exist-
`ing data, and it would have been inappropriate to conduct a hypothesis test. Now,
`the observed difference between the newly observed population mean of 533 and the
`national average of 500, by itself, would have been sufficient grounds for concluding
`that the mean SAT math score for all local freshmen exceeds the national average.
`Indeed, any observed difference in favor of the local freshmen, regardless of the size of
`the difference, would have supported this conclusion.
`If we must generalize beyond the 100 freshmen to a larger local population, as was
`actually the case, the observed difference between 533 and 500 cannot be interpreted at
`face value. The basic problem is that the sample mean for a second random sample of
`100 freshmen probably would differ, just by chance, from the sample mean of 533 for
`the first sample. Accordingly, the variability among sample means must be considered
`when we attempt to decide whether the observed difference between 533 and 500 is
`real or merely transitory.
`
`Importance of the Standard Err or
`To evaluate the effect of chance, we use the concept of a sampling distribution, that
`is, the concept of the sample means for all possible random outcomes. A key element
`in this concept is the standard error of the mean, a measure of the average amount by
`which sample means differ, just by chance, from the population mean. Dividing the
`observed difference (533−500) by the standard error (11) to obtain a value of z (3)
`locates the original observed difference along a z scale of either common outcomes
`(reasonably attributable to chance) or rare outcomes (not reasonably attributable to
`chance). If, when expressed as z, the ratio of the observed difference to the standard
`error is small enough to be reasonably attributed to chance, we retain H0. Otherwise, if
`the ratio of the observed difference to the standard error is too large to be reasonably
`attributed to chance, as in the SAT example, we reject H0.
`Before generalizing beyond the existing data, we must always measure the effect of
`chance; that is, we must obtain a value for the standard error. To appreciate the vital
`role of the standard error in the SAT example, increase its value from 11 to 33 and
`note that even though the observed difference remains the same (533−500), we would
`retain, not reject, H0 because now z would equal 1 (rather than 3) and be less than the
`critical z of 1.96.
`
`Possibility of Incorrect Decisions
`Having made a decision about the null hypothesis, we never know absolutely
`whether that decision is correct or incorrect, unless, of course, we survey the entire
`population. Even if H0 is true (and, therefore, the hypothesized distribution of z about
`H0 also is true), there is a slight possibility that, just by chance, the one observed z actu-
`ally originates from one of the shaded rejection regions of the hypothesized distribution
`of z, thus causing the true H0 to be rejected. This type of incorrect decision—rejecting a
`true H0—is referred to as a type I error or a false alarm.
`On first impulse, it might seem desirable to abolish the shaded rejection regions in
`the hypothesized sampling distribution to ensure that a true H0 never is rejected. A most
`unfortunate consequence of this strategy, however, is that no H0, not even a radically
`false H0, ever would be rejected. This second type of incorrect decision—retaining a
`false H0—is referred to as a type II error or a miss. Both type I and type II errors are
`described in more detail later in this chapter.
`
`Witte11e_c11.indd 196
`
`11/18/2016 6:12:16 PM
`
`Novo Nordisk Ex. 2095, P. 19
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`11.2 STRONG OR WEAK DECISIONS
`
`197
`
`.95
`
`.025
`
`.025
`
`–1.96
`
`0
`
`1.96
`
`z
`
`Rare
`outcomes
`
`Reject H0
`
`Common outcomes
`
`Retain H0
`
`Rare
`outcomes
`Reject H0
`
`FIGURE 11.1
`Proportions of area associated with
`common and rare outcomes (α = .05).
`
`Minimizing Incorrect Decisions
`Traditional hypothesis-testing procedures, such as the one illustrated in Figure 11.1,
`tend to minimize both types of incorrect decisions. If H0 is true, there is a high probabil-
`ity that the observed z will qualify as a common outcome under the hypothesized sam-
`pling distribution and that the true H0 will be retained. (In Figure 11.1, this probability
`equals the proportion of white area (.95) in the hypothesized sampling distribution.)
`On the other hand, if H0 is seriously false, because the hypothesized population mean
`differs considerably from the true population mean, there is also a high probability that
`the observed z will qualify as a rare outcome under the hypothesized distribution and
`that the false H0 will be rejected. (In Figure 11.1, this probability can’t be determined
`since, in this case, the hypothesized sampling distribution does not actually reflect the
`true sampling distribution. More about this later in the chapter.)
`
`Even though we never really know whether a particular decision is correct or
`incorrect, it is reassuring that in the long run, most decisions will be correct—
`assuming the null hypotheses are either true or seriously false.
`
`11.2 STRONG OR WEAK DE CISION S
`Retaining H 0 Is a Weak Decision
`There are subtle but important differences in the interpretation of decisions to
`retain H0 and to reject H0. H0 is retained whenever the observed z qualifies as a
`common outcome on the assumption that H0 is true. Therefore, H0 could be true.
`However, the same observed result also would qualify as a common outcome when
`the original value in H0 (500) is replaced with a slightly different value. Thus, the
`retention of H0 must be viewed as a relatively weak decision. Because of this weak-
`ness, many statisticians prefer to describe this decision as simply a failure to reject H0
`rather than as the retention of H0. In any event, the retention of H0 can’t be interpreted
`as proving H0 to be true. If H0 had been retained in the present example, it would have
`been appropriate to conclude not that the mean SAT math score for all local fresh-
`men equals the national average, but that the mean SAT math score could equal the
`national average, as well as many other possible values in the general vicinity of the
`national average.
`
`Witte11e_c11.indd 197
`
`11/18/2016 6:12:16 PM
`
`Novo Nordisk Ex. 2095, P. 20
`Mylan Institutional v. Novo Nordisk
`IPR2020-00324
`
`

`

`198
`
`MORE ABOUT HYPOTHESIS TESTING
`
`Rejecting H 0 Is a Strong Decision
`On the other hand, H0 is rejected whenever the observed z qualifies as a rare out-
`come—one that could have occurred just by chance with a probability of .05 or less—
`on the assumption that H0 is true. This suspiciously rare outcome implies that H0 is
`probably false (and conversely, that H1 is probably true). Therefore, the rejection of H0
`can be viewed as a strong decision. When H0 was rejected in the present example, it
`was appropriate to report a definitive conclusion that the mean SAT math score for all
`local freshmen probably exceeds the national average.
`To summarize,
`
`the decision to retain H0 implies not that H0 is probably true, but only that H0
`could be true, whereas the decision to reject H0 implies that H0 is probably false
`(and that H1 is probably true).
`
`Since most investigators hope to rej