2012 (EBOOK) robert r pagano understanding statistics in the behavioral sciences

U N D E R S TA N D I N G

S TAT I S T I C S

IN THE BEHAVIORAL SCIENCES ■ TENTH EDITION

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U N D E R S T A N D I N G

S TAT I S T I C S

IN THE BEHAVIOR AL SCIENCES ■ T E N T H E D I T I O N

© Strmko / Dreamstime.com

ROBERT R. PAGANO

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Understanding Statistics in the Behavioral
Sciences, Tenth Edition
Robert R. Pagano
Publisher: Jon-David Hague
Psychology Editor: Tim Matray
Developmental Editor: Robert Jucha
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Library of Congress Control Number: 2011934938
Student Edition:

ISBN-13: 978-1-111-83726-6
ISBN-10: 1-111-83726-0
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I dedicate this tenth edition to all truth-seekers. May this
textbook aid you in forming an objective understanding of
reality. May the data-based, objective approach taught here
help inform your decisions and beliefs to help improve your life
and the lives of the rest of us.

v
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Reproduced with permission.

ABOUT THE AUTHOR

ROBERT R. PAGANO received a Bachelor of Electrical Engineering degree from
Rensselaer P olytechnic I nstitute i n 1956 a nd a Ph.D . i n B iological P sychology f rom
Yale U niversity i n 1965. H e w as A ssistant P rofessor a nd A ssociate P rofessor i n t he
Department of Psychology at the University of Washington, Seattle, Washington, from
1965 to 1 989. He was Associate Chairman of the Department of Neuroscience at t he
University of Pittsburgh, Pittsburgh, Pennsylvania, from 1990 to June 2000. While at
the D epartment of Neuroscience, i n a ddition to h is ot her duties, he ser ved a s D irector of Undergraduate Studies, was the departmental adviser for undergraduate majors,
taught b oth u ndergraduate a nd g raduate statistics cou rses, a nd ser ved a s a s tatistical
consultant for departmental faculty. Bob was also Director of the Statistical Cores for
two NIH center grants in schizophrenia and Parkinson’s disease. He retired from the
University of Pittsburgh in June 2000. Bob’s current interests are in the physiology of
consciousness, the physiology and psychology of meditation and in Positive Psychology.
He has taught courses in introductory statistics at the University of Washington and at
the University of Pittsburgh for over thirty years. He has been a finalist for the outstanding t eaching award at t he University of Washington for h is t eaching of i ntroductory
statistics.

Bob is married to Carol A. Eikleberry and they have a 21-year-old son, Robby. In
addition, Bob has five grown daughters, Renee, Laura, Maria, Elizabeth, and Christina,
one granddaughter, Mikaela, and a yellow lab. In his undergraduate years, Bob was an
athlete, winning varsity letters in basketball, baseball and soccer. He loves tennis, but
arthritis has temporarily caused a shift in retirement ambitions from winning the singles title at Wimbledon to watching the U.S. Open and getting in shape for doubles play
sometime in the future. He also loves the outdoors, especially hiking, and his morning
coffee. He especially values his daily meditation practice. His favorite cities to visit are
Boulder, Estes Park, New York, Aspen, Santa Fe, and Santa Barbara.

vi
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BRIEF CONTENTS

P A R T

O N E

1

P A R T

OV E R V I E W 1
Statistics and Scientific Method 3

T W O

2

3
4
5
6
7

D E S C R I P TI V E STATI S TI C S

23

Basic Mathematical and Measurement Concepts 25
Frequency Distributions 47
Measures of Central Tendency and Variability 79
The Normal Curve and Standard Scores 102
Correlation 122
Linear Regression 159

PA R T THR EE

I N F E R E NTI A L S TATI S TI C S

8
9
10
11
12

Random Sampling and Probability 189
Binomial Distribution 225
Introduction to Hypothesis Testing Using the Sign Test 248

Power 277
Sampling Distributions, Sampling Distribution of the Mean, the Normal
Deviate (z) Test 298
Student’s t Test for Single Samples 327
Student’s t Test for Correlated and Independent Groups 356
Introduction to the Analysis of Variance 401
Introduction to Two-Way Analysis of Variance 445
Chi-Square and Other Nonparametric Tests 482
Review of Inferential Statistics 527

13
14
15
16
17
18

187

vii
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CONTENTS

PA R T

1

O N E

OV E R V I E W 1
Statistics and Scientific Method
Introduction 4
Methods of Knowing 4
Authority 4
Rationalism 4
Intuition 5
Scientific Method 6
Definitions 6
Experiment: Mode of Presentation and Retention
Scientific Research and Statistics 9
Observational Studies 9
True Experiments 9
Random Sampling 9
Descriptive and Inferential Statistics 10
Using Computers in Statistics 11
Statistics and the “Real World” 11

3

7

What Is the Truth?
■ Data, Data, Where Are the Data?

12
■ Authorities Are Nice, but…
13
■ Data, Data, What Are the Data?–1
14
■ Data, Data, What Are the Data?–2
15
Summary 17
Important New Terms 17
Questions and Problems 18
What Is the Truth? Questions 20
Online Study Resources 21

ix
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x

CONTENTS

PA R T

2

T W O

D E S C R I P TI V E STATI S TI C S
Basic Mathematical

and Measurement Concepts

23

25

Study Hints for the Student 26
Mathematical Notation 26
Summation 27
Order of Mathematical Operations 29
Measurement Scales 30
Nominal Scales 31
Ordinal Scales 32
Interval Scales 32
Ratio Scales 33
Measurement Scales in the Behavioral Sciences
Continuous and Discrete Variables 35
Real Limits of a Continuous Variable 36
Significant Figures 37
Rounding 38

35

Summary 38
Important New Terms 39
Questions and Problems 39
SPSS 40
Notes 44
Online Study Resources 46

3

Frequency Distributions

47

Introduction: Ungrouped Frequency Distributions 48
Grouping Scores 49
Constructing a Frequency Distribution of Grouped Scores 51
Relative Frequency, Cumulative Frequency, and Cumulative Percentage
Distributions 54
Percentiles 5 5
Computation of Percentile Points 56
Percentile Rank 59
Computation of Percentile Rank 59
Graphing Frequency Distributions 61
The Bar Graph 63
The Histogram 63
The Frequency Polygon 64
The Cumulative Percentage Curve 64
Shapes of Frequency Curves 65
Exploratory Data Analysis 67
Stem and Leaf Diagrams 67
What Is the Truth?
■ Stretch the Scale, Change the Tale

69

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Contents

Summary 70
Important New Terms 70
Questions and Problems 70
What Is the Truth? Questions 73
SPSS 73
Online Study Resources 78

4

Measures of Central Tendency and Variability
Introduction 8 0
Measures of Central Tendency 80
The Arithmetic Mean 80
The Overall Mean 83
The Median 85
The Mode 87
Measures of Central Tendency and Symmetry
Measures of Variability 89
The Range 89
The Standard Deviation 89
The Variance 95

79

88

Summary 95
Important New Terms 96
Questions and Problems 96
SPSS 99
Notes 100
Online Study Resources 101

5

The Normal Curve and Standard Scores

102

Introduction 1 03
The Normal Curve 103
Area Contained Under the Normal Curve 104
Standard Scores (z Scores) 105
Characteristics of z Scores 108
Finding the Area, Given the Raw Score 109
Finding the Raw Score, Given the Area 114
Summary 117
Important New Terms 117
Questions and Problems 117
SPSS 119
Online Study Resources 121

6

Correlation 1 22
Introduction 1 23

Relationships 1 23
Linear Relationships 123
Positive and Negative Relationships 126
Perfect and Imperfect Relationships 127

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xi


xii

CONTENTS

Correlation 1 30
The Linear Correlation Coefficient Pearson r
Other Correlation Coefficients 139
Effect of Range on Correlation 143
Effect of Extreme Scores 144
Correlation Does Not Imply Causation 144

131

What Is the Truth?
■ “Good Principal ϭ Good Elementary School,” or Does It?
■ Money Doesn’t Buy Happiness, or Does It?
147

146

Summary 148
Important New Terms 149
Questions and Problems 149
What Is the Truth? Questions 154
SPSS 155
Online Study Resources 158

7

Linear Regression

159

Introduction 1 60
Prediction and Imperfect Relationships 160
Constructing the Least-Squares Regression Line: Regression of
Y on X 162
Measuring Prediction Errors: The Standard Error of Estimate 169
Considerations in Using Linear Regression for Prediction 172
Relation Between Regression Constants and Pearson r 172
Multiple Regression 174
Summary 178
Important New Terms 178
Questions and Problems 179
SPSS 182
Online Study Resources 186

PA RT THREE

8

I N F E R E NTI A L STATI S TI C S

187

Random Sampling and Probability
Introduction 1 90
Random Sampling 190
Techniques for Random Sampling 191
Sampling With or Without Replacement 193
Probability 1 93
Some Basic Points Concerning Probability Values
Computing Probability 195
The Addition Rule 196
The Multiplication Rule 201
Multiplication and Addition Rules 211
Probability and Continuous Variables 213

189

195

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Contents

xiii

What Is the Truth?
■ “Not Guilty, I’m a Victim of Coincidence”: Gutsy Plea or Truth?
216
■ Sperm Count Decline–Male or Sampling Inadequacy?
217
■ A Sample of a Sample
218
Summary 220
Important New Terms 221
Questions and Problems 221
What Is the Truth? Questions 223
Notes 223
Online Study Resources 224

9

Binomial Distribution

225

Introduction 226
Definition and Illustration of the Binomial Distribution 226
Generating the Binomial Distribution from the Binomial Expansion
Using the Binomial Table 230
Using the Normal Approximation 239

229

Summary 244

Important New Terms 245
Questions and Problems 245
Notes 247
Online Study Resources 247

10

Introduction to Hypothesis Testing Using the Sign
Test 2 48
Introduction 24 9
Logic of Hypothesis Testing 249
Experiment: Marijuana and the Treatment of AIDS Patients
Repeated Measures Design 251
Alternative Hypothesis (H1) 252
Null Hypothesis (H0) 252
Decision Rule (␣ Level) 252
Evaluating the Marijuana Experiment 253
Type I and Type II Errors 254
Alpha Level and the Decision Process 255
Evaluating the Tail of the Distribution 257
One- and Two-Tailed Probability Evaluations 259
Size of Effect: Significant Versus Important 265
What Is the Truth?
■ Chance or Real Effect?–1
266
■ Chance or Real Effect?–2
268
■ “No Product Is Better Than Our Product”
269
■ Anecdotal Reports Versus Systematic Research

249

270

Summary 271
Important New Terms 272
Questions and Problems 272

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xiv

CONTENTS

What Is the Truth? Questions 275
Notes 275
Online Study Resources 276

11

Power 2 77
Introduction 27 8
What Is Power? 278
Pnull and Preal 27 8
Preal: A Measure of the Real Effect 279
Power Analysis of the AIDS Experiment 280
Effect of N and Size of Real Effect 281

Power and Beta (␤) 285
Power and Alpha (␣) 286
Alpha-Beta and Reality 287
Interpreting Nonsignificant Results 287
Calculation of Power 288
What Is the Truth?
■ Astrology and Science

293

Summary 295
Important New Terms 295
Questions and Problems 295
What Is the Truth? Questions 296
Notes 297
Online Study Resources 297

12

Sampling Distributions, Sampling Distribution of the
Mean, the Normal Deviate (z) Test 298
Introduction 299
Sampling Distributions 299
Generating Sampling Distributions 300
The Normal Deviate (z) Test 303
Experiment: Evaluating a School Reading Program 303
Sampling Distribution of the Mean 303
The Reading Proficiency Experiment Revisited 309
Alternative Solution Using zobt and zcrit 312
Conditions Under Which the z Test Is Appropriate 316

Power and the z Test 317
Summary 324
Important New Terms 324
Questions and Problems 324
Online Study Resources 326

13

Student’s t Test for Single Samples
Introduction 32 8
Comparison of the z and t Tests 328
Experiment: Increasing Early Speaking in Children
The Sampling Distribution of t 329
Degrees of Freedom 330

327

329

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Contents

t and z Distributions Compared 331
Early Speaking Experiment Revisited 333
Calculating tobt from Original Scores 334
Conditions Under Which the t Test Is Appropriate 338
Size of Effect Using Cohen’s d 339

Confidence Intervals for the Population Mean 341
Construction of the 95% Confidence Interval 341
Experiment: Estimating the Mean IQ of Professors 343
General Equations for Any Confidence Interval 343
Testing the Significance of Pearson r 346
Summary

349

Important New Terms

349

Questions and Problems 349
SPSS 352
Notes 355
Online Study Resources 355

14

Student’s t Test for Correlated and Independent
Groups 35 6
Introduction 3 57
Student’s t Test for Correlated Groups 358
Experiment: Brain Stimulation and Eating 358
Comparison Between Single Sample and Correlated Groups t Tests 359
Brain Stimulation Experiment Revisited and Analyzed 360
Size of Effect Using Cohen’s d 363
Experiment: Lateral Hypothalamus and Eating Behavior 364
t Test for Correlated Groups and Sign Test Compared 365

Assumptions Underlying the t Test for Correlated Groups 366
z and t Tests for Independent Groups 366
Independent Groups Design 366
z Test for Independent Groups 367
Experiment: Hormone X and Sexual Behavior 367
The_Sampling
Distribution of the Difference Between Sample Means
_
(X1 – X 2) 368
Experiment: Hormone X Experiment Revisited 369
Student’s t Test for Independent Groups 370
Comparing the Equations for zobt and tobt 370
Analyzing the Hormone X Experiment 372
Calculating tobt When n1 ϭ n2 373
Assumptions Underlying the t Test 375
Violation of the Assumptions of the t Test 376
Size of Effect Using Cohen’s d 376
Experiment: Thalamus and Pain Perception 377
Power of the t Test 378
Correlated Groups and Independent Groups Designs Compared 379
Alternative Analysis Using Confidence Intervals 382
Constructing the 95% Confidence Interval for ␮1 – ␮2 382
Conclusion Based on the Obtained Confidence Interval 384
Constructing the 99% Confidence Interval for ␮1 – ␮2 385

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xv

xvi

CONTENTS

Summary 385
Important New Terms 386
Questions and Problems 387
SPSS 392
Notes 398
Online Study Resources 400

15

Introduction to the Analysis of Variance

401

Introduction: The F Distribution 402
F Test and the Analysis of Variance (ANOVA) 404
Overview of One-Way ANOVA 405
Within-Groups Variance Estimate, MSwithin 406
Between-Groups Variance Estimate, MSbetween 408
The F Ratio 409
Analyzing Data with the ANOVA Technique 410
Experiment: Different Situations and Stress 410
Logic Underlying the One-Way ANOVA 414
Relationship Between ANOVA and the t Test 4 18
Assumptions Underlying the Analysis of Variance 418
Size of Effect Using Vˆ 2 or ␩2 419

Omega Squared, vˆ2 419
Eta Squared, ␩2 420
Power of the Analysis of Variance 420
Power and N 421
Power and the Real Effect of the Independent Variable 421
Power and Sample Variability 421
Multiple Comparisons 421
A Priori, or Planned, Comparisons 422
A Posteriori, or Post Hoc, Comparisons 423
The Tukey Honestly Significant Difference (HSD) Test 424
The Scheffé Test 425
Comparison Between Planned Comparisons, the Tukey HSD Test, and the
Scheffé Test 432
What Is the Truth?
■ Much Ado About Almost Nothing

433

Summary 435
Important New Terms 436
Questions and Problems 436
What Is the Truth? Questions 440
SPSS 440
Online Study Resources 444

16

Introduction to Two-Way Analysis of Variance
Introduction to Two-Way ANOVA–Qualitative Presentation
Quantitative Presentation of Two-Way ANOVA 450

Within-Cells Variance Estimate, MSwithin-cells 451
Row Variance Estimate, MSrows 452
Column Variance Estimate, MScolumns 453

445

446

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Contents

xvii

Interaction Variance Estimate, MSinteraction 455
Computing F Ratios 456
Analyzing an Experiment with Two-Way ANOVA 456
Experiment: Effect of Exercise on Sleep 456
Interpreting the Results 460
Multiple Comparisons 471
Assumptions Underlying Two-Way ANOVA 472
Summary 472
Important New Terms 473
Questions and Problems 473
SPSS 475
Online Study Resources 481

17

Chi-Square and Other Nonparametric Tests

482

Introduction: Distinction Between Parametric and Nonparametric Tests 483
Chi-Square (␹2) 484
Single-Variable Experiments 484
Experiment: Preference for Different Brands of Light Beer 484
Test of Independence Between Two Variables 488
Experiment: Political Affiliation and Attitude 489
Assumptions Underlying ␹2 497
The Wilcoxon Matched-Pairs Signed Ranks Test 498
Experiment: Changing Attitudes Toward Wildlife Conservation 498
Assumptions of the Wilcoxon Signed Ranks Test 501
The Mann-Whitney U Test 501
Experiment: The Effect of a High-Protein Diet on Intellectual Development 501
Tied Ranks 504
Assumptions Underlying the Mann-Whitney U Test 507
The Kruskal-Wallis Test 507
Experiment: Evaluating Two Weight Reduction Programs 507
Assumptions Underlying the Kruskal-Wallis Test 511
What Is the Truth?
■ Statistics and Applied Social Research—Useful or “Abuseful”?

512

Summary 514
Important New Terms 515
Questions and Problems 515

What Is the Truth? Questions 522
SPSS 522
Notes 525
Online Study Resources 526

18

Review of Inferential Statistics

527

Introduction 52 8
Terms and Concepts 528
Process of Hypothesis Testing 529
Single Sample Designs 530
z Test for Single Samples 530
t Test for Single Samples 531
t Test for Testing the Significance of Pearson r 531

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xviii

CONTENTS

Correlated Groups Design: Two Groups 532
t Test for Correlated Groups 532
Wilcoxon Matched-Pairs Signed Ranks Test 533

Sign Test 533
Independent Groups Design: Two Groups 534
t Test for Independent Groups 534
Mann-Whitney U Test 535
Multigroup Experiments 535
One-Way Analysis of Variance, F Test 536
Tukey’s HSD Test 538
Scheffé Test 538
One-Way Analysis of Variance, Kruskall-Wallis Test
Two-Way Analysis of Variance, F Test 539
Analyzing Nominal Data 541
Chi-Square Test 542
Choosing the Appropriate Test 542

539

Questions and Problems 544
Online Study Resources 550

APPENDIXES
A.
B.
C.
D.
E.

5 51

Review of Prerequisite Mathematics 553
Equations 563

Answers to End-of-Chapter Questions and Problems and SPSS Problems 571
Tables 590
Introduction to SPSS 615

GLOSSARY
INDEX

626

635

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PR E FACE

I have been teaching a course in introductory statistics for more than 30 years, first
within the Department of Psychology at t he University of Washington, and most recently within the Department of Neuroscience at the University of Pittsburgh. Most
of my students have been psychology majors pursuing the Bachelor of Arts degree,
but many have also come from biology, business, education, neuroscience, nursing,
the health sciences, and other fields. My introductory statistics course has been rated
quite highly. While at the University of Washington, I was a finalist for the university’s
“Outstanding Teaching” award for teaching this course.
This textbook has been the mainstay of my teaching. Because most of my students
have neither high aptitude nor strong interest in mathematics and are not well grounded
in mathematical skills, I have used an informal, intuitive approach rather than a strictly
mathematical one . M y approa ch a ssumes on ly h igh-school a lgebra f or ba ckground
knowledge, and depends very little on equation derivation. It attempts to teach the
introductory statistics material in a deep way, in a manner that facilitates conceptual

understanding and critical thinking rather than mechanical, by-the-numbers problem
solving.
My statistics course has been quite successful. Students are able to grasp the
material, even the more complicated topics like “power,” and at the same time they
often report that they enjoy learning it. Student ratings of this course have been high.
Their ratings of this textbook are even higher; among other things students say that
the text is very clear. that they like the touches of humor, and that it helps them to
have the material presented in such great detail. Some students have even commented
that “this is the best textbook I have ever had.” Admittedly, this kind of comment is
not the most frequent one offered, but for an introductory statistics textbook, coming
from psychology majors, I take it as high praise indeed.
I believe the factors that make my textbook successful are the following:
■
■

■

It promotes understanding rather than mechanical problem solving.
It is student-friendly and informally written, with touches of humor that connect
with students and help lower anxiety.
It is very clearly worded and written at the right level.
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It presents the material in great detail.
It has good visuals.
It uses a more e xtended t reatment of sa mpling d istributions a nd a pa rticularly
effective se quencing o f t he i nferential m aterial, b eginning w ith t he s ign t est
instead of the conventional approach of beginning with the z test.
It has interesting illustrative examples, and many ideally solved and end-of-chapter
problems for students to practice with.

Rationale for Introducing Inferential Statistics with
the Sign Test
Understanding the use of sampling distributions is critical to understanding inferential
statistics. The first sampling distribution discussed by most texts is the sampling distribution of the mean, used in conjunction with the z test. The problem with this approach
is that the sampling distribution of the mean is hard for students to understand. It cannot
be generated from simple probability considerations, and its definition is very abstract
and difficult to make concrete. Moreover, it is hard to relate the sampling distribution
of the mean to its use in the z test. The situation is further complicated because at the
same time as they are being asked to understand sampling distributions, students are
being asked to understand a lot of other complicated concepts such as null hypothesis,
alternative hypothesis, alpha level, Type I a nd Type II error, and so forth. As a result,
many s tudents do n ot de velop a n u nderstanding o f sa mpling d istributions a nd w hy
they are important in inferential statistics. I believe this lack of understanding persists
throughout the rest of inferential statistics and undermines their understanding of this
important material.

What appears to happ en is t hat since students do n ot understand the use o f sampling distributions, when they are asked to solve an inferential problem, they resort to
mechanically going t hrough t he s teps of (1) det ermining t he appropr iate s tatistic for
the problem, (2) solving its equation by rote, (3) looking up the probability value in an
appendix table, and (4) concluding regarding the null and alternative hypotheses. Many
students follow this procedure without any insight as to w hy they are doing it, except
that they k now doing so w ill lead to t he cor rect answer. Thus students are often able
to solve problems without understanding what they are doing, all because they fail to
develop a conc eptual u nderstanding of what a sa mpling d istribution is a nd why it is
important in inferential statistics.
To impart a basic understanding of sampling distributions, I believe it is much
better to present an extended treatment of sampling distributions, beginning with
the sign test rather than the z test. The sign test is a simple inference test for which
the b inomial d istribution is t he appropr iate sa mpling d istribution. T he b inomial
distribution is very easy to understand and it can be derived from basic probability cons iderations. M oreover, its app lication to t he i nference pro cess is c lear a nd
obvious. This combination greatly facilitates understanding inference and bolsters
student confidence in their ability to successfully handle the inferential material. In
my view, the appropriate pedagogical sequence is to present basic probability first,
followed by the binomial distribution, which is then followed by the sign test. This
is the sequence followed in this textbook (Chapters 8, 9, and 10, respectively).
Since the binomial distribution is entirely dependent on simple probability considerations, students ca n easily understand its generation a nd application. Moreover, t he
binomial distribution can also be generated by an empirical process that is use d later
in t he t ext b eginning w ith t he sa mpling d istribution o f t he mea n i n C hapter 12 a nd
continuing for all of the remaining inference tests. Generating sampling distributions

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xxi

via a n empi rical approa ch helps m ake t he conc ept of sa mpling d istribution conc rete
and facilitates student understanding a nd application of sa mpling distributions. Since
the sampling distribution of the sign test has been generated both by basic probability
considerations and empirically, it serves as an important bridge to understanding all the
sampling distributions discussed later in the textbook.
Introducing inferential statistics with the sign test has other advantages. All of the
important conc epts i nvolving hypothesis t esting ca n b e i llustrated; for example, null
hypothesis, alternative hypothesis, alpha level, Type I and Type II errors, size of effect,
and power. All of these concepts are learned before the formal discussion of sampling
distributions and the z test in Chapter 12. Hence, they don’t compete for the student’s
attention w hen t he s tudent is t rying to u nderstand sa mpling d istributions. T he s ign
test also provides an illustration of the before–after (repeated measures) experimental
design. I b elieve this is a s uperior way to b egin inference testing, because the before–
after design is familiar to most students, is more intuitive, and is easier to understand
than the single-sample design used with the z test.
After hypothesis testing is introduced using the sign test in Chapter 10, power is discussed using the sign test in Chapter 11. Many texts do not discuss power at all, or if they
do, they give it abbreviated treatment. Power is a complicated topic. Using the sign test as
the vehicle for a p ower analysis simplifies matters. Understanding power is ne cessary if
one is to grasp the methodology of scientific investigation itself. When students gain insight
into power, they can see why we bother discussing Type II errors. Furthermore, they see
for the first time why we conclude by “retaining H0” as a reasonable explanation of the data
rather than by “accepting H0 as true” (a most important and often unappreciated distinction). In this same vein, students also understand the error involved when one concludes
that two conditions are equal from data that are not statistically significant. Thus power is a
topic that brings the whole hypothesis-testing methodology into sharp focus.
At this state of the exposition, a diligent student can grasp the idea that data analysis
basically involves two steps: (1) calculating the appropriate statistic, and (2) evaluating
the statistic based on its sampling distribution. The time is ripe for a formal discussion
of sampling distributions and how they can be generated. This is done at the beginning

of Chapter 12. Then the sampling distribution of the mean is i ntroduced. Rather than
depending on an abstract theoretical definition of the sampling distribution of the mean,
the t ext d iscusses how t his sa mpling d istribution ca n b e g enerated empi rically. T his
gives a much more concrete understanding of the sampling distribution of the mean and
facilitates understanding its use with the z test.
Due to pre vious experience with the sign test and its easily understood sampling
distribution, and using the empirical approach for generating the sampling distribution
of the mean, most conscientious students have a good grasp of what sampling distributions a re a nd w hy t hey a re essen tial f or i nferential s tatistics. Wi th t his ba ckground,
students comprehend that all of the concepts of hypothesis testing are the same as we
go from inference test to inference test. What vary from experiment to experiment are
the statistics used, and the accompanying sampling distribution. The stage is then set for
moving through the remaining inference tests with understanding.

Other Important Textbook Features
There are other important features that are worth noting. Among them are the following:
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Chapter 1 d iscusses approaches for determining truth and establishes statistics
as part of the scientific method, which is u nusual for a n introductory statistics
textbook.

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Chapter 8 co vers pro bability. I t do es n ot de lve de eply i nto pro bability t heory.
I view t his as a p lus, because probability ca n be a v ery difficult topic a nd ca n
cause students much unnecessary malaise unless treated at the right level. In my
view the proper mathematical foundation for all of the inference tests contained
in t his textbook ca n b e bu ilt simply by t he use o f basic probability definitions
in conjunction w ith t he a ddition a nd multiplication r ules, a s ha s b een done i n
Chapter 8.
In Chapter 14, the t test for correlated groups is introduced directly after the t
test for single samples and is developed as a special case of the t test for single
samples, only this time using difference scores rather than raw scores. This
makes the t test for correlated groups quite easy to teach and easy for students
to understand.
In Chapter 14, understanding of power is deepened and the important principle
of using t he mos t p owerful i nference t est is i llustrated by a nalyzing t he sa me
data set with the t test for correlated groups and the sign test.

In Chapter 14, the correlated and independent groups designs are compared with
regard to power and utility.
There is a discussion of the factors influencing the power of the t test in Chapter 14
and one-way ANOVA in Chapter 15.
In Chapter 14, the confidence interval approach for evaluating the effect of the
independent variable is presented along with the conventional hypothesis-testing
approach.
Chapter 18 is a summary chapter of all of the inferential statistics material. This
chapter gives students the opportunity to choose among inference tests in solving
problems. Students particularly like the decision tree presented here.
What Is the Truth? sections: At the end of various chapters throughout the textbook, there are sections titled What Is the Truth? along with end-of chapter questions on t hese se ctions. T hese se ctions a nd questions a re i ntended to i llustrate
real-world applications of statistics and to sharpen applied critical thinking.

Tenth Edition Changes
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The following changes have been made in the textbook.

SPSS material has been greatly expanded. Because of increased use of statistical software in recent years a nd in response to re viewer advice, I ha ve greatly
expended the SPSS material. In the tenth edition, there is SPSS coverage at the
end of Chapters 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, and 17. For each chapter, this material is comprised of a detailed illustrative SPSS example and solution along with
at least two new SPSS problems to pr actice on. I n addition, a new Appendix E
contains a general introduction to SPSS. Students can now learn SPSS and practice on chapter-relevant problems without recourse to additional outside sources.
The SPSS material at the end of Chapters 4 and 6 that was contained in the ninth
edition has been dropped. The old Appendix E, Symbols, has been moved to the
inside cover of the textbook.
ANOVA symbols throughout Chapters 15 and 16 have been changed. The

symbols used in the previous editions of the textbook in the A NOVA chapters
have been changed to more conventionally used symbols. The specific changes
are a s f ollows. I n C hapter 1 5, sW 2, sB2, SST, SSW, SSB, d fT, d fW, a nd d fB ha ve
been changed to MSwithin, MSbetween, SStotal, SSwithin, SSbetween, d ftotal, d fwithin, a nd
dfbetween, res pectively. I n C hapter 1 6, sW 2, sR2, sC2, sRC2 , S ST, SSW, SSR, SSC,

Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.


Preface

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SSRC, df T, df W, df R, dfC, a nd df RC have been changed to MSwithin-cells, MSrows,
MScolumns, MSinteraction, SStotal, SSwithin-cells, SSrows, SScolumns, SSinteraction, d ftotal,
dfwithin-cells, dfrows, dfcolumns, and dfinteraction, respectively.
I m ade t hese c hanges b ecause I b elieve s tudents w ill have a n ea sier t ime

transitioning to a dvanced statistical t extbooks a nd using statistical software—
including SPSS—and because of reviewer recommendations. I have some regrets
with moving to t he new symbols, b ecause I b elieve t he old symbols provide a
better transition from the t test to A NOVA, a nd because of t he extra time a nd
effort it may require of instructors who are used to the old symbols (my apologies
to these instructors for the inconvenience).
In Chapter 15, the Newman-Keuls test has been replaced with the Scheffé
test. The Newman-Keuls test has been dropped because of recent criticism from
statistical experts that the Newman-Keuls procedure of adjusting r can result in an
experimentwise or familywise Type I error rate that exceeds the specified level.
I have replaced the Newman-Keuls test with the Scheffé test. T he Scheffé test
has the advantages that (1) it uses a modified ANOVA technique that is relatively
easy to understand and compute; (2) it is very commonly used in the research
literature; (3) it is the most flexible and conservative post hoc test available; and
(4) it provides a good contrast to the Tukey HSD test.
What Is the Truth? questions have been added at the end of the chapters that
contain What Is the Truth? sections (Chapters 1, 3, 6, 8, 10, 11, 15, and 17).
These ques tions have b een a dded to pro vide closer i ntegration of t he What Is
the Truth? sections with the rest of the textbook content and to promote applied
critical thinking.
In Chapter 7, the section titled Regression of X on Y has been dropped. This
section has been dropped because students can compute the regression of Y on X
or of X on Y by just designating the predicted variable as the Y variable. Therefore
there is little practical gain in devoting a separate section to the regression of X
on Y. Separate treatment of the regression of X on Y does contribute additional
theoretical i nsight i nto t he topi c o f re gression, bu t w as j udged n ot i mportant
enough to justify precious introductory textbook space.
The To the Student section has been amplified to include a discussion of
anxiety reduction. This material has been added to he lp students who experience excessive anxiety when dealing with the statistics material. Five options for
reducing anxiety have been presented: (1) seeking help at the university counseling center, (2) taking up the practice of meditation, (3) learning and practicing

autogenic techniques, (4) increasing bodily relaxation via progressive muscle relaxation, and (5) practicing the techniques advocated by positive psychology.
The index has been revised. I favor a det ailed index. In previous editions, the
index has only been partially revised, finally resulting in an index in the ninth
edition that has become unwieldy and redundant. In the tenth edition the index
has b een co mpletely re vised. T he res ult is a s treamlined i ndex t hat I b elieve
retains the detail necessary for a good index.
Minor wording changes have been made throughout the textbook to increase clarity.

Ancillaries
Aplia™ has replaced Enhanced WebAssign, which was used in the ninth edition. Aplia
is an online interactive learning solution that improves comprehension and outcomes by
increasing student effort and engagement. Founded by a professor to en hance his own

Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.