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vi CONTENTS
CHAPtER 3 Central Tendency 67

PREVIEW 68
3.1 Overview 68
3.2 The Mean 70
3.3 The Median 79
3.4 The Mode 83
3.5 Selecting a Measure of Central Tendency 86
3.6 Central Tendency and the Shape of the Distribution 92
Summary 94
Focus on Problem Solving 95
Demonstration 3.1 96
Problems 96
CHAPtER 4 Variability 99
PREVIEW 100
4.1 Introduction to Variability 101
4.2 Defining Standard Deviation and Variance 103
4.3 Measuring Variance and Standard Deviation for a Population 108
4.4 Measuring Standard Deviation and Variance for a Sample 111
4.5 Sample Variance as an Unbiased Statistic 117
4.6 More about Variance and Standard Deviation 119
Summary 125
Problems 128
z-Scores: Location of Scores

CHAPtER 5 and Standardized Distributions 131
PREVIEW 132
5.1 Introduction to z-Scores 133
5.2 z-Scores and Locations in a Distribution 135
5.3 Other Relationships Between z, X, 𝛍, and 𝛔 138
Copyright 2017 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).
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CONTENTS vii
5.4 Using z-Scores to Standardize a Distribution 141

5.5 Other Standardized Distributions Based on z-Scores 145
5.6 Computing z-Scores for Samples 148
5.7 Looking Ahead to Inferential Statistics 150
Summary 153
Problems 156
CHAPtER 6 Probability 159

PREVIEW 160
6.1 Introduction to Probability 160
6.2 Probability and the Normal Distribution 165
6.3 Probabilities and Proportions for Scores
from a Normal Distribution 172
6.4 Probability and the Binomial Distribution 179
Summary 186
Problems 189
Probability and Samples: The Distribution

CHAPtER 7 of Sample Means 193
PREVIEW 194
7.1 Samples, Populations, and the Distribution
of Sample Means 194
7.2 The Distribution of Sample Means for any Population
and any Sample Size 199
7.3 Probability and the Distribution of Sample Means 206
7.4 More about Standard Error 210
viii CONTENTS
Summary 219
Problems 221
CHAPtER 8 Introduction to Hypothesis Testing 223

PREVIEW 224
8.1 The Logic of Hypothesis Testing 225
8.2 Uncertainty and Errors in Hypothesis Testing 236
8.3 More about Hypothesis Tests 240
8.4 Directional (One-Tailed) Hypothesis Tests 245
8.5 Concerns about Hypothesis Testing: Measuring Effect Size 250
8.6 Statistical Power 254
Summary 260
Problems 263
CHAPtER 9 Introduction to the t Statistic 267

PREVIEW 268
9.1 The t Statistic: An Alternative to z 268
9.2 Hypothesis Tests with the t Statistic 274
9.3 Measuring Effect Size for the t Statistic 279
9.4 Directional Hypotheses and One-Tailed Tests 288
Summary 291
Problems 295
CONTENTS ix
CHAPtER 10 The t Test for Two Independent Samples 299

PREVIEW 300
10.1 Introduction to the Independent-Measures Design 300
10.2 The Null Hypothesis and the Independent-Measures t Statistic 302
10.3 Hypothesis Tests with the Independent-Measures t Statistic 310
10.4 Effect Size and Confidence Intervals for the
Independent-Measures t 316
10.5 The Role of Sample Variance and Sample Size in the
Independent-Measures t Test 322
Summary 325
Problems 329
CHAPtER 11 The t Test for Two Related Samples 335

PREVIEW 336
11.1 Introduction to Repeated-Measures Designs 336
11.2 The t Statistic for a Repeated-Measures Research Design 339
11.3 Hypothesis Tests for the Repeated-Measures Design 343
11.4 Effect Size and Confidence Intervals for the Repeated-Measures t 347
11.5 Comparing Repeated- and Independent-Measures Designs 352
Summary 355
Problems 360
CHAPtER 12 Introduction to Analysis of Variance 365

PREVIEW 366
12.1 Introduction (An Overview of Analysis of Variance) 366
12.2 The Logic of Analysis of Variance 372
12.3 ANOVA Notation and Formulas 375
x CONTENTS
12.4 Examples of Hypothesis Testing and Effect Size with ANOVA 383
12.5 Post Hoc Tests 393
12.6 More about ANOVA 397
Summary 403
Problems 408
CHAPtER 13 Repeated-Measures Analysis of Variance 413

PREVIEW 414
13.1 Overview of the Repeated-Measures ANOVA 415
13.2 Hypothesis Testing and Effect Size with the
Repeated-Measures ANOVA 420
13.3 More about the Repeated-Measures Design 429
Summary 436
Problems 441
Two-Factor Analysis of Variance

CHAPtER 14 (Independent Measures) 447
PREVIEW 448
14.1 An Overview of the Two-Factor, Independent-Measures, ANOVA: Main
Effects and Interactions 448
14.2 An Example of the Two-Factor ANOVA and Effect Size 458
14.3 More about the Two-Factor ANOVA 467
Summary 473
Problems 479
CONTENTS xi
CHAPtER 15 Correlation 485

PREVIEW 486
15.1 Introduction 487
15.2 The Pearson Correlation 489
15.3 Using and Interpreting the Pearson Correlation 495
15.4 Hypothesis Tests with the Pearson Correlation 506
15.5 Alternatives to the Pearson Correlation 510
Summary 520
Problems 524
CHAPtER 16 Introduction to Regression 529

PREVIEW 530
16.1 Introduction to Linear Equations and Regression 530
16.2 The Standard Error of Estimate and Analysis of Regression:
The Significance of the Regression Equation 538
16.3 Introduction to Multiple Regression with Two Predictor Variables 544
Summary 552
Linear and Multiple Regression 554
Problems 556
The Chi-Square Statistic: Tests for Goodness

CHAPtER 17 of Fit and Independence 559
PREVIEW 560
17.1 Introduction to Chi-Square: The Test for Goodness of Fit 561
17.2 An Example of the Chi-Square Test for Goodness of Fit 567
17.3 The Chi-Square Test for Independence 573
17.4 Effect Size and Assumptions for the Chi-Square Tests 582
17.5 Special Applications of the Chi-Square Tests 587
xii CONTENTS
Summary 591
Problems 597
CHAPtER 18 The Binomial Test 603

PREVIEW 604
18.1 Introduction to the Binomial Test 604
18.2 An Example of the Binomial Test 608
18.3 More about the Binomial Test: Relationship with Chi-Square
and the Sign Test 612
Summary 617
Problems 620
A PPE N D IX E S
A Basic Mathematics Review 625
A.1 Symbols and Notation 627
A.2 Proportions: Fractions, Decimals, and Percentages 629
A.3 Negative Numbers 635
A.4 Basic Algebra: Solving Equations 637
A.5 Exponents and Square Roots 640
B Statistical Tables 647
C Solutions for Odd-Numbered Problems in the Text 663
D General Instructions for Using SPSS 683
E Hypothesis Tests for Ordinal Data: Mann-Whitney,
Wilcoxon, Kruskal-Wallis, and Friedman Tests 687
Statistics Organizer: Finding the Right Statistics for Your Data 701
References 717
Name Index 723
Subject Index 725
PREFACE
M any students in the behavioral sciences view the required statistics course as an
intimidating obstacle that has been placed in the middle of an otherwise interest-
ing curriculum. They want to learn about human behavior—not about math and science.
As a result, the statistics course is seen as irrelevant to their education and career goals.
However, as long as the behavioral sciences are founded in science, knowledge of statistics
will be necessary. Statistical procedures provide researchers with objective and systematic
methods for describing and interpreting their research results. Scientific research is the
system that we use to gather information, and statistics are the tools that we use to distill
the information into sensible and justified conclusions. The goal of this book is not only
to teach the methods of statistics, but also to convey the basic principles of objectivity and
logic that are essential for science and valuable for decision making in everyday life.
Those of you who are familiar with previous editions of Statistics for the Behavioral
Sciences will notice that some changes have been made. These changes are summarized
in the section entitled “To the Instructor.” In revising this text, our students have been
foremost in our minds. Over the years, they have provided honest and useful feedback.
Their hard work and perseverance has made our writing and teaching most rewarding. We
sincerely thank them. Students who are using this edition should please read the section of
the preface entitled “To the Student.”
The book chapters are organized in the sequence that we use for our own statistics
courses. We begin with descriptive statistics, and then examine a variety of statistical pro-
cedures focused on sample means and variance before moving on to correlational methods
and nonparametric statistics. Information about modifying this sequence is presented in the
To The Instructor section for individuals who prefer a different organization. Each chapter
contains numerous examples, many based on actual research studies, learning checks, a
summary and list of key terms, and a set of 20–30 problems.
Ancillaries
Ancillaries for this edition include the following.
■■ MindTap® Psychology: MindTap® Psychology for Gravetter/Wallnau’s Statistics
for The Behavioral Sciences, 10th Edition is the digital learning solution that helps
instructors engage and transform today’s students into critical thinkers. Through paths
of dynamic assignments and applications that you can personalize, real-time course
analytics, and an accessible reader, MindTap helps you turn cookie cutter into cutting
edge, apathy into engagement, and memorizers into higher-level thinkers.
As an instructor using MindTap you have at your fingertips the right content and
unique set of tools curated specifically for your course, such as video tutorials that
walk students through various concepts and interactive problem tutorials that provide
students opportunities to practice what they have learned, all in an interface designed
to improve workflow and save time when planning lessons and course structure. The
control to build and personalize your course is all yours, focusing on the most relevant
xiii
xiv PREFACE
material while also lowering costs for your students. Stay connected and informed in
your course through real time student tracking that provides the opportunity to adjust
the course as needed based on analytics of interactivity in the course.
■■ Online Instructor’s Manual: The manual includes learning objectives, key terms,
a detailed chapter outline, a chapter summary, lesson plans, discussion topics, student
activities, “What If” scenarios, media tools, a sample syllabus and an expanded test
bank. The learning objectives are correlated with the discussion topics, student
activities, and media tools.
■■ Online PowerPoints: Helping you make your lectures more engaging while effec-
tively reaching your visually oriented students, these handy Microsoft PowerPoint®
slides outline the chapters of the main text in a classroom-ready presentation. The
PowerPoint® slides are updated to reflect the content and organization of the new
edition of the text.
■■ Cengage Learning Testing, powered by Cognero®: Cengage Learning Testing,
Powered by Cognero®, is a flexible online system that allows you to author, edit,
and manage test bank content. You can create multiple test versions in an instant and
deliver tests from your LMS in your classroom.
Acknowledgments
It takes a lot of good, hard-working people to produce a book. Our friends at Cengage
have made enormous contributions to this textbook. We thank: Jon-David Hague, Product
Director; Timothy Matray, Product Team Director; Jasmin Tokatlian, Content Develop-
ment Manager; Kimiya Hojjat, Product Assistant; and Vernon Boes, Art Director. Special
thanks go to Stefanie Chase, our Content Developer and to Lynn Lustberg who led us
through production at MPS.
Reviewers play a very important role in the development of a manuscript. Accordingly,
we offer our appreciation to the following colleagues for their assistance: Patricia Case,
University of Toledo; Kevin David, Northeastern State University; Adia Garrett, Univer-
sity of Maryland, Baltimore County; Carrie E. Hall, Miami University; Deletha Hardin,
University of Tampa; Angela Heads, Prairie View A&M University; Roberto Heredia,
Texas A&M International University; Alisha Janowski, University of Central Florida;
Matthew Mulvaney, The College at Brockport (SUNY); Nicholas Von Glahn, California
State Polytechnic University, Pomona; and Ronald Yockey, Fresno State University.
To the Instructor
Those of you familiar with the previous edition of Statistics for the Behavioral Sciences will
notice a number of changes in the 10th edition. Throughout this book, research examples
have been updated, real world examples have been added, and the end-of-chapter problems
have been extensively revised. Major revisions for this edition include the following:
1. Each section of every chapter begins with a list of Learning Objectives for that
specific section.
2. Each section ends with a Learning Check consisting of multiple-choice questions
with at least one question for each Learning Objective.
PREFACE xv
3. The former Chapter 19, Choosing the Right Statistics, has been eliminated and
an abridged version is now an Appendix replacing the Statistics Organizer, which
appeared in earlier editions.
Other examples of specific and noteworthy revisions include the following.
Chapter 1 The section on data structures and research methods parallels the new
Appendix, Choosing the Right Statistics.
Chapter 2 The chapter opens with a new Preview to introduce the concept and purpose
of frequency distributions.
Chapter 3 Minor editing clarifies and simplifies the discussion the median.
Chapter 4 The chapter opens with a new Preview to introduce the topic of Central
Tendency. The sections on standard deviation and variance have been edited to increase
emphasis on concepts rather than calculations.
Chapter 5 The section discussion relationships between z, X, μ, and σ has been

expanded and includes a new demonstration example.
Chapter 6 The chapter opens with a new Preview to introduce the topic of Probability.
The section, Looking Ahead to Inferential Statistics, has been substantially shortened and
simplified.
Chapter 7 The former Box explaining difference between standard deviation and
standard error was deleted and the content incorporated into Section 7.4 with editing to
emphasize that the standard error is the primary new element introduced in the chapter.
The final section, Looking Ahead to Inferential Statistics, was simplified and shortened to
be consistent with the changes in Chapter 6.
Chapter 8 A redundant example was deleted which shortened and streamlined the
remaining material so that most of the chapter is focused on the same research example.
Chapter 9 The chapter opens with a new Preview to introduce the t statistic and explain
why a new test statistic is needed. The section introducing Confidence Intervals was edited
to clarify the origin of the confidence interval equation and to emphasize that the interval
is constructed at the sample mean.
Chapter 10 The chapter opens with a new Preview introducing the independent-mea-
sures t statistic. The section presenting the estimated standard error of (M1 – M2) has been
simplified and shortened.
Chapter 11 The chapter opens with a new Preview introducing the repeated-measures t
statistic. The section discussing hypothesis testing has been separated from the section on
effect size and confidence intervals to be consistent with the other two chapters on t tests.
The section comparing independent- and repeated-measures designs has been expanded.
Chapter 12 The chapter opens with a new Preview introducing ANOVA and explaining
why a new hypothesis testing procedure is necessary. Sections in the chapter have been
reorganized to allow flow directly from hypothesis tests and effect size to post tests.
xvi PREFACE
Chapter 13 Substantially expanded the section discussing factors that influence the
outcome of a repeated-measures hypothesis test and associated measures of effect size.
Chapter 14 The chapter opens with a new Preview presenting a two-factor research
example and introducing the associated ANOVA. Sections have been reorganized so that
simple main effects and the idea of using a second factor to reduce variance from indi-
vidual differences are now presented as extra material related to the two-factor ANOVA.
Chapter 15 The chapter opens with a new Preview presenting a correlational research
study and the concept of a correlation. A new section introduces the t statistic for evaluat-
ing the significance of a correlation and the section on partial correlations has been simpli-
fied and shortened.
Chapter 16 The chapter opens with a new Preview introducing the concept of regression and
its purpose. A new section demonstrates the equivalence of testing the significance of a correla-
tion and testing the significance of a regression equation with one predictor variable. The sec-
tion on residuals for the multiple-regression equation has been edited to simplify and shorten.
Chapter 17 A new chapter Preview presents an experimental study with data consisting
of frequencies, which are not compatible with computing means and variances. Chi-square
tests are introduced as a solution to this problem. A new section introduces Cohen’s w as
a means of measuring effect size for both chi-square tests.
Chapter 18 Substantial editing clarifies the section explaining how the real limits for
each score can influence the conclusion from a binomial test.
The former Chapter 19 covering the task of matching statistical methods to specific
types of data has been substantially shortened and converted into an Appendix.
■■Matching the Text to Your Syllabus

The book chapters are organized in the sequence that we use for our own statistics courses.
However, different instructors may prefer different organizations and probably will choose
to omit or deemphasize specific topics. We have tried to make separate chapters, and even
sections of chapters, completely self-contained, so they can be deleted or reorganized to fit
the syllabus for nearly any instructor. Some common examples are as follows.
■■ It is common for instructors to choose between emphasizing analysis of variance
(Chapters 12, 13, and 14) or emphasizing correlation/regression (Chapters 15 and 16).
It is rare for a one-semester course to complete coverage of both topics.
■■ Although we choose to complete all the hypothesis tests for means and mean
differences before introducing correlation (Chapter 15), many instructors prefer to
place correlation much earlier in the sequence of course topics. To accommodate
this, Sections 15.1, 15.2, and 15.3 present the calculation and interpretation of
the Pearson correlation and can be introduced immediately following Chapter 4
(variability). Other sections of Chapter 15 refer to hypothesis testing and should be
delayed until the process of hypothesis testing (Chapter 8) has been introduced.
■■ It is also possible for instructors to present the chi-square tests (Chapter 17) much
earlier in the sequence of course topics. Chapter 17, which presents hypothesis tests
for proportions, can be presented immediately after Chapter 8, which introduces the
process of hypothesis testing. If this is done, we also recommend that the Pearson
correlation (Sections 15.1, 15.2, and 15.3) be presented early to provide a foundation
for the chi-square test for independence.
PREFACE xvii
To the Student
A primary goal of this book is to make the task of learning statistics as easy and painless
as possible. Among other things, you will notice that the book provides you with a number
of opportunities to practice the techniques you will be learning in the form of Learning
Checks, Examples, Demonstrations, and end-of-chapter problems. We encourage you to
take advantage of these opportunities. Read the text rather than just memorizing the for-
mulas. We have taken care to present each statistical procedure in a conceptual context that
explains why the procedure was developed and when it should be used. If you read this
material and gain an understanding of the basic concepts underlying a statistical formula,
you will find that learning the formula and how to use it will be much easier. In the “Study
Hints,” that follow, we provide advice that we give our own students. Ask your instructor
for advice as well; we are sure that other instructors will have ideas of their own.
Over the years, the students in our classes and other students using our book have given
us valuable feedback. If you have any suggestions or comments about this book, you can
write to either Professor Emeritus Frederick Gravetter or Professor Emeritus Larry Wallnau
at the Department of Psychology, SUNY College at Brockport, 350 New Campus Drive,
Brockport, New York 14420. You can also contact Professor Emeritus Gravetter directly at
fgravett@brockport.edu.
■■Study Hints
You may find some of these tips helpful, as our own students have reported.
■■ The key to success in a statistics course is to keep up with the material. Each new
topic builds on previous topics. If you have learned the previous material, then the
new topic is just one small step forward. Without the proper background, however,
the new topic can be a complete mystery. If you find that you are falling behind, get
help immediately.
■■ You will learn (and remember) much more if you study for short periods several
times per week rather than try to condense all of your studying into one long session.
For example, it is far more effective to study half an hour every night than to have
a single 3½-hour study session once a week. We cannot even work on writing this
book without frequent rest breaks.
■■ Do some work before class. Keep a little ahead of the instructor by reading the appro-
priate sections before they are presented in class. Although you may not fully under-
stand what you read, you will have a general idea of the topic, which will make the
lecture easier to follow. Also, you can identify material that is particularly confusing
and then be sure the topic is clarified in class.
■■ Pay attention and think during class. Although this advice seems obvious, often it is
not practiced. Many students spend so much time trying to write down every example
presented or every word spoken by the instructor that they do not actually understand
and process what is being said. Check with your instructor—there may not be a need
to copy every example presented in class, especially if there are many examples like
it in the text. Sometimes, we tell our students to put their pens and pencils down for a
moment and just listen.
■■ Test yourself regularly. Do not wait until the end of the chapter or the end of the
week to check your knowledge. After each lecture, work some of the end-of-chapter
problems and do the Learning Checks. Review the Demonstration Problems, and
be sure you can define the Key Terms. If you are having trouble, get your questions
answered immediately—reread the section, go to your instructor, or ask questions in
class. By doing so, you will be able to move ahead to new material.
xviii PREFACE
■■ Do not kid yourself! Avoid denial. Many students observe their instructor solve
problems in class and think to themselves, “This looks easy, I understand it.” Do
you really understand it? Can you really do the problem on your own without having
to leaf through the pages of a chapter? Although there is nothing wrong with using
examples in the text as models for solving problems, you should try working a prob-
lem with your book closed to test your level of mastery.
■■ We realize that many students are embarrassed to ask for help. It is our biggest chal-
lenge as instructors. You must find a way to overcome this aversion. Perhaps contact-
ing the instructor directly would be a good starting point, if asking questions in class
is too anxiety-provoking. You could be pleasantly surprised to find that your instruc-
tor does not yell, scold, or bite! Also, your instructor might know of another student
who can offer assistance. Peer tutoring can be very helpful.
Frederick J Gravetter
Larry B. Wallnau
A B o U t tH E AU tH o R S
Frederick J Gravetter is Professor Emeritus of Psychology at the

State University of New York College at Brockport. While teaching at
Brockport, Dr. Gravetter specialized in statistics, experimental design, and
cognitive psychology. He received his bachelor’s degree in mathematics from
M.I.T. and his Ph.D in psychology from Duke University. In addition to pub-
lishing this textbook and several research articles, Dr. Gravetter co-authored
Research Methods for the Behavioral Science and Essentials of Statistics for
the Behavioral Sciences.
Frederick Gravetter
Larry B. WaLLnau is Professor Emeritus of Psychology at the State

University of New York College at Brockport. While teaching at Brockport,
he published numerous research articles in biopsychology. With
Dr. Gravetter, he co-authored Essentials of Statistics for the Behavioral
Sciences. Dr. Wallnau also has provided editorial consulting for numerous
publishers and journals. He has taken up running and has competed in 5K
races in New York and Connecticut. He takes great pleasure in adopting
neglected and rescued dogs.
Larry B. Wallnau
xix
CH A P T ER
Introduction to Statistics 1
© Deborah Batt
PREVIEW
1.1 Statistics, Science, and Observations
1.2 Data Structures, Research Methods, and Statistics
1.3 Variables and Measurement
1.4 Statistical Notation
Summary
Focus on Problem Solving
Demonstration 1.1
Problems
PREVIEW
Before we begin our discussion of statistics, we ask you The objectives for this first chapter are to provide
to read the following paragraph taken from the philoso- an introduction to the topic of statistics and to give you
phy of Wrong Shui (Candappa, 2000). some background for the rest of the book. We discuss
the role of statistics within the general field of scientific
The Journey to Enlightenment
inquiry, and we introduce some of the vocabulary and
In Wrong Shui, life is seen as a cosmic journey,
notation that are necessary for the statistical methods
a struggle to overcome unseen and unexpected
that follow.
obstacles at the end of which the traveler will find
As you read through the following chapters, keep
illumination and enlightenment. Replicate this quest
in mind that the general topic of statistics follows a
in your home by moving light switches away from
well-organized, logically developed progression that
doors and over to the far side of each room.*
leads from basic concepts and definitions to increas-
Why did we begin a statistics book with a bit of twisted ingly sophisticated techniques. Thus, each new topic
philosophy? In part, we simply wanted to lighten the serves as a foundation for the material that follows. The
mood with a bit of humor—starting a statistics course is content of the first nine chapters, for example, provides
typically not viewed as one of life’s joyous moments. In an essential background and context for the statistical
addition, the paragraph is an excellent counterexample for methods presented in Chapter 10. If you turn directly
the purpose of this book. Specifically, our goal is to do to Chapter 10 without reading the first nine chapters,
everything possible to prevent you from stumbling around you will find the material confusing and incomprehen-
in the dark by providing lots of help and illumination as sible. However, if you learn and use the background
you journey through the world of statistics. To accomplish material, you will have a good frame of reference for
this, we begin each section of the book with clearly stated understanding and incorporating new concepts as they
learning objectives and end each section with a brief quiz are presented.
to test your mastery of the new material. We also intro-
duce each new statistical procedure by explaining the pur-
pose it is intended to serve. If you understand why a new *Candappa, R. (2000). The little book of wrong shui. Kansas City:
procedure is needed, you will find it much easier to learn. Andrews McMeel Publishing. Reprinted by permission.
1.1 Statistics, Science, and Observations

LEARNING OBJECTIVEs 1. Define the terms population, sample, parameter, and statistic, and describe the
relationships between them.
2. Define descriptive and inferential statistics and describe how these two general
categories of statistics are used in a typical research study.
3. Describe the concept of sampling error and explain how this concept creates the
fundamental problem that inferential statistics must address.
■■Definitions of Statistics
By one definition, statistics consist of facts and figures such as the average annual snowfall
in Denver or Derrick Jeter’s lifetime batting average. These statistics are usually informative
and time-saving because they condense large quantities of information into a few simple fig-
ures. Later in this chapter we return to the notion of calculating statistics (facts and figures)
but, for now, we concentrate on a much broader definition of statistics. Specifically, we use
the term statistics to refer to a general field of mathematics. In this case, we are using the
term statistics as a shortened version of statistical procedures. For example, you are prob-
ably using this book for a statistics course in which you will learn about the statistical tech-
niques that are used to summarize and evaluate research results in the behavioral sciences.
SEctIon 1.1 | Statistics, Science, and Observations 3
Research in the behavioral sciences (and other fields) involves gathering information.
To determine, for example, whether college students learn better by reading material on
printed pages or on a computer screen, you would need to gather information about stu-
dents’ study habits and their academic performance. When researchers finish the task of
gathering information, they typically find themselves with pages and pages of measure-
ments such as preferences, personality scores, opinions, and so on. In this book, we present
the statistics that researchers use to analyze and interpret the information that they gather.
Specifically, statistics serve two general purposes:
1. Statistics are used to organize and summarize the information so that the researcher can
see what happened in the research study and can communicate the results to others.
2. Statistics help the researcher to answer the questions that initiated the research by
determining exactly what general conclusions are justified based on the specific
results that were obtained.
DEFInItIon The term statistics refers to a set of mathematical procedures for organizing, sum-
marizing, and interpreting information.
Statistical procedures help ensure that the information or observations are presented
and interpreted in an accurate and informative way. In somewhat grandiose terms, statistics
help researchers bring order out of chaos. In addition, statistics provide researchers with a
set of standardized techniques that are recognized and understood throughout the scientific
community. Thus, the statistical methods used by one researcher will be familiar to other
researchers, who can accurately interpret the statistical analyses with a full understanding
of how the analysis was done and what the results signify.
■■Populations and Samples

Research in the behavioral sciences typically begins with a general question about a specific
group (or groups) of individuals. For example, a researcher may want to know what factors
are associated with academic dishonesty among college students. Or a researcher may want
to examine the amount of time spent in the bathroom for men compared to women. In the
first example, the researcher is interested in the group of college students. In the second
example, the researcher wants to compare the group of men with the group of women. In sta-
tistical terminology, the entire group that a researcher wishes to study is called a population.
DEFInItIon A population is the set of all the individuals of interest in a particular study.
As you can well imagine, a population can be quite large—for example, the entire set
of women on the planet Earth. A researcher might be more specific, limiting the population
for study to women who are registered voters in the United States. Perhaps the investigator
would like to study the population consisting of women who are heads of state. Populations
can obviously vary in size from extremely large to very small, depending on how the inves-
tigator defines the population. The population being studied should always be identified by
the researcher. In addition, the population need not consist of people—it could be a popula-
tion of rats, corporations, parts produced in a factory, or anything else an investigator wants
to study. In practice, populations are typically very large, such as the population of college
sophomores in the United States or the population of small businesses.
Because populations tend to be very large, it usually is impossible for a researcher to
examine every individual in the population of interest. Therefore, researchers typically select
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With sands of sleep, from slumber’s sea.
I try my best awake to stay,
But I am tired out with play;
“I’ll never see him!” mother says,
And mother tells the truth—always!
—Marie Van Vorst
BILLY BINKS
(d art) (pl ace) (d ance)

st art le f ace pr ance
c ast les (eight) (st ar)

n eigh ed f ar ther
h urr y
p urr (sm ile) (r oof)
m ile h oof
(f elt)
m elt waul (r oar)
s oar
pres ent ly trav eled
en e mies
en tered fin ished
for tune
blazed hor ri ble
sau cers
di rect ly front
prom ise
ter ri ble ter ri fied
broom
dis ap peared re mem ber
Once upon a time a little boy named Billy Binks set out to seek his
fortune. He traveled alone for many a weary mile, but at last he met
a little gray pony.
“Where are you going, Billy Binks?” neighed the pony.
“I am going to seek my fortune,” said Billy Binks.
“May I go, too?”
“If I take you, will you help me win my fortune?”
“Yes.”
“How?”
“I will carry you on my back and kick all your enemies with my hard
hoofs.”
“Very well, you may come along.”
Then they went on a little farther and met a cow.
“Where are you going, Billy Binks?” mooed the cow.
“I am going to seek my fortune,” answered Billy Binks.
“Yes.”
“How?”
“I will moo, and toss your enemies on my sharp horns.”
“Very well, you may come.”
When they had walked on a little farther they met a dog.
“Where are you going, Billy Binks?” barked the dog.
“Yes.”
“How?”
“I will bark, and bite your enemies with my sharp teeth.”
After walking a little farther they met a cat.
“Where are you going, Billy Binks?” mewed the cat.
“Yes.”
“How?”
“I will purr, and scratch your enemies with my sharp claws.”
They continued their journey and presently met a raven.
“Where are you going, Billy Binks?” croaked the raven.
“I am going to seek my fortune.”
“Yes.”
“How?”
“I will croak, and peck your enemies’ eyes out with my sharp
beak.”
On and on they walked till at last they entered a deep, dark wood.
All day they journeyed through this forest, which grew denser and
darker as night came on.
“We are near a clearing in this wood,” croaked the raven, who had
been soaring above the treetops. “Let us keep right on.”
Suddenly all were startled by a bright light, the brightest any of
them had ever seen. It flashed out through the trees directly in front
of them. It fairly dazzled and blinded them. Then it as suddenly
disappeared, and left them standing terrified in the pitch-black
darkness of the night.
Again the light flashed out, and again disappeared.
“What can it be?” asked Billy Binks, hoarsely, as soon as he could
find his voice.
“Perhaps it is a lamp,” mewed the cat.
“No, it is too bright for a lamp,” answered Billy Binks.
“It might be a house on fire,” barked the dog.
“No, if it were, we could see the light all the time; and besides,
there is no house here. I have flown this way before,” answered the
raven.
“It may be a lighthouse,” said Billy Binks.
“No,” replied the raven, “the sea is miles from here. You all keep
still while I fly over the treetops and find out what it is.”
Billy Binks and his animal friends kept ever so quiet, while the
raven flew up and quickly disappeared in the darkness. It seemed
hours before he returned.
“Oh, my friends,” croaked the raven, alighting in their midst at last,
“you never saw such a sight! There’s the most horrible, monstrous
hob-goblin over there in the clearing. He has a nose as long as a
broomstick—”
“Oh! Oh! Oh!” cried Billy Binks and his friends.
“—Eyes as big as saucers and as green as the sea—”
“—And a mouth big enough to swallow us all!”
“He has a great fire blazing among some rocks. That is the light
you saw. When he walks in front of it you cannot see the light. That
is why you thought it disappeared.”
“I see! I see! I see!” said Billy Binks and his friends.
“He is busy melting gold, and he has piles of gold and jewels
hidden in his cave—”
“Ah, ha!” laughed Billy Binks, as he climbed bravely upon his gray
pony.
“His cave is full of nice plump field mice—”
“Mew! Mew!” cried the cat, as she scrambled up behind Billy
Binks.
“In the bushes back of the cave live many rabbits—”
“Bow-wow!” barked the dog, as he bounded toward Billy Binks.
“Near the cave is a large green meadow, with the sweetest grass
and the coolest brook in the world—”
“Moo! Moo!” lowed the cow, as she, too, hurried up beside Billy
Binks.
“And there is a tall tree that will make a fine home for me,” finished
the raven, as she flew over Billy Binks’s head.
“Come on, friends,” whispered Billy Binks, boldly. “It is time to win
my fortune. Remember you have all promised to help me.”
“Yes, yes, I’ll help. And I think I see my fortune, too,” answered
each of the animals, now as bold as Billy Binks.
Softly, quietly, and slowly they crept through the forest. Presently
they came to the clearing. There stood the ugly, black hob-goblin,
bending over his fire. His back was turned toward them.
“Now!” shouted Billy Binks, and they all rushed at the terrible
monster.
The raven dashed into his face and pecked at his large green
eyes.
The cat scratched great gashes in his long nose.
The dog bit him, and the horse kicked him.
The enraged cow rushed upon him with lowered head, caught him
on her horns, and tossed him as high as the treetops.
Then the cow began to bellow.
The dog began to howl.
The cat began to waul.
The raven began to caw.
The pony began to prance.
And Billy Binks began to shout with all his might.
Such a frightful din that old hob-goblin had never heard! He picked
himself up from the sharp rocks where he had fallen, and dashed
away with might and main through the forest. If he hasn’t stopped,
he is running still.
“Ho, ho!” cried Billy Binks, springing from the gray pony and
running to the mouth of the cave. “This heap of gold and this pile of
jewels will do for my fortune. If you carry them safely home for me,
Pony, I will build you a beautiful stable, and you shall have a full crib
of oats before you all the rest of your life. That will be your fortune.”
“This cave, full of good, plump mice, is my fortune,” called the cat,
as she pounced on the first unlucky mouse.
“All these rabbits shall be my fortune,” barked the dog, as he set
off in hot haste after a fleeing bunny.
“And this green meadow is my fortune,” mooed the cow, as she
began to crop the sweet grass.
“Who could have a better fortune than this?” croaked the raven,
flying to the top of a tall tree.
So Billy Binks said “Good-by” to his friends, and left them each
with his fortune. He quickly bagged the gold and jewels, threw them
across the pony’s back, and mounting, hurried off homeward.
The pony smelled oats all the way, while Billy Binks saw castles
and lands on all sides.
Some Things to think About
WHEN THE LITTLE BOY RAN AWAY
(s ist er) (r oam) (under)

tw ist ed f oam ing th under
wan der ed ech o par ents
aw ful trun dle

When the little boy ran away from home,
The birds in the tree-top knew,
And they all sang, “Stay!” but he wandered away
Under the skies of blue.
And the wind came whispering from the tree,
“Follow me, follow me!”
And it sang him a song that was soft and sweet
And scattered the roses before his feet
That day, that day,
When the little boy ran away.
The violets whispered, “Your eyes are blue

And lovely and bright to see,
And so are mine, and I’m kin to you,
So dwell in the light with me.”
But the little boy laughed, while the wind in glee
Sang, “Follow, follow me!”
And the wind called the clouds from their home in the skies
And said to the violet, “Shut your eyes!”
That day, that day,
Then the wind played leapfrog over the hills

And twisted each leaf and limb;
And all the rivers and all the rills
Were foaming mad with him;
And ’twas dark as the darkest night could be,
But still came the wind’s voice, “Follow me!”
And over the mountain and up from the hollow
Came echoing voices with, “Follow him; follow!”
That awful day,
Then the little boy cried, “Let me go, let me go!”

For a scared, scared boy was he.
But the thunder growled from a black cloud, “No!”
And the wind roared, “Follow me!”
And an old gray owl from a tree-top flew,
Saying: “Who are you-oo? Who are you-oo?”
And the little boy sobbed, “I’m lost away!
And I want to go home where my parents stay.”
O, the awful day
When the little boy ran away!
Then the moon looked out from a cloud and said:

“Are you sorry you ran away?
If I light you home to your trundle bed,
Will you stay, little boy, will you stay?”
And the little boy promised—and cried and cried—
He never would leave his mother’s side,
And the moonlight led him over the plain;
And his mother welcomed him home again.
But, O, what a day
When the little boy ran away!
HOW THE BEAN GOT ITS BLACK SEAM
(ea gle) (r ope) sew ed
ea ger h ope
hul lo
(h ush) (m ean)
cr ush b ean cru el
mo ment gur gling tor rent
quar rel four both er
coun try pour ing a las
in stant ly
Once upon a time there was a poor old woman living in a village of
a far country. She had gathered some beans and was making ready
to cook them. She built a fire of sticks, but, as these were damp, they
did not burn well. So she thrust in a handful of dry straw. Now the
flames leaped up, and the sticks snapped and crackled in the blaze.
A live red coal flew out of the fire, fell on the ground beside a
straw, and lay there smoking. Just then a bean dropped from the pot
which the old woman was filling, rolled away, and came to rest close
to the coal and the straw.
“Hullo, Mr. Coal,” said the straw. “How you smoke! Are you
frightened? Where did you come from?”
“I just sprang out of that fire,” answered the coal. “Had I not
jumped just as I did, I should now be nothing but ashes. My, look at
that blaze!”
“I, too, jumped in the nick of time,” spoke up the bean. “That cruel
old woman was just pouring me into the pot when I leaped over the
edge, and here I am.”
“Yes, here you are, silly thing,” broke out the coal and the straw
together. “But what are you going to do? As soon as the old woman
turns around she will spy you, then back you’ll go into the pot. It’s
hotter now than when you left it.”
“Don’t bother about me; think of yourselves,” answered the bean,
angrily. “When the old woman picks me up, she’ll tread on you, Mr.
Coal, and crush your life out. And you, Mrs. Straw, she’ll stick into
the blaze. It’s hotter there than in the pot.”
“Come, come,” said the straw, softly, “let’s not quarrel. Let’s be
friends and stick together. Perhaps we can save ourselves yet.”
“You are quite right, Mrs. Straw,” said the coal.
The bean said nothing, but she listened eagerly to the plans of the
two others. These soon agreed to travel together to a far country,
where they hoped to find their fortune. They set out without delay,
and the bean rolled along behind.
Soon the three travelers came to a little gurgling brook. It seemed
to them a mighty rushing and roaring torrent.
“Oh, dear, what shall we do now?” asked the bean, speaking for
the first time since the journey began. “We can never get across
these awful waters. Hear them thunder down the rocky cliffs!”
“Don’t worry, little Bean,” said the straw, proudly. “I’ll help you and
Mr. Coal across in a twinkling.”
Thereupon the straw laid herself across the stream. She was just
long enough to reach from bank to bank.
“Now walk over the bridge, Mr. Coal and Miss Bean,” called the
straw.
The coal hastened on to the straw bridge while the bean watched
in wonder. All went well until the middle of the stream was reached,
when the bridge bent so low under the weight of the coal and the
waters thundered so loudly that the coal stopped in fright.
The coal stood still for only a moment. But, alas, that was a
moment too long.
The dry straw smoked, burst into a tiny flame, and broke in two.
Down fell the coal into the water below and was instantly drowned.
The burning straw bridge also fell into the water, which put out the
flames, and the two pieces of straw went floating away down stream.
All this the little bean saw, watching safely from the bank. And she
thought it the funniest thing that ever happened. So she laughed and
she laughed—until she burst!
This would have been the end of little Miss Bean, had not a tailor
passed that way just then. He was sorry for the poor bean, so he
picked up the two parts tenderly, and quickly sewed them together.
But the thread that he used was black. And ever since that time
some beans have a black seam around them.
FRIENDS
(tw ist) ferns com fort ed

wh ist ling North gent ians
North Wind came whistling through the wood

Where the tender, sweet things grew—
The tall fair ferns and the maiden hair,
And the gentle gentians blue.
“It’s very cold! Are we growing old?”
They sighed, “What shall we do?”
The sigh went up to the loving leaves.

“We must help,” they whispered low.
“They are frightened and weak, O brave old trees!
But we love you well, you know.”
And the trees said, “We are strong—make haste!
Down to the darlings go.”
So the leaves went floating, floating down,

All yellow, and brown, and red,
And the frail little trembling, thankful things
Lay still, and were comforted.
And the blue sky smiled through the bare old trees,
Down on their soft warm beds.
—L. G. Warner.
HELP ONE ANOTHER
(m outh) splen did (m ount ain)

s outh f ount ain
“Help one another,” the snowflakes said,

As they cuddled down in their fleecy bed.
“One of us here would not be felt,
One of us here would quickly melt;
But I’ll help you, and you help me,
And then what a splendid drift there’ll be.”
“Help one another,” the maple spray

Said to its fellow leaves one day;
“The sun would wither me here alone,
Long enough ere the day is gone;
But I’ll help you, and you help me,
And then what a splendid shade there’ll be.”

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(eBook PDF) Statistics for The

Behavioral Sciences 10th Edition

Statistics for the behavioral sciences 10th Edition

(eBook PDF) Essentials of Statistics for the Behavioral

(eBook PDF) Statistics for the Behavioral Sciences 5th

(Original PDF) Basic Statistics for the Behavioral

(eBook PDF) Essentials of Statistics for The Behavioral

Essentials of Statistics for The Behavioral Sciences

(eBook PDF) Essentials of Statistics for the Behavioral

(eBook PDF) Fundamental Statistics for the Behavioral

CHAPtER 3 Central Tendency 67

z-Scores: Location of Scores

5.4 Using z-Scores to Standardize a Distribution 141

CHAPtER 6 Probability 159

Probability and Samples: The Distribution

CHAPtER 8 Introduction to Hypothesis Testing 223

CHAPtER 9 Introduction to the t Statistic 267

CHAPtER 10 The t Test for Two Independent Samples 299

CHAPtER 11 The t Test for Two Related Samples 335

CHAPtER 12 Introduction to Analysis of Variance 365

CHAPtER 13 Repeated-Measures Analysis of Variance 413

Two-Factor Analysis of Variance

CHAPtER 15 Correlation 485

CHAPtER 16 Introduction to Regression 529

The Chi-Square Statistic: Tests for Goodness

CHAPtER 18 The Binomial Test 603

Chapter 5 The section discussion relationships between z, X, μ, and σ has been

■■Matching the Text to Your Syllabus

Frederick J Gravetter is Professor Emeritus of Psychology at the

Larry B. WaLLnau is Professor Emeritus of Psychology at the State

1.1 Statistics, Science, and Observations

■■Populations and Samples

—Marie Van Vorst

(d art) (pl ace) (d ance)

c ast les (eight) (st ar)

(s ist er) (r oam) (under)

wan der ed ech o par ents

aw ful trun dle

The violets whispered, “Your eyes are blue

Then the wind played leapfrog over the hills

Then the little boy cried, “Let me go, let me go!”

Then the moon looked out from a cloud and said:

mo ment gur gling tor rent

quar rel four both er

coun try pour ing a las

(tw ist) ferns com fort ed

North Wind came whistling through the wood

The sigh went up to the loving leaves.

So the leaves went floating, floating down,

(m outh) splen did (m ount ain)

“Help one another,” the snowflakes said,

“Help one another,” the maple spray

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