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STATISTICS
Eleventh Edition
Robert S. Witte
Emeritus, San Jose State University
John S. Witte
University of California, San Francisco
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ISBN: 978-1-119-25451-5(PBK)
ISBN: 978-1-119-25445-4(EVALC)
Library of Congress Cataloging-in-Publication Data
Names: Witte, Robert S. | Witte, John S.
Title: Statistics / Robert S. Witte, Emeritus, San Jose State University,
John S. Witte, University of California, San Francisco.
Description: Eleventh edition. | Hoboken, NJ: John Wiley & Sons, Inc.,
[2017] | Includes index.
Identifiers: LCCN 2016036766 (print) | LCCN 2016038418 (ebook) | ISBN
9781119254515 (pbk.) | ISBN 9781119299165 (epub)
Subjects: LCSH: Statistics.
Classification: LCC QA276.12 .W57 2017 (print) | LCC QA276.12 (ebook) | DDC
519.5—dc23
LC record available at https://lccn.loc.gov/2016036766
The inside back cover will contain printing identification and country of origin if omitted from this page.
In addition, if the ISBN on the back cover differs from the ISBN on this page, the one on the back cover
is correct.
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To Doris
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Preface
TO THE READER
Students often approach statistics with great apprehension. For many, it is a required
course to be taken only under the most favorable circumstances, such as during a quarter or semester when carrying a light course load; for others, it is as distasteful as a visit
to a credit counselor—to be postponed as long as possible, with the vague hope that
mounting debts might miraculously disappear. Much of this apprehension doubtless
rests on the widespread fear of mathematics and mathematically related areas.
This book is written to help you overcome any fear about statistics. Unnecessary
quantitative considerations have been eliminated. When not obscured by mathematical
treatments better reserved for more advanced books, some of the beauty of statistics, as
well as its everyday usefulness, becomes more apparent.
You could go through life quite successfully without ever learning statistics. Having
learned some statistics, however, you will be less likely to flinch and change the topic
when numbers enter a discussion; you will be more skeptical of conclusions based on
loose or erroneous interpretations of sets of numbers; you might even be more inclined
to initiate a statistical analysis of some problem within your special area of interest.
TO THE INSTRUCTOR
Largely because they panic at the prospect of any math beyond long division, many
students view the introductory statistics class as cruel and unjust punishment. A halfdozen years of experimentation, first with assorted handouts and then with an extensive
set of lecture notes distributed as a second text, convinced us that a book could be written for these students. Representing the culmination of this effort, the present book
provides a simple overview of descriptive and inferential statistics for mathematically
unsophisticated students in the behavioral sciences, social sciences, health sciences,
and education.
PEDAGOGICAL FEATURES
• Basic concepts and procedures are explained in plain English, and a special effort
has been made to clarify such perennially mystifying topics as the standard deviation, normal curve applications, hypothesis tests, degrees of freedom, and analysis of variance. For example, the standard deviation is more than a formula; it
roughly reflects the average amount by which individual observations deviate
from their mean.
• Unnecessary math, computational busy work, and subtle technical distinctions
are avoided without sacrificing either accuracy or realism. Small batches of data
define most computational tasks. Single examples permeate entire chapters or
even several related chapters, serving as handy frames of reference for new concepts and procedures.
iv
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P R E FA C E
v
• Each chapter begins with a preview and ends with a summary, lists of important
terms and key equations, and review questions.
• Key statements appear in bold type, and step-by-step summaries of important
procedures, such as solving normal curve problems, appear in boxes.
• Important definitions and reminders about key points appear in page margins.
• Scattered throughout the book are examples of computer outputs for three of the
most prevalent programs: Minitab, SPSS, and SAS. These outputs can be either
ignored or expanded without disrupting the continuity of the text.
• Questions are introduced within chapters, often section by section, as Progress
Checks. They are designed to minimize the cumulative confusion reported by
many students for some chapters and by some students for most chapters. Each
chapter ends with Review Questions.
• Questions have been selected to appeal to student interests: for example, probability calculations, based on design flaws, that re-create the chillingly high likelihood of the Challenger shuttle catastrophe (8.18, page 165); a t test analysis of
global temperatures to evaluate a possible greenhouse effect (13.7, page 244);
and a chi-square test of the survival rates of cabin and steerage passengers aboard
the Titanic (19.14, page 384).
• Appendix B supplies answers to questions marked with asterisks. Other appendices provide a practical math review complete with self-diagnostic tests, a glossary of important terms, and tables for important statistical distributions.
INSTRUCTIONAL AIDS
An electronic version of an instructor’s manual accompanies the text. The instructor’s
manual supplies answers omitted in the text (for about one-third of all questions), as well
as sets of multiple-choice test items for each chapter, and a chapter-by-chapter commentary
that reflects the authors’ teaching experiences with this material. Instructors can access
this material in the Instructor Companion Site at http://www.wiley.com/college/witte.
An electronic version of a student workbook, prepared by Beverly Dretzke of the
University of Minnesota, also accompanies the text. Self-paced and self-correcting, the
workbook contains problems, discussions, exercises, and tests that supplement the text.
Students can access this material in the Student Companion Site at http://www.wiley.
com/college/witte.
CHANGES IN THIS EDITION
• Update discussion of polling and random digit dialing in Section 8.4
• A new Section 14.11 on the “file drawer effect,” whereby nonsignificant statistical findings are never published and the importance of replication.
• Updated numerical examples.
• New examples and questions throughout the book.
• Computer outputs and website have been updated.
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vi
P R E FA C E
USING THE BOOK
The book contains more material than is covered in most one-quarter or one-semester
courses. Various chapters can be omitted without interrupting the main development.
Typically, during a one-semester course we cover the entire book except for analysis of
variance (Chapters 16, 17, and 18) and tests of ranked data (Chapter 20). An instructor
who wishes to emphasize inferential statistics could skim some of the earlier chapters,
particularly Normal Distributions and Standard Scores (z) (Chapter 5), and Regression
(Chapter 7), while an instructor who desires a more applied emphasis could omit Populations, Samples, and Probability (Chapter 8) and More about Hypothesis Testing
(Chapter 11).
ACKNOWLEDGMENTS
The authors wish to acknowledge their immediate family: Doris, Steve, Faith, Mike,
Sharon, Andrea, Phil, Katie, Keegan, Camy, Brittany, Brent, Kristen, Scott, Joe, John,
Jack, Carson, Sam, Margaret, Gretchen, Carrigan, Kedrick, and Alika. The first author
also wishes to acknowledge his brothers and sisters: Henry, the late Lila, J. Stuart, A.
Gerhart, and Etz; deceased parents: Henry and Emma; and all friends and relatives,
past and present, including Arthur, Betty, Bob, Cal, David, Dick, Ellen, George, Grace,
Harold, Helen, John, Joyce, Kayo, Kit, Mary, Paul, Ralph, Ruth, Shirley, and Suzanne.
Numerous helpful comments were made by those who reviewed the current and
previous editions of this book: John W. Collins, Jr., Seton Hall University; Jelani Mandara, Northwestern University; L. E. Banderet, Northeastern University; S. Natasha
Beretvas, University of Texas at Austin; Patricia M. Berretty, Fordham University;
David Coursey, Florida State University; Shelia Kennison, Oklahoma State University; Melanie Kercher, Sam Houston State University; Jennifer H. Nolan, Loyola
Marymount University; and Jonathan C. Pettibone, University of Alabama in Huntsville; Kevin Sumrall, Montgomery College; Sky Chafin, Grossmont College; Christine
Ferri, Richard Stockton College of NJ; Ann Barich, Lewis University.
Special thanks to Carson Witte who proofread the entire manuscript twice.
Excellent editorial support was supplied by the people at John Wiley & Sons, Inc.,
most notably Abidha Sulaiman and Gladys Soto.
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Contents
PREFACE
iv
ACKNOWLEDGMENTS
1
INTRODUCTION
vi
1
1.1
WHY STUDY STATISTICS? 2
1.2
WHAT IS STATISTICS? 2
1.3
MORE ABOUT INFERENTIAL STATISTICS
1.4
THREE TYPES OF DATA 6
1.5
LEVELS OF MEASUREMENT 7
1.6
TYPES OF VARIABLES 11
1.7
HOW TO USE THIS BOOK 15
Summary 16
Important Terms 17
Review Questions 17
3
PART 1 Descriptive Statistics: Organizing
and Summarizing Data 21
2
DESCRIBING DATA WITH TABLES AND GRAPHS
TABLES (FREQUENCY DISTRIBUTIONS)
2.1
2.2
2.3
2.4
2.5
2.6
2.7
22
23
FREQUENCY DISTRIBUTIONS FOR QUANTITATIVE DATA 23
GUIDELINES 24
OUTLIERS 27
RELATIVE FREQUENCY DISTRIBUTIONS 28
CUMULATIVE FREQUENCY DISTRIBUTIONS 30
FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA
INTERPRETING DISTRIBUTIONS CONSTRUCTED BY OTHERS 32
GRAPHS
31
33
2.8
GRAPHS FOR QUANTITATIVE DATA 33
2.9
TYPICAL SHAPES 37
2.10 A GRAPH FOR QUALITATIVE (NOMINAL) DATA
2.11 MISLEADING GRAPHS 40
2.12 DOING IT YOURSELF 41
Summary 42
Important Terms 43
Review Questions 43
39
vii
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CONTENTS
3
DESCRIBING DATA WITH AVERAGES
47
3.1
MODE 48
3.2
MEDIAN 49
3.3
MEAN 51
3.4
WHICH AVERAGE? 53
3.5
AVERAGES FOR QUALITATIVE AND RANKED DATA
Summary 56
Important Terms 57
Key Equation 57
Review Questions 57
4
DESCRIBING VARIABILITY
55
60
4.1
INTUITIVE APPROACH 61
4.2
RANGE 62
4.3
VARIANCE 63
4.4
STANDARD DEVIATION 64
4.5
DETAILS: STANDARD DEVIATION 67
4.6
DEGREES OF FREEDOM (df ) 75
4.7
INTERQUARTILE RANGE (IQR) 76
4.8
MEASURES OF VARIABILITY FOR QUALITATIVE AND RANKED DATA
Summary 78
Important Terms 79
Key Equations 79
Review Questions 79
5
NORMAL DISTRIBUTIONS AND STANDARD (z) SCORES
5.1
THE NORMAL CURVE 83
5.2
z SCORES 86
5.3
STANDARD NORMAL CURVE 87
5.4
SOLVING NORMAL CURVE PROBLEMS
5.5
FINDING PROPORTIONS 90
5.6
FINDING SCORES 95
5.7
MORE ABOUT z SCORES 100
Summary 103
Important Terms 103
Key Equations 103
Review Questions 103
6
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82
89
DESCRIBING RELATIONSHIPS: CORRELATION
6.1
6.2
6.3
6.4
6.5
6.6
78
107
AN INTUITIVE APPROACH 108
SCATTERPLOTS 109
A CORRELATION COEFFICIENT FOR QUANTITATIVE DATA: r
DETAILS: COMPUTATION FORMULA FOR r 117
OUTLIERS AGAIN 118
OTHER TYPES OF CORRELATION COEFFICIENTS 119
113
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CONTENTS
ix
6.7
COMPUTER OUTPUT 120
Summary 123
Important Terms and Symbols 124
Key Equations 124
Review Questions 124
7
REGRESSION
126
7.1
TWO ROUGH PREDICTIONS 127
7.2
A REGRESSION LINE 128
7.3
LEAST SQUARES REGRESSION LINE 130
7.4
STANDARD ERROR OF ESTIMATE, sy |x 133
7.5
ASSUMPTIONS 135
7.6
INTERPRETATION OF r 2 136
7.7
MULTIPLE REGRESSION EQUATIONS 141
7.8
REGRESSION TOWARD THE MEAN 141
Summary 143
Important Terms 144
Key Equations 144
Review Questions 144
PART 2 Inferential Statistics: Generalizing
Beyond Data 147
8
POPULATIONS, SAMPLES, AND PROBABILITY
POPULATIONS AND SAMPLES
8.1
8.2
8.3
8.4
8.5
8.6
149
POPULATIONS 149
SAMPLES 150
RANDOM SAMPLING 151
TABLES OF RANDOM NUMBERS 151
RANDOM ASSIGNMENT OF SUBJECTS
SURVEYS OR EXPERIMENTS? 154
PROBABILITY
153
155
8.7
DEFINITION 155
8.8
ADDITION RULE 156
8.9
MULTIPLICATION RULE 157
8.10 PROBABILITY AND STATISTICS
Summary 162
Important Terms 163
Key Equations 163
Review Questions 163
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x
CONTENTS
9
SAMPLING DISTRIBUTION OF THE MEAN
168
9.1
WHAT IS A SAMPLING DISTRIBUTION? 169
9.2
CREATING A SAMPLING DISTRIBUTION FROM SCRATCH
9.3
SOME IMPORTANT SYMBOLS 173
9.4
MEAN OF ALL SAMPLE MEANS (μ ) 173
X
9.5
STANDARD ERROR OF THE MEAN (σ ) 174
X
9.6
SHAPE OF THE SAMPLING DISTRIBUTION 176
9.7
OTHER SAMPLING DISTRIBUTIONS 178
Summary 178
Important Terms 179
Key Equations 179
Review Questions 179
10
INTRODUCTION TO HYPOTHESIS TESTING: THE z TEST
170
182
10.1 TESTING A HYPOTHESIS ABOUT SAT SCORES 183
10.2 z TEST FOR A POPULATION MEAN 185
10.3 STEP-BY-STEP PROCEDURE 186
10.4 STATEMENT OF THE RESEARCH PROBLEM 187
10.5 NULL HYPOTHESIS (H0) 188
10.6 ALTERNATIVE HYPOTHESIS (H1) 188
10.7 DECISION RULE 189
10.8 CALCULATIONS 190
10.9 DECISION 190
10.10 INTERPRETATION 191
Summary 191
Important Terms 192
Key Equations 192
Review Questions 193
11
MORE ABOUT HYPOTHESIS TESTING
195
11.1 WHY HYPOTHESIS TESTS? 196
11.2 STRONG OR WEAK DECISIONS 197
11.3 ONE-TAILED AND TWO-TAILED TESTS 199
11.4 CHOOSING A LEVEL OF SIGNIFICANCE ( ) 202
11.5 TESTING A HYPOTHESIS ABOUT VITAMIN C 203
11.6 FOUR POSSIBLE OUTCOMES 204
11.7 IF H0 REALLY IS TRUE 206
11.8 IF H0 REALLY IS FALSE BECAUSE OF A LARGE EFFECT 207
11.9 IF H0 REALLY IS FALSE BECAUSE OF A SMALL EFFECT 209
11.10 INFLUENCE OF SAMPLE SIZE 211
11.11 POWER AND SAMPLE SIZE 213
Summary 216
Important Terms 217
Review Questions 218
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CONTENTS
12
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ESTIMATION (CONFIDENCE INTERVALS)
221
12.1 POINT ESTIMATE FOR μ 222
12.2 CONFIDENCE INTERVAL (CI) FOR μ 222
12.3 INTERPRETATION OF A CONFIDENCE INTERVAL 226
12.4 LEVEL OF CONFIDENCE 226
12.5 EFFECT OF SAMPLE SIZE 227
12.6 HYPOTHESIS TESTS OR CONFIDENCE INTERVALS? 228
12.7 CONFIDENCE INTERVAL FOR POPULATION PERCENT 228
Summary 230
Important Terms 230
Key Equation 230
Review Questions 231
13
t TEST FOR ONE SAMPLE
233
13.1 GAS MILEAGE INVESTIGATION 234
13.2 SAMPLING DISTRIBUTION OF t 234
13.3 t TEST 237
13.4 COMMON THEME OF HYPOTHESIS TESTS 238
13.5 REMINDER ABOUT DEGREES OF FREEDOM 238
13.6 DETAILS: ESTIMATING THE STANDARD ERROR (s X )
13.7 DETAILS: CALCULATIONS FOR THE t TEST 239
13.8 CONFIDENCE INTERVALS FOR BASED ON t 241
13.9 ASSUMPTIONS 242
Summary 242
Important Terms 243
Key Equations 243
Review Questions 243
14
t TEST FOR TWO INDEPENDENT SAMPLES
238
245
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
EPO EXPERIMENT 246
STATISTICAL HYPOTHESES 247
SAMPLING DISTRIBUTION OF X1 – X 2 248
t TEST 250
DETAILS: CALCULATIONS FOR THE t TEST 252
p-VALUES 255
STATISTICALLY SIGNIFICANT RESULTS 258
ESTIMATING EFFECT SIZE: POINT ESTIMATES AND CONFIDENCE
INTERVALS 259
14.9 ESTIMATING EFFECT SIZE: COHEN’S d 262
14.10 META-ANALYSIS 264
14.11 IMPORTANCE OF REPLICATION 264
14.12 REPORTS IN THE LITERATURE 265
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CONTENTS
14.13 ASSUMPTIONS 266
14.14 COMPUTER OUTPUT 267
Summary 268
Important Terms 268
Key Equations 269
Review Questions 269
15
t TEST FOR TWO RELATED SAMPLES (REPEATED MEASURES)
15.1 EPO EXPERIMENT WITH REPEATED MEASURES 274
15.2 STATISTICAL HYPOTHESES 277
15.3 SAMPLING DISTRIBUTION OF D 277
15.4 t TEST 278
15.5 DETAILS: CALCULATIONS FOR THE t TEST 279
15.6 ESTIMATING EFFECT SIZE 281
15.7 ASSUMPTIONS 283
15.8 OVERVIEW: THREE t TESTS FOR POPULATION MEANS 283
15.9 t TEST FOR THE POPULATION CORRELATION COEFFICIENT, ρ
Summary 287
Important Terms 288
Key Equations 288
Review Questions 288
16
ANALYSIS OF VARIANCE (ONE FACTOR)
273
285
292
16.1
TESTING A HYPOTHESIS ABOUT SLEEP DEPRIVATION
AND AGGRESSION 293
16.2 TWO SOURCES OF VARIABILITY 294
16.3 F TEST 296
16.4 DETAILS: VARIANCE ESTIMATES 299
16.5 DETAILS: MEAN SQUARES (MS ) AND THE F RATIO 304
16.6 TABLE FOR THE F DISTRIBUTION 305
16.7 ANOVA SUMMARY TABLES 307
16.8 F TEST IS NONDIRECTIONAL 308
16.9 ESTIMATING EFFECT SIZE 308
16.10 MULTIPLE COMPARISONS 311
16.11 OVERVIEW: FLOW CHART FOR ANOVA 315
16.12 REPORTS IN THE LITERATURE 315
16.13 ASSUMPTIONS 316
16.14 COMPUTER OUTPUT 316
Summary 317
Important Terms 318
Key Equations 318
Review Questions 319
17
ANALYSIS OF VARIANCE (REPEATED MEASURES)
17.1
17.2
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322
SLEEP DEPRIVATION EXPERIMENT WITH REPEATED MEASURES
F TEST 324
323
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CONTENTS
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17.3 TWO COMPLICATIONS 325
17.4 DETAILS: VARIANCE ESTIMATES 326
17.5 DETAILS: MEAN SQUARE (MS ) AND THE F RATIO
17.6 TABLE FOR F DISTRIBUTION 331
17.7 ANOVA SUMMARY TABLES 331
17.8 ESTIMATING EFFECT SIZE 333
17.9 MULTIPLE COMPARISONS 333
17.10 REPORTS IN THE LITERATURE 335
17.11 ASSUMPTIONS 336
Summary 336
Important Terms 336
Key Equations 337
Review Questions 337
18
ANALYSIS OF VARIANCE (TWO FACTORS)
329
339
18.1 A TWO-FACTOR EXPERIMENT: RESPONSIBILITY IN CROWDS
18.2 THREE F TESTS 342
18.3 INTERACTION 344
18.4 DETAILS: VARIANCE ESTIMATES 347
18.5 DETAILS: MEAN SQUARES (MS ) AND F RATIOS 351
18.6 TABLE FOR THE F 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
340
365
2
ONE-VARIABLE χ TEST 366
19.1
19.2
19.3
19.4
19.5
SURVEY OF BLOOD TYPES 366
STATISTICAL HYPOTHESES 366
2
DETAILS: CALCULATING χ 367
2
TABLE FOR THE χ DISTRIBUTION
2
χ TEST 370
TWO-VARIABLE χ2 TEST
19.6
19.7
19.8
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369
372
LOST LETTER STUDY 372
STATISTICAL HYPOTHESES 373
2
DETAILS: CALCULATING χ 373
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CONTENTS
19.9 TABLE FOR THE χ DISTRIBUTION 376
2
19.10 χ 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
2
20
TESTS FOR RANKED (ORDINAL) DATA
386
20.1
20.2
20.3
20.4
20.5
USE ONLY WHEN APPROPRIATE 387
A NOTE ON TERMINOLOGY 387
MANN–WHITNEY U TEST (TWO INDEPENDENT SAMPLES)
WILCOXON T TEST (TWO RELATED SAMPLES) 392
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?
387
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
C TABLES 457
D GLOSSARY 471
INDEX
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STATISTICS
Eleventh Edition
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C H APTER Introduction
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
WHY STUDY STATISTICS?
WHAT IS STATISTICS?
MORE ABOUT INFERENTIAL STATISTICS
THREE TYPES OF DATA
LEVELS OF MEASUREMENT
TYPES OF VARIABLES
HOW TO USE THIS BOOK
Summary / Important Terms / Review Questions
Preview
Statistics deals with variability. You’re different from everybody else (and, we hope,
proud of it). Today differs from both yesterday and tomorrow. In an experiment
designed to detect whether psychotherapy improves self-esteem, self-esteem scores
will differ among subjects in the experiment, whether or not psychotherapy improves
self-esteem.
Beginning with Chapter 2, descriptive statistics will provide tools, such as tables,
graphs, and averages, that help you describe and organize the inevitable variability
among observations. For example, self-esteem scores (on a scale of 0 to 50) for a
group of college students might approximate a bell-shaped curve with an average score
of 32 and a range of scores from 18 to 49.
Beginning with Chapter 8, inferential statistics will supply powerful concepts that,
by adjusting for the pervasive effects of variability, permit you to generalize beyond
limited sets of observations. For example, inferential statistics might help us decide
whether—after an adjustment has been made for background variability (or chance)—
an observed improvement in self-esteem scores can be attributed to psychotherapy
rather than to chance.
Chapter 1 provides an overview of both descriptive and inferential statistics, and
it also introduces a number of terms—some from statistics and some from math
and research methods—with which you already may have some familiarity. These
terms will clarify a number of important distinctions that will aid your progress
through the book.
1
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2
IN T R O D U C T ION
1 . 1 W H Y S T U D Y S TAT I S T I C S ?
You’re probably taking a statistics course because it’s required, and your feelings
about it may be more negative than positive. Let’s explore some of the reasons why
you should study statistics. For instance, recent issues of a daily newspaper carried
these items:
■
■
■
The annual earnings of college graduates exceed, on average, those of high
school graduates by $20,000.
On the basis of existing research, there is no evidence of a relationship between
family size and the scores of adolescents on a test of psychological adjustment.
Heavy users of tobacco suffer significantly more respiratory ailments than do
nonusers.
Having learned some statistics, you’ll not stumble over the italicized phrases. Nor, as
you continue reading, will you hesitate to probe for clarification by asking, “Which
average shows higher annual earnings?” or “What constitutes a lack of evidence about
a relationship?” or “How many more is significantly more respiratory ailments?”
A statistical background is indispensable in understanding research reports within
your special area of interest. Statistical references punctuate the results sections of
most research reports. Often expressed with parenthetical brevity, these references provide statistical support for the researcher’s conclusions:
■
■
■
Subjects who engage in daily exercise score higher on tests of self-esteem than
do subjects who do not exercise [p .05].
Highly anxious students are perceived by others as less attractive than nonanxious students [t (48) 3.21, p .01, d .42].
Attitudes toward extramarital sex depend on socioeconomic status [x2 (4, n
185) 11.49, p .05, 2c .03].
Having learned some statistics, you will be able to decipher the meaning of these symbols and consequently read these reports more intelligently.
Sometime in the future—possibly sooner than you think—you might want to plan a
statistical analysis for a research project of your own. Having learned some statistics,
you’ll be able to plan the statistical analysis for modest projects involving straightforward research questions. If your project requires more advanced statistical analysis,
you’ll know enough to consult someone with more training in statistics. Once you
begin to understand basic statistical concepts, you will discover that, with some guidance, your own efforts often will enable you to use and interpret more advanced statistical analysis required by your research.
1 . 2 W H AT I S S TAT I S T I C S ?
It is difficult to imagine, even as a fantasy exercise, a world where there is no
variability—where, for example, everyone has the same physical characteristics,
intelligence, attitudes, etc. Knowing that one person is 70 inches tall, and has an
intelligence quotient (IQ) of 125 and a favorable attitude toward capital punishment,
we could immediately conclude that everyone else also has these characteristics.
This mind-numbing world would have little to recommend it, other than that there
would be no need for the field of statistics (and a few of us probably would be looking for work).
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1 .3 MO R E ABOUT INFERENTIAL STATISTICS
3
Descriptive Statistics
Statistics exists because of the prevalence of variability in the real world. In its simplest form, known as descriptive statistics, statistics provides us with tools—tables,
graphs, averages, ranges, correlations—for organizing and summarizing the inevitable variability in collections of actual observations or scores. Examples are:
1. A tabular listing, ranked from most to least, of the total number of romantic
affairs during college reported anonymously by each member of your stat class
2. A graph showing the annual change in global temperature during the last 30 years
3. A report that describes the average difference in grade point average (GPA)
between college students who regularly drink alcoholic beverages and those who
don’t
Inferential Statistics
Statistics also provides tools—a variety of tests and estimates—for generalizing
beyond collections of actual observations. This more advanced area is known as inferential statistics. Tools from inferential statistics permit us to use a relatively small
collection of actual observations to evaluate, for example:
1. A pollster’s claim that a majority of all U.S. voters favor stronger gun control laws
2. A researcher’s hypothesis that, on average, meditators report fewer headaches
than do nonmeditators
3. An assertion about the relationship between job satisfaction and overall happiness
In this book, you will encounter the most essential tools of descriptive statistics
(Part 1), beginning with Chapter 2, and those of inferential statistics (Part 2), beginning
with Chapter 8.
Progress Check *1.1 Indicate whether each of the following statements typifies descriptive statistics (because it describes sets of actual observations) or inferential statistics (because
it generalizes beyond sets of actual observations).
(a) Students in my statistics class are, on average, 23 years old.
(b) The population of the world exceeds 7 billion (that is, 7,000,000,000 or 1 million multiplied
by 7000).
(c) Either four or eight years have been the most frequent terms of office actually served by
U.S. presidents.
(d) Sixty-four percent of all college students favor right-to-abortion laws.
Answers on page 420.
1 . 3 M O R E A B O U T I N F E R E N T I A L S TAT I S T I C S
Population
Any complete collection of observations or potential observations.
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Populations and Samples
Inferential statistics is concerned with generalizing beyond sets of actual observations, that is, with generalizing from a sample to a population. In statistics, a population
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4
Sample
Any smaller collection of actual
observations from a population.
IN T R O D U C T ION
refers to any complete collection of observations or potential observations, whereas a
sample refers to any smaller collection of actual observations drawn from a population. In everyday life, populations often are viewed as collections of real objects (e.g.,
people, whales, automobiles), whereas in statistics, populations may be viewed more
abstractly as collections of properties or measurements (e.g., the ethnic backgrounds of
people, life spans of whales, gas mileage of automobiles).
Depending on your perspective, a given set of observations can be either a population
or a sample. For instance, the weights reported by 53 male statistics students in Table 1.1
can be viewed either as a population, because you are concerned about exceeding the
load-bearing capacity of an excursion boat (chartered by the 53 students to celebrate successfully completing their stat class!), or as a sample from a population because you wish
to generalize to the weights of all male statistics students or all male college students.
Table 1.1
QUANTITATIVE DATA: WEIGHTS (IN POUNDS) OF MALE
STATISTICS STUDENTS
160
193
226
157
180
205
165
168
169
160
163
172
151
157
133
245
170
152
160
220
190
170
160
180
158
170
166
206
150
152
150
225
145
152
172
165
190
156
135
185
159
175
158
179
190
165
152
156
154
165
157
156
135
Ordinarily, populations are quite large and exist only as potential observations (e.g.,
the potential scores of all U.S. college students on a test that measures anxiety). On
the other hand, samples are relatively small and exist as actual observations (the actual
scores of 100 college students on the test for anxiety). When using a sample (100 actual
scores) to generalize to a population (millions of potential scores), it is important that
the sample represent the population; otherwise, any generalization might be erroneous.
Although conveniently accessible, the anxiety test scores for the 100 students in stat
classes at your college probably would not be representative of the scores for all students. If you think about it, these 100 stat students might tend to have either higher or
lower anxiety scores than those in the target population for numerous reasons including, for instance, the fact that the 100 students are mostly psychology majors enrolled
in a required stat class at your particular college.
Random Sampling (Surveys)
Random Sampling
A procedure designed to ensure
that each potential observation in
the population has an equal chance
of being selected in a survey.
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Whenever possible, a sample should be randomly selected from a population in
order to increase the likelihood that the sample accurately represents the population.
Random sampling is a procedure designed to ensure that each potential observation
in the population has an equal chance of being selected in a survey. Classic examples
of random samples are a state lottery where each number from 1 to 99 in the population
has an equal chance of being selected as one of the five winning numbers or a nationwide opinion survey in which each telephone number has an equal chance of being
selected as a result of a series of random selections, beginning with a three-digit area
code and ending with a specific seven-digit telephone number.
Random sampling can be very difficult when a population la