Inferential Statistics
Question;1
As you have been on this journey, you havelearned of the two main approaches in research qualitative and quantitative. The line between quantitative and qualitative can be an interesting one because there is really no pure version of one or the other. Having an understanding of the essential differences between qualitative and quantitative methods can help in choosing the optimum study design and in balancing the two approaches.
In your writing, carefully analyze the differences between each of the research approaches. Incorporate the advantages, disadvantages, and limitations that may be present for each approach using citations and references to validate your argument.
2) In research, appropriate sampling is a critical component to maximize credibility and believability of results in order to generalize results to the population from which the sample was drawn.
This prompt will focus on the following question:If your goal is to generalize from a sample to a population, then which is more important: random selection or random assignment? Explain your answer.In your writing, use appropriate citations and references to support your view.
3) In the realm of statistics, it is known that a one-tailed test is more powerful than a two-tailed test. However, a cause and a situation exists for the use of both.
In your writing,discuss different situations that would call for a two-tailed test over the one-tailed test as well as a one-tailed test over a two-tailed test,using citations and references to validate your argument.
4) In research, the threat of internal and external validity is commonly discussed. However, some researchers view one more important than the other.
In your writing, compare and contrast internal and external validity, and make a determination based on your research/reading for which of the two validity factors is most critical and why,using citations and references to validate your argument.
5) Throughout your doctoral journey, you have touched on a critical componentconcerning ethical considerations.
In your writing, discuss in detail why ethical considerations are so vital for credibility and believability in conducting research,using citations and references to validate your argument.
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APA Style
Central Limit
Theorem
Chi-Square
Choosing
Statistics
Correlation
Factorial ANOVA
Hypothesis Testing
One-Way ANOVA
Scale of
Measurement
Scatter Plots
Standard Error
t-test for Between
Groups and Related
Groups
t-test for One Sample
Tests of Means
Two-Way ANOVA
Z Scores
APA Style
Between vs. Within
Designs
Common Errors in
Student Research
(and How to Avoid
Them)
Controls
Designing a Survey
Effective Debriefing
Ethical Issues
Evaluating Published
Research
Getting Ideas for a
Study
Manipulation Checks
in Experimental
Research
Non-Experimental
Approaches to
Research
Operational
Definitions
Reliability and
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and Dependent
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Australia Brazil Canada Mexico Singapore Spain
United Kingdom United States
Ninth Edition
Basic Statistics
Tales of Distributions
Chris Spatz
Hendrix College
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Basic Statistics: Tales of Distributions, Ninth Edition
Chris Spatz
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http://www.thomsonrights.com
About the Author
Chris Spatz is at Hendrix College in Conway, Arkansas, where he has
twice served as chair of the Psychology Department. After completing
undergraduate work at Hendrix, Spatz earned a Ph.D. in experimental
psychology from Tulane University in New Orleans. He subsequently
completed postdoctoral fellowships in animal behavior at the University
of Michigan and the University of California, Berkeley. Before return-
ing to Hendrix to teach, Spatz held positions at The University of the
South and the University of Arkansas at Monticello.
Spatz has served as a reviewer for the journal Teaching of Psychol-
ogy for more than 20 years, written chapters for edited books, and is a
co-author with Edward P. Kardas of the textbook Research Methods in
Psychology: Ideas, Techniques, and Reports. He was a section editor for
the Encyclopedia of Statistics in Behavioral Science.
Spatz is married to Thea Siria Spatz, and they have three children and seven grand-
children. Aside from writing, Spatz enjoys the outdoors, especially camping and
canoeing. He swims several times a week and is active in the United Methodist Church.
iii
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With love and affection,
this textbook is dedicated to
Thea Siria Spatz, Ed.D., CHES.
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Brief Contents
Preface xv
1 Introduction 1
2 Frequency Distributions and Graphs 24
3 Central Tendency and Variability 40
4 Other Descriptive Statistics 69
5 Correlation and Regression 84
6 Theoretical Distributions Including the Normal Distribution 119
7 Samples, Sampling Distributions, and Confidence Intervals 141
8 Hypothesis Testing and Effect Size: One-Sample Designs 167
9 Hypothesis Testing, Effect Size, and Confidence Intervals:
Two-Sample Designs 191
10 Analysis of Variance: One-Way Classification 223
11 Analysis of Variance: One-Factor Repeated Measures 250
12 Analysis of Variance: Factorial Design 262
13 Chi Square Tests 294
14 More Nonparametric Tests 317
15 Choosing Tests and Writing Interpretations 344
Appendixes
A Arithmetic and Algebra Review 359
B Grouped Frequency Distributions and Central Tendency 373
C Tables 378
D Glossary of Words 399
E Glossary of Symbols 403
F Glossary of Formulas 405
G Answers to Problems 412
References 465
Index 471
v
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Contents
Preface xv
chapter 1 Introduction 1
What Do You Mean, Statistics? 2
clue to the future 4
Whats in It for Me? 4
Some Terminology 5
Problems and Answers 8
Scales of Measurement 9
Statistics and Experimental Design 12
Experimental Design Variables 13
Statistics and Philosophy 15
Statistics: Then and Now 16
Helpful Features of This Book 16
Concluding Thoughts for This Introductory Chapter 19
Additional Help for Chapter 1 21
Key Terms 21
transition passage to descriptive
statistics 23
chapter 2 Frequency Distributions
and Graphs 24
Simple Frequency Distributions 26
error detection 27
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Grouped Frequency Distributions 28
Graphs of Frequency Distributions 30
Describing Distributions 34
The Line Graph 36
More on Graphics 36
A Moment to Reflect 37
Additional Help for Chapter 2 38
Key Terms 39
chapter 3 Central Tendency
and Variability 40
Measures of Central Tendency 41
Finding Central Tendency of Simple Frequency
Distributions 44
error detection 46
error detection 47
When to Use the Mean, Median, and Mode 47
Determining Skewness from the Mean and Median 49
The Weighted Mean 50
Variability 52
The Range 53
Interquartile Range 54
The Standard Deviation 55
The Standard Deviation as a Descriptive Index
of Variability 56
error detection 57
error detection 59
error detection 61
s as an Estimate of s 61
error detection 64
clue to the future 65
The Variance 65
clue to the future 66
Contents vii
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Estimating Answers 66
Additional Help for Chapter 3 68
Key Terms 68
chapter 4 Other Descriptive Statistics 69
Using z Scores to Describe Individuals 70
clue to the future 72
Boxplots 73
error detection 75
Effect Size Index 76
The Descriptive Statistics Report 79
Additional Help for Chapter 4 82
Key Terms 82
transition passage to bivariate
distributions 83
chapter 5 Correlation and Regression 84
Bivariate Distributions 86
Positive Correlation 87
Negative Correlation 89
Zero Correlation 91
clue to the future 91
The Correlation Coefficient 92
error detection 93
clue to the future 96
error detection 96
Scatterplots 97
Interpretations of r 98
Uses of r 100
Strong Relationships but Low Correlations 103
error detection 106
Other Kinds of Correlation Coefficients 106
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Linear Regression 107
Making Predictions from a Linear Equation 107
The Regression EquationA Line of Best Fit 108
error detection 112
Additional Help for Chapter 5 116
Key Terms 116
What Would You Recommend? Chapters 15 116
transition passage to inferential
statistics 118
chapter 6 Theoretical Distributions Including
the Normal Distribution 119
Probability 120
A Rectangular Distribution 121
clue to the future 122
A Binomial Distribution 122
Comparison of Theoretical and Empirical Distributions 124
The Normal Distribution 125
error detection 132
clue to the future 138
Comparison of Theoretical and Empirical Answers 138
Other Theoretical Distributions 139
Additional Help for Chapter 6 140
Key Terms 140
chapter 7 Samples, Sampling Distributions,
and Confidence Intervals 141
Random Samples 143
Biased Samples 146
Research Samples 146
Sampling Distributions 147
clue to the future 148
Contents ix
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The Sampling Distribution of the Mean 148
Central Limit Theorem 149
Constructing a Sampling Distribution When s Is
Not Available 155
The t Distribution 156
Confidence Interval about a Sample Mean 159
clue to the future 159
error detection 160
Categories of Inferential Statistics 163
Additional Help for Chapter 7 164
Key Terms 165
transition passage to hypothesis
testing 166
chapter 8 Hypothesis Testing and Effect Size:
One-Sample Designs 167
The Logic of Null Hypothesis Statistical Testing (NHST) 168
clue to the future 171
Using the t Distribution for Null Hypothesis
Statistical Testing 172
A Problem and the Accepted Solution 174
The One-Sample t Test 176
An Analysis of Possible Mistakes 178
The Meaning of p in p .05 180
One-Tailed and Two-Tailed Tests 181
Effect Size Index 184
Other Sampling Distributions 185
Using the t Distribution to Test the Significance of a
Correlation Coefficient 186
clue to the future 186
Why .05? 188
Additional Help for Chapter 8 190
Key Terms 190
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chapter 9 Hypothesis Testing, Effect Size,
and Confidence Intervals:
Two-Sample Designs 191
A Short Lesson on How to Design an Experiment 192
NHST: The Two-Sample Example 194
Degrees of Freedom 196
Paired-Samples Designs and Independent-Samples
Designs 197
clue to the future 197
The t Test for Independent-Samples Designs 200
clue to the future 203
The t Test for Paired-Samples Designs 205
error detection 208
Significant Results and Important Results 210
Effect Size Index 211
Establishing a Confidence Interval about a Mean
Difference 213
error detection 214
Reaching Correct Conclusions 215
Statistical Power 217
Additional Help for Chapter 9 220
Key Terms 220
What Would You Recommend? Chapters 69 221
transition passage to more complex
designs 222
chapter 10 Analysis of Variance:
One-Way Classification 223
Rationale of ANOVA 225
More New Terms 232
clue to the future 232
Sums of Squares 232
Contents xi
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error detection 236
Mean Squares and Degrees of Freedom 237
error detection 238
Calculation and Interpretation of F Values Using the
F Distribution 238
Schedules of ReinforcementA Lesson in Persistence 240
Comparisons among Means 242
Assumptions of the Analysis of Variance 245
Effect Size Index 246
Additional Help for Chapter 10 249
Key Terms 249
chapter 11 Analysis of Variance: One-Factor
Repeated Measures 250
A Data Set 251
One-Factor Repeated-Measures ANOVA: The Rationale 252
An Example Problem 252
Tukey HSD Tests 256
Type I and Type II Errors 257
Some Behind-the-Scenes Information about
Repeated-Measures ANOVA 258
Additional Help for Chapter 11 261
Key Terms 261
chapter 12 Analysis of Variance:
Factorial Design 262
Factorial Design 263
Main Effects and Interaction 267
clue to the future 272
A Simple Example of a Factorial Design 273
error detection 277
error detection 279
error detection 281
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Analysis of a 2 3 Design 282
Comparing Levels within a FactorTukey HSD Tests 289
Effect Size Indexes for Factorial ANOVA 290
Restrictions and Limitations 291
Additional Help for Chapter 12 292
Key Terms 292
transition passage to nonparametric
statistics 293
chapter 13 Chi Square Tests 294
error detection 295
The Chi Square Distribution and the Chi Square Test 296
Chi Square as a Test of Independence 297
error detection 299
Shortcut for Any 2 2 Table 300
Effect Size Index for 2 2 Chi Square Data 301
Chi Square as a Test for Goodness of Fit 303
Chi Square with More Than One Degree of Freedom 306
Small Expected Frequencies 310
When You May Use Chi Square 313
error detection 313
Additional Help for Chapter 13 316
Key Terms 316
chapter 14 More Nonparametric Tests 317
The Rationale of Nonparametric Tests 318
Comparison of Nonparametric to Parametric Tests 319
clue to the future 320
The MannWhitney U Test 321
error detection 322
error detection 323
Contents xiii
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error detection 324
The Wilcoxon Matched-Pairs Signed-Ranks T Test 327
The WilcoxonWilcox Multiple-Comparisons Test 333
Correlation of Ranked Data 336
error detection 338
My Final Word 339
Additional Help for Chapter 14 341
Key Terms 342
What Would You Recommend? Chapters 1014 342
chapter 15 Choosing Tests and Writing
Interpretations 344
A Review 344
Future Steps 345
Choosing Tests and Writing Interpretations 346
Additional Help for Chapter 15 356
Key Terms 356
Appendixes
A Arithmetic and Algebra Review 359
B Grouped Frequency Distributions
and Central Tendency 373
C Tables 378
D Glossary of Words 399
E Glossary of Symbols 403
F Glossary of Formulas 405
G Answers to Problems 412
References 465
Index 471
xiv Contents
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Preface
Even if our statistical appetite is far from keen, we all of us should
like to know enough to understand, or to withstand, the statistics
that are constantly being thrown at us in print or conversation
much of it pretty bad statistics. The only cure for bad statistics is
apparently more and better statistics. All in all, it certainly appears
that the rudiments of sound statistical sense are coming to be an
essential of a liberal education.
Robert Sessions Woodworth
Basic Statistics: Tales of Distributions, Ninth Edition, is a textbook for a one-term sta-
tistics course in the social or behavioral sciences, education, or the allied health/
nursing field. Its focus is conceptualization, understanding, and interpretation, rather
than computation. Although designed to be comprehensible and complete for students
who take only one statistics course, it includes many elements that prepare students
for additional statistics courses. Basic experimental design terms such as independent
and dependent variables are explained so that students can be expected to write fairly
complete interpretations of their analyses. In many places, the student is invited to stop
and think or stop and do an exercise. Some problems simply ask the student to decide
which statistical technique is appropriate. In sum, this books approach reinforces
instructors who emphasize critical thinking in their course.
This textbook has been remarkably successful for more than 30 years, at times
being a Wadsworth best-seller among statistics texts. Reviewers have praised the
book as have students and professors. A common refrain is that the book has a
conversational style that is engaging, especially for a statistics text. Other features that
distinguish this textbook from others include:
Problems are interspersed throughout the chapter rather than grouped at
the end
Answers to problems are extensive; there are more than 50 pages of
detailed answers
Examples and problems come from a variety of disciplines and everyday life
Most problems are based on actual studies rather than fabricated scenarios
xv
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Computer software analyses are illustrated with SPSS printouts
Interpretation is emphasized; interpretation headings in the answers are
highlighted
Important words and phrases are defined in the margin when they first occur
The effect size index is treated as a descriptive statistic and not just an add-on
to hypothesis-testing problems
Objectives at the beginning of each chapter serve first as an orientation list
and later as a review list
Clues to the Future alert students to concepts that will be repeated
Error Detection boxes tell ways to detect or prevent mistakes
Transition Passages alert students to changes in focus that are part of the
chapters that follow
Comprehensive Problems encompass all (or most) of the techniques in a
chapter
What Would You Recommend? problems require choices from among the
techniques in several chapters
The Wadsworth website has a variety of student aids for each chapter
New to the Ninth Edition
The three ANOVA chapters are reorganized to reflect the way many
instructors teach their course. Factorial ANOVA now comes after one-factor
repeated-measures ANOVA
Nine examples in the text are accompanied by SPSS printouts, reflecting the
increasing use of SPSS in psychology and related fields
Problems based on contemporary data are all updated, including new height
data for Americans
Twenty graphs are new or revised
New notation for the problems makes the answers easier to find in the
appendix
Sections that are heavily revised include:
Statistical power (now focuses on making correct decisions)
The relationship between p and d (addressed and made explicit)
The mean/median relationship in skewed distributions (the old rule of
thumb can be wrong)
Personal Control scores (replaced with the Satisfaction With Life Scale)
Additions to the text include
An operational definition of outliers as 1.5 IQR from the 25th and 75th
percentiles
d as an effect size index for ANOVA
Deletions include
J curves
The explanation of the limits of decimal numbers
xvi Preface
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There are several ancillary publications that supplement this textbook. For
students, the companion website has multiple-choice questions, flashcards, and links
to workshops on many statistical topics. Visit it at www.thomsonedu.com/
psychology/spatz. The Spatz Premium Website has a chapter on power and a study
guide that includes chapter summaries, multiple-choice questions, and problems. The
Premium Website also has hundreds of multiple-choice, fill-in-the-blank, matching,
and computation problems. Some of the problems use definitional formulas, a
technique that improves understanding, and others are pacedcorrect answers are
required at each intermediate step before the program proceeds. Most of the problems
ask for an interpretation. Students can log in at www.thomsonedu.com/psychology/
spatz/premium/spatz_9e. For professors, the Instructors Manual and Test Bank has
teaching suggestions and almost 2000 test items, most of which have been classroom
tested. The Instructors Manual and Test Bank is also available in electronic form.
Students who engage themselves in this book and in their course can expect to
Understand and explain statistical reasoning
Choose correct statistical techniques for the data from simple experiments
Solve statistical problems
Write explanations that are congruent with statistical analyses
A gentle revolution is going on in the practice of statistics. In the past, statistics
moved toward more sophisticated ways to test a null hypothesis. Recently, the
direction shifted to an emphasis on descriptive statistics and graphs, simpler analyses,
and less reliance on null hypothesis statistical testing (NHST). (See the initial report
and the follow-up report of the APA Task Force on Statistical Inference at
www.apa.org/science/bsaweb-tfsi.html.) This edition reflects many of those changes.
Acknowledgments
I am pleased to acknowledge all the help I received from students, colleagues, and
Hendrix College. Roger E. Kirk, my consulting editor for the first six editions, deserves
special thanks for identifying errors and teaching me some statistics. Rob Nichols wrote
sampling programs, and Bob Eslinger produced accurate graphs of the F, t, x2, and
normal distributions. My student assistants were Nicole Loggans, Nick Gowen, and
Adrienne Crowell. Anita Wagner copyedited the manuscript, fixing many subtle errors,
and Jason Thomas shepherded the manuscript through production. I especially want
to acknowledge James O. Johnston, my friend and former co-author, who suggested
that we do a statistics book, dreamed up the subtitle, and worked with me on the first
three editions.
I also want to acknowledge the help of reviewers for this edition:
Preface xvii
Adansi Amankwaa, Albany State
College
Michael Baird, San Jacinto College
Daniel Calcagnetti, Fairleigh
Dickinson University
Sky Chafin, Palomar College
Yong Dai, Louisiana State University
Kathleen Dillon, Western New
England College
Jennifer Peszka, Hendrix College
Marilyn Pugh, Texas Weslyan
University
Francisco Silva, University of
Redlands
00c-W4221-FM.qxd 4/4/07 11:53 AM Page xvii
www.thomsonedu.com/psychology/spatz
www.thomsonedu.com/psychology/spatz
www.thomsonedu.com/psychology/spatz/premium/spatz_9e
www.thomsonedu.com/psychology/spatz/premium/spatz_9e
www.apa.org/science/bsaweb-tfsi.html
In addition to the reviewers for this edition, I have benefited from the criticism of more
than 75 other professors who formally reviewed previous editions of this book,
including Evelyn Blanch-Payne, Albany State University; Chris Bloom, University of
Southern Indiana; Curtis Brant, Baldwin-Wallace College; Thomas Capo, University
of Maryland; Kathleen Dillon, Western New England College; Beverly Dretzke,
University of WisconsinEau Claire; Alexis Grosofsky, Beloit College; Laura Heinze,
University of Kansas; Marcel Satsky Kerr, Tarleton State UniversityCentral Texas;
Gerald Lucker, University of Texas, El Paso; Sandra McIntire, Rollins College; Craig
Nagoshi, Arizona State University; Jennifer Peszka, Hendrix College; David Schwebel,
University of Alabama at Birmingham; Christy Scott, Pepperdine University; Elizabeth
Ann Spatz, Hendrix College; Boyd Spencer, Eastern Illinois University; Greg Streib,
Georgia State University; Philip Tolin, Central Washington University; and Anthony
Walsh, Salve Regina University.
I am grateful to the Longman Group UK Ltd., on behalf of the Literary Executor
of the late Sir Ronald A. Fisher, F.R.S., and Dr. Frank Yates, F.R.S., for permission to
reproduce Tables III, IV, and VII from their book Statistical Tables for Biological,
Agricultural, and Medical Research, Sixth Edition (1974).
My most important acknowledgment goes to my wife and family, who helped and
supported me in many ways over the life of this project. Words are not adequate here.
Ive always had a touch of the teacher in mefirst as an older sibling, then as a
parent and professor, and now as a grandfather. Education is a first-class task, in my
opinion. I hope this book conveys my enthusiasm for teaching and also my philosophy
of teaching. (By the way, if you are a student who is so thorough as to read the whole
preface, you should know that I included phrases and examples in a number of places
that reward your kind of diligence.)
If you find errors in this book, please report them to me at [emailprotected]
I will post corrections at www.hendrix.edu/statistics9thED.
xviii Preface
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www.hendrix.edu/statistics9thED
chapter 1
Introduction
O B J E C T I V E S F O R C H A P T E R 1
After studying the text and working the problems in this chapter, you should
be able to:
1. Distinguish between descriptive and inferential statistics
2. Define the words population, sample, parameter, statistic, and variable as
these terms are used in statistics
3. Distinguish between quantitative and qualitative variables
4. Identify the lower and upper limits of a quantitative measurement
5. Identify four scales of measurement and distinguish among them
6. Distinguish between statistics and experimental design
7. Define some experimental-design termsindependent variable, dependent
variable, and extraneous variableand identify these variables in the
description of an experiment
8. Describe the relationship of statistics to epistemology
9. Identify a few events in the history of statistics
THIS IS A book about statistics that is written for people who do not plan to become
statisticians. In fact, I was not trained as a statistician myself; my field in graduate
school was psychology. At that time, I studied statistics so I could analyze, understand,
and explain quantitative data from my experiments (and also because the courses were
required). Afterward, I realized that statistical techniques and reasoning are valuable
in many other arenas.
Many disciplines use quantitative data. In all of these disciplines, understanding
statistics is at least helpful and may even be necessary. Lawyers, for example,
sometimes have cases in which statistics can help establish more convincing evidence
for their clients. I have assisted lawyers at times, occasionally testifying in court about
the proper interpretation of data. (You will analyze and interpret some of these data in
later chapters.) Statistics is a powerful method for getting answers from data, and it is
sometimes the best way to persuade others that the conclusions are correct.
1
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Whatever your current thoughts about your future as a statistician, I believe you
will benefit from this course. When a statistics course is successful, students learn to
identify the questions that a set of data can answer, determine the statistical procedures
that will provide the answers, carry out the procedures, and then, using plain English
and graphs, tell the story the data reveal. (Also, they find statistics helpful in other
arenas of their lives.)
The best way for you to acquire all these skills (especially the part about telling
the story) is to engage statistics. Engaged students are easily recognized; they are
prepared for exams, not easily distracted while studying, and generally finish
assignments on time. Becoming an engaged student may not be so easy, but many have
achieved it. Here are my recommendations. Read with the goal of understanding. Attend
class. Do all the assignments (on time). Write down questions. Ask for explanations.
Expect to understand. (Disclaimer: Im not suggesting that you marry statistics, but
just engage for this one course.)
Are you uncertain about your arithmetic and algebra skills? Appendix A in the
back of this book may help. It consists of a pretest (to see if you need to refresh your
memory) and a review (to provide that refresher).
What Do You Mean, Statistics?
The Oxford English Dictionary says that the word statistics came into use more than
200 years ago. At that time, statistics referred to a countrys quantifiable political
characteristicscharacteristics such as population, taxes, and area. Statistics meant
state numbers. Tables and charts of those numbers turned out to be a very satisfactory
way to compare different countries and to make projections about the future. Later,
the techniques of using tables and charts proved helpful to people studying trade
(economics) and natural phenomena (science). Statistics was spreading.
Today two different techniques are called statistics. One technique,
descriptive statistics,1 produces a number or a figure that summarizes
or describes a set of data. You are already familiar with some descriptive
statistics. For example, you know about the arithmetic average, called the
mean.You have probably known how to compute a mean since elementary
schooljust add up the numbers and divide the total by the number of
entries. As you
