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Library of Congress Cataloging‑in‑Publication Data
Urdan, Timothy C.
Statistics in plain English / Tim Urdan. -- 3rd ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-415-87291-1
1. Statistics--Textbooks. I. Title.
QA276.12.U75 2010
519.5--dc22 2010000438
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the Psychology Press Web site at
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ISBN 0-203-85117-X Master e-book ISBN
To Ella and Nathaniel. Because you rock.
Contents
Preface i x
Chapter 1 Introduction to Social Science Research Principles and Terminology 1
Populations and Samples, Statistics and Parameters 1
Sampling Issues 3
Types of Variables and Scales of Measurement 4
Research Designs 4
Making Sense of Distributions and Graphs 6
Wrapping Up and Looking Forward 1 0
Glossary of Terms for Chapter 1 1 0
Chapter 2 Measures of Central Tendency 1 3
Measures of Central Tendency in Depth 1 4
Example: The Mean, Median, and Mode of a Skewed Distribution 1 5
Writing it Up 17
Wrapping Up and Looking Forward 1 7
Glossary of Terms and Symbols for Chapter 2 18
Chapter 3 Measures of Variability 1 9
Measures of Variability in Depth 2 0
Example: Examining the Range, Variance, and Standard Deviation 2 4
Wrapping Up and Looking Forward 2 8
Glossary of Terms and Symbols for Chapter 3 28
Chapter 4 The Normal Distribution 2 9
The Normal Distribution in Depth 3 0
Example: Applying Normal Distribution Probabilities to a Nonnormal Distribution 3 3
Wrapping Up and Looking Forward 3 4
Glossary of Terms for Chapter 4 3 4
Chapter 5 Standardization and z Scores 3 7
Standardization and z Scores in Depth 3 7
Examples: Comparing Raw Scores and z Scores 45
Wrapping Up and Looking Forward 4 7
Glossary of Terms and Symbols for Chapter 5 4 7
Chapter 6 Standard Errors 4 9
Standard Errors in Depth 49
Example: Sample Size and Standard Deviation Effects on the Standard Error 5 8
Wrapping Up and Looking Forward 5 9
Glossary of Terms and Symbols for Chapter 6 6 0
v
vi ■ Contents
Chapter 7 Statistical Significance, Effect Size, and Confidence Intervals 61
Statistical Significance in Depth 6 2
Effect Size in Depth 6 8
Confidence Intervals in Depth 7 1
Example: Statistical Significance, Confidence Interval, and Effect Size for a
One-Sample t Test of Motivation 7 3
Wrapping Up and Looking Forward 7 6
Glossary of Terms and Symbols for Chapter 7 7 7
Recommended Reading 7 8
Chapter 8 Correlation 7 9
Pearson Correlation Coefficients in Depth 81
A Brief Word on Other Types of Correlation Coefficients 8 8
Example: The Correlation between Grades and Test Scores 8 9
Writing It Up 9 0
Wrapping Up and Looking Forward 9 0
Glossary of Terms and Symbols for Chapter 8 9 1
Recommended Reading 9 2
Chapter 9 t Tests 9 3
Independent Samples t Tests in Depth 9 4
Paired or Dependent Samples t Tests in Depth 9 8
Example: Comparing Boys’ and Girls’ Grade Point Averages 100
Example: Comparing Fifth-and Sixth-Grade GPAs 102
Writing It Up 103
Wrapping Up and Looking Forward 103
Glossary of Terms and Symbols for Chapter 9 104
Chapter 10 One-Way Analysis of Variance 105
One-Way ANOVA in Depth 106
Example: Comparing the Preferences of 5-, 8-, and 12-Year-Olds 113
Writing It Up 116
Wrapping Up and Looking Forward 116
Glossary of Terms and Symbols for Chapter 10 117
Recommended Reading 118
Chapter 11 Factorial Analysis of Variance 119
Factorial ANOVA in Depth 120
Example: Performance, Choice, and Public versus Private Evaluation 128
Writing It Up 129
Wrapping Up and Looking Forward 129
Glossary of Terms for Chapter 11 130
Recommended Reading 130
Chapter 12 Repeated-Measures Analysis of Variance 131
Repeated-Measures ANOVA in Depth 133
Example: Changing Attitudes about Standardized Tests 138
Writing It Up 143
Contents ■ vii
Wrapping Up and Looking Forward 143
Glossary of Terms and Symbols for Chapter 12 144
Recommended Reading 144
Chapter 13 Regression 145
Regression in Depth 146
Multiple Regression 152
Example: Predicting the Use of Self-Handicapping Strategies 156
Writing It Up 159
Wrapping Up and Looking Forward 159
Glossary of Terms and Symbols for Chapter 13 159
Recommended Reading 160
Chapter 14 The Chi-Square Test of Independence 161
Chi-Square Test of Independence in Depth 162
Example: Generational Status and Grade Level 165
Writing It Up 166
Wrapping Up and Looking Forward 166
Glossary of Terms and Symbols for Chapter 14 166
Chapter 15 Factor Analysis and Reliability Analysis: Data Reduction Techniques 169
Factor Analysis in Depth 169
A More Concrete Example of Exploratory Factor Analysis 172
Reliability Analysis in Depth 178
Writing It Up 180
Wrapping Up 180
Glossary of Symbols and Terms for Chapter 15 181
Recommended Reading 182
Appendices 183
Appendix A : Area under the Normal Curve beyond z 185
Appendix B: Critical Values of the t Distributions 187
Appendix C: Critical Values of the F Distributions 189
Appendix D: Critical Values of the Studentized Range Statistic (for the Tukey HSD Test) 195
Appendix E: Critical Values of the χ2 Distributions 199
References 201
Glossary of Symbols 203
Index 205
Preface
Why Use Statistics?
As a researcher who uses statistics frequently, and as an avid listener of talk radio, I find myself
yelling at my radio daily. Although I realize that my cries go unheard, I cannot help myself. As
radio talk show hosts, politicians making political speeches, and the general public all know,
there is nothing more powerful and persuasive than the personal story, or what statisticians
call anecdotal evidence. My favorite example of this comes from an exchange I had with a staff
member of my congressman some years ago. I called his office to complain about a pamphlet his
office had sent to me decrying the pathetic state of public education. I spoke to his staff member
in charge of education. I told her, using statistics reported in a variety of sources (e.g., Berliner
and Biddle’s The Manufactured Crisis and the annual “Condition of Education” reports in the
Phi Delta Kappan written by Gerald Bracey), that there are many signs that our system is doing
quite well, including higher graduation rates, greater numbers of students in college, rising
standardized test scores, and modest gains in SAT scores for students of all ethnicities. The staff
member told me that despite these statistics, she knew our public schools were failing because
she attended the same high school her father had, and he received a better education than she. I
hung up and yelled at my phone.
Many people have a general distrust of statistics, believing that crafty statisticians can “make
statistics say whatever they want” or “lie with statistics.” In fact, if a researcher calculates the
statistics correctly, he or she cannot make them say anything other than what they say, and sta-
tistics never lie. Rather, crafty researchers can interpret what the statistics mean in a variety of
ways, and those who do not understand statistics are forced to either accept the interpretations
that statisticians and researchers offer or reject statistics completely. I believe a better option is
to gain an understanding of how statistics work and then use that understanding to interpret the
statistics one sees and hears for oneself. The purpose of this book is to make it a little easier to
understand statistics.
Uses of Statistics
One of the potential shortfalls of anecdotal data is that they are idiosyncratic. Just as the con-
gressional staffer told me her father received a better education from the high school they both
attended than she did, I could have easily received a higher quality education than my father
did. Statistics allow researchers to collect information, or data, from a large number of people
and then summarize their typical experience. Do most people receive a better or worse educa-
tion than their parents? Statistics allow researchers to take a large batch of data and summarize
it into a couple of numbers, such as an average. Of course, when many data are summarized
into a single number, a lot of information is lost, including the fact that different people have
very different experiences. So it is important to remember that, for the most part, statistics do
not provide useful information about each individual’s experience. Rather, researchers generally
use statistics to make general statements about a population. Although personal stories are often
moving or interesting, it is often important to understand what the typical or average experience
is. For this, we need statistics.
Statistics are also used to reach conclusions about general differences between groups. For
example, suppose that in my family, there are four children, two men and two women. Suppose
that the women in my family are taller than the men. This personal experience may lead me to
the conclusion that women are generally taller than men. Of course, we know that, on average,
ix
Description:This inexpensive paperback provides a brief, simple overview of statistics to help readers gain a better understanding of how statistics work and how to interpret them correctly. Each chapter describes a different statistical technique, ranging from basic concepts like central tendency and describin
