Wk3 Bad Graph and Good Graph Data Presentation Discussion Statistics about Examining Data After reviewing Week 3 material for discussion and Text Book （Fu

Wk3 Bad Graph and Good Graph Data Presentation Discussion Statistics about Examining Data

After reviewing Week 3 material for discussion and Text Book （Fundamental Statistics for the Social and Behavioral Sciences）CHAPTER 2, find one graph that you think does a horrible job of representing a set of data and one graph that you think does a good job of representing a set of data.

For Bad Graph：What are some problems with the graph? What did you learn or fail to learn from the graph? How do you think the graph could be improved?

For Good Graph： Why do you think the graph is effective? What did you learn from the graph? What is the main message you think the author was trying to reinforce with the graph? Week 3 Materials
Readings
Textbook Readings
Chapter 2 Examining Data
Examining Data: Tables and Figures
Before Analyzing
Before analyzing data, researchers first examine them to:
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gain an initial sense of the data,
detect data coding or data entry errors,
identify outliers,
evaluate research methodology, and
determine whether data meet statistical criteria and assumptions.
Chapter 2 describe these reasons in detail. Please pay close attention to this material.
Tables
Researchers typically organize their data in tables known as frequency distribution tables.
What is a distribution? Distributions tell us what values a variable takes and how often it
takes those values.
Tables and graphs are common ways to display distributions. The table on the left
provides the same information as the graph on the right (courtesy
of http://www.citefactor.org/impactfactor/journal/2999/Impact-factor-of-Evaluation-&The-Health-Professions)
The distribution below are reported in table form and tell us how many cases have been
accounted for out of the total number of cases. In this example, 9 people were asked
about the total number of parking tickets they’ve gotten.
These distributions can also show percentages of each individual score (the 3rd column)
and/or the cumulative percentage (the 4th column).
Displaying Distributions for Categorical Variables
For categorical variables we use pie charts and bar graphs (also called bar charts) to
display distributions.
Pie charts show the distribution of a categorical variable as a “pie” whose slices represent
the counts or percentages for each category.
All the categories for that one variable must be represented and the total should add up to
100% (but sometimes doesn’t because of rounding error).
Bar graphs are another way to display the distributions of categorical variables.
Each category is represented by a bar and the height of the bar represents the count or
percent.
Which type of graph to use?
Do you prefer one over the other?
Bar graphs are “more flexible” than pie charts because they can be used to compare
quantities that are not part of a whole.
For example, what technological devices do you love?
See? This graph compares different things, not parts of the same whole.
Displaying Distributions for Quantitative Variables
For quantitative variables (variables that take numerical values), we use histograms and
frequency polygons.
The most common graph of the distribution of one quantitative variable is a histogram.
Histograms break the range of values of a variable into classes and display only the count
of the observations that fall into each class.
Each class must be the same width. Histograms are drawn with no spaces between the
bars to indicate that all values of the variable are covered.
For example, here is a histogram that shows the height of students in a class. Each class
has the same width, 10 centimeters.
We interpret histograms by looking at their overall pattern.
When describing histograms, we focus on their shape, center and spread.
these more in upcoming chapters.
Histogram Shapes
We’ll cover
This is a normally shaped frequency distribution a.k.a., bell-shaped curve.
Many variables take this normal (bell-shaped) frequency distribution. Can you think of
any?
The number of seeds on a strawberry is normally distributed. IQ is normally distributed
in the population.
Variations of the Normal Distribution
A bimodal distribution has two different frequently occurring scores (i.e., two peaks).
Distributions can also have different symmetry. We call this skew.
In a positively skewed distribution, the tail is pointing towards the high (i.e., positive)
scores.
It has more low than high scores.
In a negatively skewed distribution, the tail is pointing towards the low (i.e., negative)
scores.
It has more high than low scores.
Non-normal Frequency Distributions
Leptokurtic & Platykurtic Distributions
Leptokurtic distributions are more pointed than the normal distribution whereas
platykurtic distributions are more flat.
Fundamental Statistics for the Social and Behavioral Sciences
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To my kids, Meagan and Will, and my parents, Katsumi and Grayce Tokunaga.
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Fundamental Statistics for the Social and
Behavioral Sciences
Howard T. Tokunaga
San Jose State University
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FOR INFORMATION:
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Detailed Contents
Preface
Acknowledgments
About the Author
Chapter 1. Introduction to Statistics
Chapter 2. Examining Data: Tables and Figures
Chapter 3. Measures of Central Tendency
Chapter 4. Measures of Variability
Chapter 5. Normal Distributions
Chapter 6. Probability and Introduction to Hypothesis Testing
Chapter 7. Testing One Sample Mean
Chapter 8. Estimating the Mean of a Population
Chapter 9. Testing the Difference between Two Means
Chapter 10. Errors in Hypothesis Testing, Statistical Power, and Effect Size
Chapter 11. One-Way Analysis of Variance (ANOVA)
Chapter 12. Two-Way Analysis of Variance (ANOVA)
Chapter 13. Correlation and Linear Regression
Chapter 14. Chi-Square
Tables
Appendix: Review of Basic Mathematics
Glossary
References
Index
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Preface
It may surprise students to learn they have something in common with writers of books
such as this one: When you get close to finishing a writing assignment, you get a bit tired
and a bit lazy. The first attempt at this preface was written shortly after final drafts of
chapters were sent to my editor at SAGE, Vicki Knight. After reading it, she said, “It’s not
bad, but it reads like the ‘typical’ Preface. I think it would be useful for the reader to have a
sense of why you wrote this book and why you wrote it the way you did.”
In responding to my editor’s plea for self-analysis, I found that this book’s journey began in
college. When I entered college, I thought my path would take me to law school; however,
taking an Intro to Psych class my freshman year made me realize I enjoy the challenge of
trying to understand the human mind. The school I attended, UC Santa Cruz, was a fairly
unconventional university, but somehow in the midst of a sea of humanistic psychologists,
I became attracted to the empirical and methodological aspects of psychology. This was a
result of taking classes with instructors such as David Harrington and Dane Archer, who
showed me that statistics could appeal to students if taught using a gentle, guiding
approach that addresses questions relevant to students’ lives. After graduating from college,
I was able to get a job as a research assistant for a human resource consulting firm. Despite
my lack of work experience, I was hired primarily as a result of having taken statistics and
research methods courses, which taught me that learning statistics has benefits both inside
and outside of the classroom.
Several years later, I started grad school at UC Berkeley, where two events critical to this
book took place. First, serving as a teaching assistant, I found I really enjoyed helping
students, particularly in statistics and research methods classes that were often viewed with
fear and suspicion. Second, I took graduate classes from Geoff Keppel, who had developed
his own unique method and system for analyzing experimental research designs. His
lectures and books were instrumental in showing me that statistics can be taught in a
systematic way that highlights similarities rather than differences between different research
situations. Geoff managed to transform something as daunting sounding as a “3 × 2 × 4
research design” into the mathematical equivalent of playing with wooden toy alphabet
blocks labeled “A,” “B,” and “C.” For a long time, I thought my gratitude to Geoff was an
isolated occurrence. However, the appreciation others have for his approach to teaching
statistics was made apparent to me several years later when I watched him receive an
American Psychological Association (APA) Lifetime Achievement award.
After leaving Cal, I took on a teaching position at San Jose State, where my teaching
responsibilities included an introductory statistics course aimed at students with a wide
range of background, ability, and motivation. As I needed to select a textbook to use in this
course, for the first time I looked carefully at the wide range of offerings. What I found
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striking (and still find striking) was that the majority of books focused on providing
formulas and very small sets of data designed to demonstrate how to correctly calculate the
correct numbers from these formulas. Little emphasis, however, was given to what these
numbers meant or implied. Given my own experiences learning statistics, I thought a book
was needed that discusses statistics in a thematic manner, focusing on how they are used to
answer questions and test ideas within the larger research process.
The primary purpose of this book is to not just teach students how to calculate statistics but
how to interpret the results of statistical analyses in light of a study’s research hypothesis
and to communicate one’s results and interpretations to a broader audience. Hopefully, this
book will not only help students understand the purpose and use of statistics but also give
them a greater understanding of how research studies are conceived, conducted, and
communicated.
The 14 chapters of this book may be placed into three general categories. The first four
chapters are designed to introduce students to the research process and how data that have
been collected may be organized, presented, and summarized. Chapters 5 through 10
discuss the process of conducting statistical analyses to test research questions and
hypotheses, as well as issues and controversies regarding this process. The final four chapters
of this book, Chapters 11 to 14, discuss different statistical procedures used in research
situations that vary in the number of independent variables in the study as well as how the
independent and dependent variables have been measured.
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A Few Tips for Students
To you, the college student about to read this book as part of taking a statistics course:
“Welcome!” and “Great job!” I welcome you because you’re about to embark on a
semester-long journey that I hope will enhance your skills and widen your perspective; I
congratulate you because it’s a journey not everyone is willing to take.
At the present moment, I know my encouragement and appreciation may be of little
comfort to you as you might be somewhat anxious about having to learn statistics. Some of
you might be anxious about having to learn statistical concepts and formulas; some of you
might be anxious because the research process seems pretty complicated. Talking with
students who have taken my courses over the years has helped me assemble the following
advice:
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Master the Material Presented in the Early Chapters
Chapters 1 through 6 discuss how research is often conducted, how data are summarized
and described, and the process by which researchers conduct statistical analyses to test their
ideas. It is absolutely critical for you to have a firm understanding of these chapters as they
lay the groundwork for later chapters that discuss a variety of statistical procedures used by
researchers to test hypotheses.
What does it mean to master this material? First, read the chapters both before and after
they’re discussed in class. By reading the chapters beforehand, you’ll be able to identify
anything that’s unclear to you and have your questions addressed by your instructor.
Rereading the chapters after they’re discussed in class will help confirm your understanding
of the material. Next, be able to define and explain key concepts presented in these chapters.
These concepts are highlighted in bold-faced type, and it is important to learn them when
they’re first introduced because they’ll appear throughout the remainder of the book. Next,
do the learning checks within the chapters and the exercises at the end of the chapters. The
learning checks include both exercises and review questions you can ask yourself to assess
your understanding of the material. Most important, do not miss class during the early part of
the semester! It’s been my experience that students who miss critical lectures at the beginning
of the term often have difficulty keeping up as the semester continues.
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Review High School Algebra
If you read newspapers or watch television, you might conclude that the most complicated
data analysis people can comprehend is a pie chart. As frustrating as this is to researchers
and statistics instructors, they understand that statistics can be confusing. If you happen to
move beyond the introductory statistics course for which you are reading this book, you’ll
find that statistical procedures are often conducted using computers and statistical software
rather than hand calculations. Consequently, some statistics textbooks no longer include
mathematical formulas but instead have students conduct analyses using statistical software
or Microsoft Excel. However, this book has chosen a different approach for two main
reasons. First, I believe that to comprehend the results of data analysis, one must
understand the underlying foundation of statistical procedures. Learning statistics via
computer software can lead to a “brain-dead” approach in which students are at the mercy
(rather than control) of their computers. I refer to this as the “I’m only as smart as my
printout” method of learning statistics, also known as “Because this is what my computer
told me.”
Second, my steadfast and somewhat stubborn adherence to an approach emphasizing
mathematical formulas and calculations is based on a simple reason: The statistics in this
book are not hard to calculate! To assess whether you’re adequately prepared to read this
book, take the following test:
1. Do you know how to add, subtract, multiply, and divide?
2. Do you know how to calculate the “square” or “square root” of a number?
3. Do you understand the “order of operations” and how to use parentheses within
mathematical calculations?
If your answers to these questions are yes, congratulations! You possess the ability to
conduct every mathematical calculation in this book. None of the formulas in this book
requires knowledge of geometry, trigonometry, or calculus. However, if you’re unsure of
your mathematical ability, you may want to review your high school algebra. At the end of
this book is an appendix that includes the mathematical concepts and operations needed to
conduct the statistical analyses in this book. I highly recommend you read this appendix to
review and assess your mathematical skills.
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Learn to Use a Statistical Calculator
Although learning the statistics in this book doesn’t require the use of computers or
software, you will need a hand calculator. Calculators with statistical capabilities are
typically identified as statistical or scientific calculators. Although there’s a wide selection of
brands and models, one simple criterion to use in selecting a calculator is price. The
statistical calculators most appropriate for this book cost somewhere in the $10 to $15
range at the time of this writing. I do not recommend you use or purchase a more expensive
calculator! I prefer these simpler calculators because I’ve found students are able to conduct
the calculations in this book more quickly and with fewer errors. I also recommend you
purchase a calculator similar to the one your instructor uses as he or she will be more
familiar with its features and idiosyncrasies.
In selecting a calculator, look closely at the keyboard; you’ll need a calculator whose keys
have labels such as “ X ¯ ,” “σ,” and “ΣX” (Chapters 3 and 4 discuss what these symbols
represent). When you go calculator shopping, you’ll find calculators that have keys with
labels such as “ΣY” and “XY.” Although calculators with these “Y” symbols are only slightly
more expensive than calculators with just the “X” symbols, I do not recommend their
purchase because these features are not needed to perform the calculations in this book. In
fact, I’ve found students with “Y” calculators have a more difficult time performing simpler
calculations.
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Ask Questions
Conducting research is the process of asking and answering questions. Accordingly,
throughout this book, issues are often framed in the form of questions, which I hope
encourages you to ask questions as well. The first person you should direct any questions to
is yourself. As you work your way through the chapters, get into the habit of asking
yourself, “What does this mean?” A good test of your level of comprehension is whether
you can explain the material to yourself in a meaningful way.
Also, be sure to work with your instructor to confirm your level of understanding and
clarify unanswered questions. Instructors often say to students, “The only ‘bad’ question is
the one you don’t ask.” Don’t be hesitant about asking questions in class. Instructors will
tell you they use one student’s question to assess an entire class’ level of understanding. This
is what I call the “pencil test”—when one student asks a question, I look to see how many
other pencils get raised, which reflects the number of students who had the same question
and are ready to write down the response. Asking questions enhances the learning
experience for yourself, your classmates, and your instructor.
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Form a Study Group
No matter how much I encourage students to ask questions in class, it seems they hesitate
for fear of drawing attention to themselves. As a result, I turn to another well-traveled
saying: “Misery loves company.” Forming a study group to meet with other students on a
regular basis will help you keep up with reading assignments, confirm your comprehension
of the material, clarify any confusion you have, prepare for exams, and receive an invaluable
source of social support. I do suggest that your group contain at least one person who will
raise the group’s questions and concerns to the instructor in class or office hours.
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Practice, Practice, Practice
The best way to learn the topics covered by this book is to obtain as much practice as
possible. Throughout the chapters are examples in which the cal…
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