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Based on the attached reading, formulate a written response answering these questions based on take-aways from the readings Please answer the following prompts after reading the chapters.Explain what you think is the major take-home message from chapter 1 or discuss why you think this author chose to put this chapter at the beginning of his statistics textbook?In chapter 1, the author propose nine (9) strategies for succeeding in a statistics course. Which of the strategies are you most likely to employ (don’t choose buying a calculator)? Do you think you can commit to doing this strategy for the next four weeks? After reading chapter 2, discuss how doing your own rational emotive therapy can help you overcome math anxiety.
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SECTION I
Essentials for Statistics
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
I
f you are one of the “terrified” for whom this book is intended, the chapters
in this section may be particularly helpful. Chapter 1 provides an introduction to the text. Because the nature and content of statistics courses typically
differ from that of courses in many fields of study, this chapter offers study
tips for students of statistics. Chapter 2 presents some general strategies and
techniques for dealing with the uncomfortable feelings that many students
experience when taking a course in statistics. One common problem experienced by students in statistics courses is not being able to demonstrate on tests
what they have learned because of anxiety. If you think you might be one of
these people, this chapter may help. Chapter 3 reviews basic math concepts
that you may have known at one time but have gotten rusty through disuse or
that you have just plain forgotten. You need to know these concepts to learn
statistics. Just like when building a house, you must have a firm foundation
on which to construct statistical knowledge. Also presented in this chapter are
sample problems that will allow you to practice and to test your ability to use
these basic math concepts.
The chapters in Section I are intended to help you get off to a running start
and may well be worth your time and energy. Of course, if you are already
comfortable with numbers and know all the basics, you may not get much out
of these chapters. Nonetheless, “Heck, I already know all this stuff” is a great
way to begin reading a book on statistics, especially if you think it might be
terrifying!
1
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CHAPTER 1
Effective Strategies for
Studying Statistics
WHAT YOU’LL LEARN:
• Self-Assessment
• Assumptions about the Reader
• Effective Strategies for Studying
Statistics
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
“You haven’t told me yet,” said Lady Nuttal, “what it is your fiancé
does for a living.”
“He’s a statistician,” replied Lamia, with an annoying sense of
being on the defensive.
L a dy N utta l wa s o b v io usly t ake n abac k. I t had not
occurred to her that statisticians entered into normal
social relationships. The species, she would have surmised,
was perpetuated in some collateral manner, like mules.
“But Aunt Sara, it’s a very interesting profession,” said Lamia
warmly. “I don’t doubt it,” said her aunt, who obviously doubted
it very much. “To express anything important in mere figures
is so plainly impossible that there must be endless scope for
well-paid advice on how to do it. But don’t you think that life
with a statistician would be rather, shall we say, humdrum?”
Lamia was silent. She felt reluctant to discuss the
surprising depth of emotional possibility which she had
discovered below Edward’s numerical veneer.
“It’s not the figures themselves,” she said finally, “it’s
what you do with them that matters.”
—K. A. C. Manderville, The Undoing of Lamia Gurdleneck1
Republished with permission of Oxford University Press, from The Advanced Theory of Statistics, Vol. 2: Classical Inference and Relationship by Maurice Kendall, Alan Stuart, and J. Keith
Ord, 1978; permission conveyed through Copyright Clearance Center, Inc.
1
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4 Section I • Essentials for Statistics
A
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
nother statistics book! There are now so many statistics books on the
market that it seems strange even to me that there be another one. As someone who has taken statistics courses, worked as a teaching assistant in statistics
courses, and taught statistics courses, I have been dissatisfied with the available
books because they seem aimed at students who whizzed right through college
algebra and considered majoring in math just for the sheer joy of it. A number of my students in social science programs are not like that. Many of them
would respond with a hearty “true” to many of the following self-test statements. I invite you to test yourself to see if you too fit the pattern:
1. I have never been very good at math.
2. When my teacher tried to teach me long division in the fourth grade, I seriously considered dropping out of school.
3. When we got to extracting square roots, thoughts of suicide flashed through
my mind.
4. Word problems! My head felt like a solid block of wood when I was asked to
solve problems like, “If it takes Mr. Jones 3 hours to mow a lawn and Mr. Smith
2 hours to mow the same lawn, how long will it take if they mow it together?”
5. Although I never dropped out of school, I became a quantitative dropout
soon after my first algebra course.
6. I avoided courses like chemistry and physics because they required math.
7. I decided early on that there were some careers I could not pursue because
I was poor in math.
8. When I take a test that includes math problems, I get so upset that my mind
goes blank and I forget all the material I studied.
9. Sometimes I wonder if I am a little stupid.
10. I feel nervous just thinking about taking a statistics course.
Did you answer “true” to some of these items? If so, this book may be
helpful to you. When writing it, I also made some assumptions about you:
1. You are studying statistics only because it is a requirement in your major
area of study.
2. You are terrified (or at least somewhat anxious) about math and are not
sure that you can pass a course in statistics.
3. It has been a long time since you studied math, and what little you knew
then has been long forgotten.
4. With a little instruction and a lot of hard work, you can learn statistics.
If you can stay calm while baking a cake or reading your bank statement,
there is hope for you.
5. You may never learn to love statistics, but you can change your statistics
self-concept. When you finish your statistics course, you will be able to say,
truthfully, “I am the kind of person who can learn statistics!”
The aim of this book is to help you achieve two important objectives. The
first is to deal with math anxiety and avoidance responses that interfere with
learning statistics. The second is to understand and compute the most widely
used elemental statistics.
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Chapter 1 • Effective Strategies for Studying Statistics
5
Effective Strategies for Studying Statistics
The following is some advice on studying statistics that you will find useful as
we move toward these two objectives.
Buy a Calculator
Because statistics require you to work with numbers, you should consider buying a calculator. Make sure that it has at least one memory and that it can take
square roots (almost all calculators can do this). Before you buy a calculator,
though, check out your personal computer—virtually all desktop and laptop
computers come with a calculator program that will easily handle the problems
in this book. If you don’t need your calculator during exams, that may be all
you need. In any case, read the manual that comes with your calculator and
learn how to use your calculator effectively and efficiently.
Develop a Solid Math Foundation
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Most statistics courses are cumulative. New concepts are constantly added to
and built on previous concepts. Most statistics courses begin with relatively
straightforward and concrete concepts and quickly become more complex and
abstract. It’s important to master the basic math concepts used in the computation of all statistics because that will make success later in the course more
likely. Nothing is more frustrating than understanding the statistics concept and
what to do to solve a problem but not getting the right answer because of a silly
computation error.
Form a Study Group
Study groups can be extremely helpful while preparing for exams, completing
homework, taking notes, sharing learning strategies, and providing emotional
support. The optimum size for study groups is three people. Effective groups
tend to have no more than five members, however. Exchange telephone numbers and times when you can be reached. Meet regularly in a distraction-free
environment. Talk about what you are studying and offer to help others (you
may learn best by teaching others). When you are stuck with a problem that
you can’t solve, don’t hesitate to ask others for their help. Very likely, they will
have some of the same feelings and difficulties you do. Not everyone gets stuck
on the same topics, so you can help each other.
Keep Up
If you are in a statistics class, go to class every day and take complete notes.
Complete all the assigned reading and homework as soon as possible and
before new material is covered. This ensures that new concepts are fresh in your
mind and linked to previously learned material. Students who are “terrified” of
statistics are susceptible to falling behind, often because of their general dislike
of the content. Playing “catch-up” in a statistics class is very difficult. Don’t let
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Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
6 Section I • Essentials for Statistics
Source: Glen Baxter, www.glenbaxter.com. Used with permission.
this happen to you. The material in the next chapter on overcoming math anxiety might be helpful if you are one of these people.
Time Management
A widely used rule of thumb for the amount of time to spend studying for a college course is 2 hours of study time per credit hour per week. For a three-credit
class, you should plan to spend 6 hours studying outside class each week. Is this
enough time for a statistics class for you? Maybe. Maybe not. For many of my
students, statistics is the hardest class they will take. You should take as much
time as you need to do all the assigned homework and reading and to understand the material. Regardless of the amount of time you need to learn statistics,
spread the amount of time you spend studying over a number of days rather
than on 1 or 2 days per week. For example, if you plan to devote 10 hours per
week to the study of statistics, spend 2 hours studying at the same time for 5
days each week. Don’t cram 10 hours of study time into 1 or 2 days each week!
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Chapter 1 • Effective Strategies for Studying Statistics
7
Study Actively
Be actively involved in the learning process. Take responsibility for
understanding the material. Recognize when you don’t understand something
and get help. Be an active participant in class. But if you’re not comfortable
asking or answering questions in class, when you have difficulty grasping a new
statistical concept, seek out assistance from your instructor during his or her
office hours, from fellow students in your study group, or from support services
or materials (e.g., resource center, peer tutors, or professional tutors). This book
may be a good place to start, but find help elsewhere if you need it.
Concepts, Concepts, Concepts
Don’t try to memorize formulas. When using statistics in the so-called real
world, you will always be able to use notes, books, friends, and colleagues to
help out when encountering any difficulties related to statistics. Instead, focus
on understanding the concepts underlying the use of statistics. It’s much more
important to know when to use which statistical methods and what the results
of statistical analyses mean and their limitations.
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Practice, Practice, Practice
Statistics is learned best by doing, not by reading a textbook. Don’t waste your
time memorizing formulas! Focus instead on the concepts underlying the use
and interpretation of statistics. Do the assigned homework and as many other
problems and exercises as possible. In the beginning, statistics problems will be
straightforward and involve only one step. Increasingly, you will be presented
with problems that require you to take several steps to solve them and to make
important choices at each step. Keep in mind that these problems can be broken down into a series of small steps, each of which can be solved individually
before moving on to the next. Divide and conquer!
Show Your Work
When working on statistics problems, resist the temptation to skip steps when
solving a problem. Showing your work helps you locate logical or calculation
mistakes. Sometimes partial credit is given on homework and exams for the
correct portions of an answer because it shows the instructor what you do
know. Write out all numbers and variables clearly so that they can be easily
distinguished. Using lined or graph paper helps to organize problems on your
page. If your answer is not correct, rework the problem; don’t just work it out
in your head and convince yourself that you could get the right answer.
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CHAPTER 2
Overcoming Math Anxiety
WHAT YOU’LL LEARN:
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
• What Causes Math Anxiety?
• Overview of Rational Emotive
Therapy
• Irrational Beliefs
• How to Deal with Math Anxiety
A statistics major was completely hungover the day of his final
exam. It was a true/false test, so he decided to flip a coin for
the answers. The statistics professor watched the student
the entire two hours as he was flipping the coin . . . writing the
answer . . . flipping the coin . . . writing the answer. At the end of
the two hours, everyone else had left the final except for the one
student. The professor walks up to his desk and interrupts the
student, saying, “Listen, I have seen that you did not study for
this statistics test, you didn’t even open the exam. If you are just
flipping a coin for your answer, what is taking you so long?” The
student replies bitterly (as he is still flipping the coin), “Shhh! I’m
checking my answers!”
I
f you are what might be termed a “math-anxious” or “math-avoidant” person, this chapter may be helpful to you. Most of the material in this chapter
is drawn from the theory and practice of rational emotive therapy, originally
developed by the psychologist Albert Ellis. Rational emotive therapy has been
shown through research to be quite effective in helping people overcome problems like yours. Unfortunately, in a book devoted to statistics, I can introduce
you to only some of the basic ideas and techniques. If you are interested, you
8
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Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Chapter 2 • Overcoming Math Anxiety
9
can enrich your understanding by reading books like Albert Ellis and Robert A.
Harper’s A Guide to Rational Living or G. D. Kranzler’s You Can Change How
You Feel. (Notice the sneaky way of getting in a plug for my dad’s book?)
Fear of math, or math anxiety, is what is called a debilitative emotion.
Debilitative emotions such as math anxiety are problem emotions because (a)
they are extremely unpleasant, and (b) they tend to lead to self-defeating behavior, such as “freezing” on a test or avoiding courses or occupations that you
otherwise would enjoy.
What you do about your math anxiety (or any other problem) will
depend on your theory of what is causing the problem. For example, some
people believe that the cause is hereditary: “I get my fear of math from
mother, who always had the same problem.” Others believe that the cause
lies in the environment: “Women are taught from a very young age that they
are not supposed to be good in math, to avoid it, and to be afraid of it.”
The implication of these theories is that if the cause is hereditary, you can’t
do much about the problem (you can’t change your genetic structure), or if
the cause is the culture in which you live, by the time you can change what
society does to its young, it will still be too late to help you. Although there
may be some truth in both the hereditarian and the environmental theories,
I believe that they can, at most, set only general limits to your performance.
Within these limits, your performance can fluctuate considerably. Although
you have very little power to change society and no ability to change the
genes you inherited, you still have enormous power to change yourself if
you choose to do so, if you know how to bring about that change, and if
you work hard at it.
Let’s begin with the ABCs. A stands for an activating event or experience,
such as taking a difficult math test; C stands for the emotional consequence,
such as extreme nervousness. Most people seem to believe that A causes C. In
fact, this theory seems to be built right into our language. Consider the following examples:
Activating Event
Cause
Emotional Consequence
“Something happens . . .
that causes me . . .
to feel . . .”
“When you talk about math . . .
that causes me . . .
to feel . . .”
“This test . . .
makes me . . .
nervous.”
The implications of this A-causes-C theory are (a) that you can’t help how you
feel and (b) that the way to deal with the problem is to avoid or escape from
activating events such as math tests.
But is the A-causes-C theory true? Respond to the following items by indicating how you would feel if you were to experience the event. Use a scale that
ranges from −5, indicating very unpleasant emotions (such as rage, depression,
or extreme anxiety), to +5, indicating an emotion that is extremely positive
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10 Section I • Essentials for Statistics
(such as elation or ecstasy), or use a 0 if you would experience neutral, neither
positive nor negative, feelings:
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
1.
2.
3.
4.
Handling snakes
Giving a speech in front of one of your classes
Seeing your 8-year-old son playing with dolls
The death of a loved one in an automobile accident
I have administered items like this to hundreds of people and have found that
for items 1 through 3, the responses have ranged all the way from −5 to +5.
On the item concerning the death of a loved one, most people respond with
a −5, but when questioned, they have heard of cultures where even death is
considered to be a positive event (in the United States, everyone wants to go
to Heaven, but nobody wants to die). Why is it that, given the same activating
event, people’s emotional consequences vary so much?
Differing responses like this suggest that maybe A → C isn’t the whole
story. There must be something else, something that accounts for the different
ways people respond to the same stimulus. I believe that it is not A, the activating event, that causes C, the emotional consequence. Rather, it is B, your
belief about A, that causes you to feel as you do at point C. Take the example
of observing your 8-year-old son playing with dolls. What does a person who
experiences feelings of joy believe about what he or she sees? Perhaps something like, “Isn’t that wonderful! He’s learning nurturing attitudes and tenderness. I really like that!” But the person who experiences very negative feelings
probably is thinking, “Isn’t that awful! If he keeps that up, he’ll surely turn into
an effeminate man, or even be gay, and that really would be terrible!”
Ellis has identified some specific beliefs that most of us have learned and that
cause us a great deal of difficulty. He calls these beliefs “irrational beliefs.” A number of these beliefs have particular relevance to the phenomenon of math anxiety:
I must be competent and adequate in all possible respects if I am to consider myself to be a worthwhile person. (If I’m not good at math, I’m not a
very smart person.)
• It’s catastrophic when things are not the way I’d like them to be. (It’s terrible and awful to have trouble with statistics.)
• When something seems dangerous or about to go wrong, I must constantly
worry about it. (I can’t control my worrying and fretting about statistics.)
• My unhappiness is externally caused. I can’t help feeling and acting as I do,
and I can’t change my feelings or actions. (Having to do math simply makes
me feel awful; that’s just what it does to me.)
• Given my childhood experiences and the past I have had, I can’t help being
as I am today, and I’ll remain this way indefinitely. (I’ll never change; that’s
just how I am.)
• I can’t settle for less than the right or perfect solution to my problems.
(Since I can’t be a math whiz, there’s no sense in trying to do math at all.)
• It is better for me to avoid life’s frustrations and difficulties than to deal
with them. (Since math always makes me feel bad, the only sensible thing to
do is to avoid math.)
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Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Chapter 2 • Overcoming Math Anxiety
11
Source: Jason Love, www.CartoonStock.com. Used with permission.
Do any of these sound familiar? If they do, chances are good not only that
you learned to believe them a long time ago but also that you keep the belief
going by means of self-talk. The first step in changing is to increase your awareness of the kind of self-talk that you do. When you think, you think with words,
sentences, and images. If you pay attention to these cognitive events, you may
notice one or more of the following types of self-talk, which may indicate your
underlying irrational beliefs.
Catastrophizing
This type of self-talk is characterized by the use of terms or phrases such as “It’s
awful!,” “It’s terrible!,” or “I can’t stand it!” Now, there are some events that
most of us would agree are extremely bad, such as bombing innocent people
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12 Section I • Essentials for Statistics
and earthquakes that kill thousands. Chances are good that you will never be
the victim of such an event. But your mind is powerful: If you believe that your
misfortunes are catastrophes, then you will feel accordingly. Telling yourself
how catastrophic it is to do badly on a statistics test will almost guarantee that
you will feel awful about it. And that emotional response, in turn, can affect
how you deal with the situation. It is appropriate to be concerned about doing
well on a test because concern motivates you to prepare and to do your best.
But when you are overconcerned, you can make yourself so nervous that your
performance goes down instead of up.
Do you see how all this relates to the first irrational belief on our list?
Performing poorly on a statitics test would be awful because you believe that
you must be competent in all possible respects. If you were to fail at something important to you, that would make you a failure: someone who couldn’t
respect himself or herself. One of the oddest things about irrational beliefs like
this is the uneven way we apply them. Your friend could bomb a test, and you’d
still think him or her a worthwhile person. But do badly yourself, and the sky
falls in!
When you indoctrinate yourself with catastrophic ideas, when you tell
yourself over and over again how horrible it would be if you were to perform
poorly, then you defeat yourself because you become so anxious that you help
bring about the very thing you’re afraid of, or you avoid the experience that
could benefit you.
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Overgeneralizing Self-Talk
When you overgeneralize, you take a bit of evidence and draw conclusions that
go beyond the data. If you experienced difficulty with math as a child, you may
have concluded, “I’ll never be good at math” or “I’m stupid in math.” If you
failed a math course, then you tended to think of yourself as a failure who will
never be able to succeed, and trying harder would be completely useless.
Rationally, though, failing once doesn’t make you a “failure.” Because you
had difficulty in the past doesn’t mean that you will never succeed. If it did,
nobody would ever learn to walk!
The most pernicious form of overgeneralizing is self-evaluation. We have
a tendency to tie up our feelings of self-worth with our performance. When
we do well at something, we say, “Hey! I’m a pretty good [or competent or
worthwhile] person!” But when we perform poorly, we tend to believe that
we are now worthless as a person. This process begins in childhood. When
Johnny does something we consider bad, we tend to encourage overgeneralization by saying, “Johnny, you are a bad boy” (i.e., you are worthless as a
person).
If you were a worthless or stupid person, you wouldn’t have gotten far
enough in your education to be reading this book. True, in the past, you may
have had difficulty in math, and math may be difficult for you now. But how
does that prove you can’t learn it? There is absolutely no evidence that your
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Chapter 2 • Overcoming Math Anxiety
13
situation is hopeless or that it is useless to try. The only way to make it hopeless
is to tell yourself, over and over, how hopeless it is.
Demanding Self-Talk
This type of self-talk includes the use of words such as “should,” “must,” and
“need.” If you are math anxious, chances are that you use these words to beat
up on yourself. You make a mistake and say, “I shouldn’t have made that mistake! How could I have been so stupid?” I have a tennis partner who informed
me that she finds it difficult to concentrate on her work for the rest of the
day after she has played poorly. She believes that she should have done better.
Instead of being calmly regretful for having made some errors and thinking
about how to do better next time, she bashes herself over the head psychologically for not doing perfectly well every time.
“But,” you may say, “I need to be successful” or “I have to pass this course.”
Have to? The first time? Or you can’t survive? It would be nice to be successful given the advantages it would bring you, but lots of people do manage to
function in life even after doing badly in a statistics course. To the degree that
you believe you need a certain level of performance, you will experience anxiety
about possible failure and thereby increase the chance of failure.
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
How to Deal with Math Anxiety
What can you do about a way of thinking that seems so automatic, so ingrained?
Here is a series of steps that will probably help. I’d suggest that you try them
out, in order, even though you may not expect them to work for you. You might
just be surprised!
Step 1. Record Your Feelings (C)
When you notice that you are feeling anxious, guilty, angry, or depressed
about some aspect of your statistics course, record your emotional experience.
Describe your feelings as accurately as you can. You might write things such as,
“I feel guilty about not having taken more math as an underclassman,” “I feel
really nervous about the test we’re having next week,” “I’m too shy to ask questions in class,” or “I just get furious that they make us take statistics when I’ll
never have to use it.” Write down all the unpleasant feelings you have at the
time. When you have done this, you will have described C, the emotional consequence part of the ABC paradigm.
Step 2. Describe the Activating Event or Experience (A)
Briefly write down what it was that seemed to trigger your feelings. Here are
some common activating events for math anxiety. When you write your own
activating events, record the thing that is most likely to have happened. Find the
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14 Section I • Essentials for Statistics
immediate trigger, the thing that happened just before your experience of the
negative emotion. Here are some examples:
•
•
•
I was assigned some difficult statistics problems, and I don’t know how to
do them.
I thought about a test coming up, one that I will almost surely fail.
I discovered that I need more information about some of the material, but
I’m afraid to ask about it in class because I’ll look stupid.
Step 3. Identify Your Irrational Beliefs (B)
As accurately as you can, record what you were saying to yourself before and
during the time when you experienced the emotions you recorded in Step 1.
The first few times you do this, you may have difficulty because you don’t usually pay much attention to the thoughts that seem to race through your head.
Although it is difficult to become aware of your thoughts, it is not impossible.
One technique you can use is to ask yourself, “What must I have been saying to
myself about A (the activating event) at point B in order to experience C (the
emotional consequence)?” Suppose your first three steps looked like this:
Step 1. (Describing C, the emotional consequence) I feel really nervous and
miserable.
Copyright © 2017. Rowman & Littlefield Publishers. All rights reserved.
Step 2. ( The activating event, A) My adviser told me I need to take a statistics
class.
Step 3. Identify B, the belief that leads from A to C. Obviously, you’re not saying, “Wow, I’m really going to enjoy that class!” You must have been
saying something like the following:
“If I fail, that’ll be awful!”
“I’ll be a real loser!”
“I’ll never be any good at statistics!”
“I’m going to have a terrible term and hate every minute of it.”
“What will the other students and the professor think of me when
I do badly?”
Step 4. Challenge Each of the Beliefs You Have Identified
After you have written down your self-talk in Step 3, look at each statement
and dispute it. One question you can ask to test the rationality of any belief is,
“Where’s the evidence for this belief?” Let’s look at each of the examples listed
in Step 3 above:
1. Where’s the evidence that it will be awful if I fail? True, failure would be
unfortunate, but would it be catastrophic? I’d do better to remember that if
I’m overconcerned with doing well, I will be even more likely to fail.
2. Where’s the evidence that if I fail the test, I, as a person, will be a failure?
The worst I can possibly be is an FHB (a fallible human being) along with
the rest of the human race.
Kranzler, J. H. (2017). Statistics for the terrified. ProQuest Ebook Central http://ebookcentral.proques
Created from lynnu on 2021-01-21 05:58:42.
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Chapter 2 • Overcoming Math Anxiety
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3. Where’s the evidence that I’ll never be good in statistics? I may have some
evidence that similar material was difficult for me in the past, but how can
that prove anything about the future?
4. Where’s the evidence that I will hate ev
