Psychology

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Statistics for Psychology* (3rd Edition) by Arthur Aron, and Elaine N.
Aron (Prentice Hall) In the 1950s and 1960s statistics texts were dry, daunting,
mathematical tomes that quickly left most students behind. In the 1970s, there
was a revolution‑in swept the intuitive approach, with much less emphasis on
derivations, proofs, and mathematical foundations. The approach worked. Students
became less afraid of statistics courses and found the material more accessible,
even if not quite clear.

The intuitive trend continued in the 1980s, adding in the 1990s some nicely straightforward writing. A few texts have now also begun to encourage students to use the computer to do statistical analyses. However, discussions of intuitive understandings are becoming briefer and briefer. The standard is a cursory overview of the key idea and sometimes the associated definitional formula for each technique. Then come the procedures and examples for actually doing the computation, using another "computational" formula.

Even with all this streamlining, or perhaps because of it, at the end of the course most students cannot give a clear explanation of the logic behind the techniques they have learned. A few months later they can rarely carry out the procedures either. Most important, the three main purposes of the introductory statistics course are not accomplished: Students are not able to make sense of the results of psychology research articles, they are poorly prepared for further courses in statistics (where instructors must inevitably spend half the semester reteaching the introductory course), and the exposure to deep thinking that is supposed to justify the course's meeting general education requirements in the quantitative area has not occurred.

We continue to do what the best of the newer books are already doing well: emphasizing the intuitive, de-emphasizing the mathematical, and explaining everything in direct, simple language. But what we have done differs from these other books in 11 key respects.

1. The definitional formulas are brought to center stage
because they provide a concise symbolic summary of the logic of each particular
procedure. All our explanations, examples, practice problems, and test bank
items are based on these definitional formulas. (The amount of data to be
processed in practice problems and test bank items are reduced appropriately to
keep computations manageable.)

Why this approach? To date, statistics texts have failed to adjust to
technological reality. What is important is not that the students learn to
calculate a test with a large data set‑computers can do that for them. What is
important is that students work problems in a way that they remain constantly
aware of the underlying logic of what they are doing. Consider the population
variance‑the average of the squared deviations from the mean. This concept is
directly displayed in the definitional formula (once the student is used to the
symbols): Variance. Repeatedly working problems using this formula engrains the
meaning in the student's mind. In contrast, the usual computational version of
this formula only obscures this meaning: Teaching the old computational formulas
today is an anachronism. Researchers do their statistics on computers now. At
the same time, the use of statistical software makes the understanding of the
basic principles, as they are symbolically expressed in the definitional
formulas, more important than ever. Students still need to work lots of problems
by hand to learn the material. But they need to work them using the definitional
formulas that reinforce the concepts, not using the computational formulas that
obscure them. Those formulas once made some sense as timesavers for researchers
who had to work with large data sets by hand, but they were always poor teaching
tools. (Because some instructors may feel naked without them, we still provide
the computational formulas, usually in a brief footnote, at the point in the
chapter where they would traditionally have been introduced.)

2. Each procedure is taught both verbally and numerically‑and usually visually
as well. In fact, when we introduce every formula, it has attached to it a
concise statement of the formula in words. Typically, each example lays out the
procedures in worked‑out formulas, in words (often with a list of steps), and
illustrated with an easy‑to‑grasp figure. Practice problems and test bank
items, in turn, require the student to calculate results, write a short
explanation in layperson's language of what they have done, and make a sketch
(for example of the distributions involved in a t test). The chapter material
completely prepares the student for these kinds of practice problems and test
questions.

It is our repeated experience that these different ways of expressing an idea
are crucial for permanently establishing a concept in a student's mind. Many
psychology students are more at ease with words than with numbers. In fact,
some have a positive fear of all mathematics. Writing the formula in words and
providing the lay‑language explanation gives them an opportunity to do what they
do best.

3. A main goal of any introductory statistics course in psychology is to prepare
students to read research articles. The way a procedure such as a t test or an
analysis of variance is described in a research article is often quite
different from what the student expects from the standard textbook discussions.
Therefore, as this book teaches a statistical method, it also gives examples of
how that method is reported in the journals (excerpts from current articles).
And we don't just leave it there. The practice problems and test bank items also
include excerpts from articles for the student to explain.

4. The book is unusually up to date. For some reason, most introductory
statistics textbooks read as if they were written in the 1950s. The basics are
still the basics, but statisticians and researchers think far more subtly about
those basics now. Today, the basics are undergirded by a new appreciation of
effect size, power, the accumulation of results through meta‑analysis, the
critical role of models, the underlying unity of difference and association
statistics, the growing prominence of regression and associated methods, and a
whole host of new orientations arising from the central role of the computer. We
are much engaged in the latest developments in statistical theory and
application, and this book reflects that engagement. For example, we devote an
entire early chapter to effect size and power and then return to these topics
as we teach each technique.

5. We capitalize on the students' motivations. We do this in two ways. First,
our examples emphasize topics or populations that students seem to find most
interesting. The very first example is from a real study in which 151 students
in their first week of an introductory statistics class rate how much stress
they feel they are under. Other examples emphasize clinical, organizational,
social, and educational psychology while being sure to include sufficient
interesting examples from cognitive, developmental, behavioral and cognitive
neuroscience, and other areas to inspire students with the value of those
specialties. (Also, our examples continually emphasize the usefulness of
statistical methods and ideas as tools in the research process, never allowing
students to feel that what they are learning is theory for the sake of theory.)

Second, we have worked to make the book extremely straightforward and systematic
in its explanation of basic concepts so that students can have frequent "aha"
experiences. Such experiences bolster self‑confidence and motivate further
learning. It is quite inspiring to us to see even fairly modest students glow
from having mastered some concept like negative correlation or the distinction
between failing to reject the null hypothesis and supporting the null
hypothesis. At the same time, we do not constantly remind them how greatly
oversimplified we have made things, as some books do. Instead, we show students,
in the controversy sections in particular, how much there is for them to
consider deeply, even in an introductory course.

6. We emphasize statistical methods as a living, growing field of research. We
take the time to describe the issues, such as the recent upheaval about the
value of significance testing. In addition, each chapter includes one or more
"boxes" about famous statisticians or interesting side‑lights. The goal is for
students to see statistical methods as human efforts to make sense out of the
jumble of numbers generated by a research study; to see that statistics are not
"given" by nature, not infallible, not perfect descriptions of the events they
try to describe but rather constitute a language that is constantly improving
through the careful thought of those who use it. We hope that this orientation
will help them maintain a questioning, alert attitude as students and later as
professionals.

7. Chapter 16 integrates the major techniques that have been taught, explaining
that the t test is a special case of the analysis of variance and that both the
t test and the analysis of variance are special cases of correlation and
regression. (In short, we introduce the general linear model.) In the past, when
this point has been made at all, it has usually been only in advanced texts. But
many students find it valuable for digesting and retaining what they have
learned, as well as for sensing that they have penetrated deeply into the
foundations of statistical methods.

8. The final chapter looks at advanced procedures without actually teaching them
in detail. It explains in simple terms how to make sense out of these statistics
when they are encountered in research articles. Most psychology research
articles today use methods such as analysis of covariance, multivariate analysis
of variance, hierarchical multiple regression, factor analysis, or structural
equation modeling. Students completing the ordinary introductory statistics
course are ill‑equipped to comprehend most of the articles they must read to
prepare a paper or study a course topic in further depth. This chapter makes use
of the basics that students have just learned (along with extensive excerpts
from current research articles) to give a rudimentary understanding of these
advanced procedures. This chapter also serves as a reference guide that students
can keep and use in the future when reading such articles.

9. The accompanying Student's Study Guide and Computer Workbook focuses on
mastering concepts and also includes instructions and examples for working
problems on the computer. Most study guides concentrate on plugging numbers into
formulas and memorizing rules (which is consistent with the emphasis of the
textbooks they accompany). For each chapter, our Student's Study Guide and
Computer Workbook provides learning objectives, a detailed chapter outline, the
chapter's formulas (with all symbols defined), and summaries of steps of
conducting each procedure covered in the chapter, plus a set of self tests,
including multiple-choice, fill‑in, and problem/essay questions. In addition,
for each procedure covered in the chapter, the study guide furnishes a thorough
outline for writing an essay explaining the procedure to a person who has never
had a course in statistics (a task they are frequently given in the practice
problems and test bank items.).

Also, our Student's Study Guide and Computer Workbook provides the needed
support for teaching students to carry out analyses on the computer. First,
there is a special appendix on getting started with SPSS. Then, in each chapter
corresponding to the text chapters, there is a section showing in detail how to
carry out the chapter's procedures with SPSS. (These sections include
step‑by‑step instructions, examples, and illustrations of how each menu and each
output appears on the screen.) There are also special activities for using the
computer to strengthen understanding. As far as we know, no other statistics
textbook package provides this much depth of explanation.

10. We have written an Instructor's Resource Manual that really helps teach the
course. The manual begins with a chapter summarizing what we have gleaned from
our own teaching experience and the research literature on effectiveness in
college teaching. The next chapter discusses alternative organizations of the
course, including tables of possible schedules and a sample syllabus. Then each
chapter, corresponding to the text chapters, provides full lecture outlines and
additional worked‑out examples not found in the text (in a form suitable for
copying onto transparencies or for student handouts). These worked‑out examples
are especially useful to new instructors or those using our book for the first
time, since creating good examples is one of the most difficult parts of
preparing statistics lectures.

11. Our Test Bank makes preparing exams easy. We supply approximately 40
multiple‑choice, 25 fill‑in, and 10 to 12 problem/essay questions for each
chapter. Considering that the emphasis of the course is so conceptual, the
multiplechoice questions will be particularly useful for those of you who do
not have the resources to grade essays.

We did the revision for the third edition over a summer in Tiburon, a small town overlooking the San Francisco Bay. We hope that this has not resulted in a loss of whatever romance the first edition gained from being written in Paris. On the other hand, this edition has been leavened by some beautiful Bay views.

More important, this revision is enriched by what we learned teaching with the first and second editions and by what we learned from the many instructors and students who have written to us about their experiences using the book. This revision is also informed by our own use of statistical methods. The last several years have been quite productive for the two of us in our own research programs in personality and social psychology. Our most recent adventure has been in social neuroscience, learning brain‑imaging techniques, which it turns out are almost as fascinating for the statistical analysis challenges they pose as for the opportunities they provide for deepening knowledge of the issues we were previously studying with more conventional methods. Perhaps particularly useful has been that one of us (A. A.) has been serving as an associate editor for the Journal of Personality and Social Psychology. This has kept us in touch with how the best researchers are using statistics (as well as how reviewers assess their colleagues' use of statistics). In addition to reworking the book to keep it up to date in obvious and subtle ways, we have made a special effort in this edition to bring in to the text significant new pedagogical features.

1. New pedagogic features. The most obvious changes to
those familiar with the book will be the following additions we made to ease the
learning process:

• "How Are You Doing?" sections. These are brief self‑tests focusing on
concepts, inserted at three or four appropriate points in each chapter. These
give students a chance to check that they have learned what they have just read,
help them identify the central material in what they have just read, reinforce
this material before going on to the next section, and divide the chapter into
more accessible "chunks."

• Doubling the number of practice problems. Each chapter now has at least 20.
This provides the instructor with greater flexibility in the kinds and numbers
of problems to assign.

• Examples of Worked‑Out Computational Problems. These are included just before
the practice problems at the end of each chapter. These give the student the
chance to check their knowledge before starting their assigned problems and
provide a model to follow when working them out, thus easing anxiety and helping
the student do the problems correctly.

• With each new formula there is a boxed concise statement of the formula in
words. This is important for helping students who fear symbols and math to see
the underlying principle embedded in the formula, and keeps this verbal
understanding directly available to them as they become accustomed to working
with the symbols.

2. Writing. We have once again in this revision thoroughly reviewed every
sentence, simplifying constructions and terminology wherever possible and
sometimes rewriting from scratch entire paragraphs or sections. It is hard
enough to learn statistics without having to read complicated sentences.

3. Updating examples. We have replaced over 60 examples from the second edition
with new ones published in the last year or two. This is particularly important
for the sections on how to understand and evaluate statistics in research
articles.

4. Updating content and controversies. Most obvious to those familiar with
earlier editions will be the discussion of the APA Task Force report and the new
APA Publication Manual's statements on data analysis. But the updates are
everywhere in subtle ways‑even with newly identified anecdotes about historical
figures in the boxes!

5. Reworking of some specific topics students had found difficult. We have
substantially reworked our treatment of a few topics that some students were
struggling with, including grouped frequency tables, raw‑score regression,
confidence intervals, and effect size in analysis of variance. We have also made
some changes in emphasis and coverage in response to instructors' suggestions,
including more on the issue of causality and correlation and a fuller treatment
of multiple comparisons in analysis of variance.

6. There is now a unique Web page available to instructors who adopt the book
and to their students. We are particularly excited about the potential of the
Web for aiding learning of statistics. Elliot Coups, has created an outstanding,
dramatically innovative site. Some unique features (in addition to the usual
chapter outline and objectives) include:

• For instructors: Powerpoint presentation materials for teaching the course,
including examples from .the text and examples from the Instructor's Resource
Manual that are not in the text.

• Downloadable mini‑chapter for students on applying statistics in their own
research projects.

• Downloadable mini‑chapter for students on repeated measures analysis of
variance.

Chapter objectives

• Downloadable mini‑chapter on the logic and language of
research (this was Appendix A in the earlier editions)

• Tips for Success: What to practice, and what to study.

• Learn More! sections: Practice problems that include tables from the text on
the Web, giving the students the opportunity to use the tables to work through
problems.

• On-line student study guide, including practice problems, true/false
questions, and fill in the blanks.

Flash card exercises for each chapter's key terms. All formulas

• Links to statistic sites

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