Comprehending Behavioral Statistics (2nd Edition)
The only textbook featuring eyeball-estimation and progressive cumulative review

Preface


Preface Topics
Introduction
Eyeball-estimation
Eyeball-calibration
Progressive Cumulative Review
ESTAT Computer Simulation Package
Instructor's Flexibility in Using the Text
Organization for the Convenience of Students
What's New in the Second Edition

See also Table of Contents

Introduction

Modern learning theory holds that constructive visualization, active involvement, immediate feedback, and multiple discrimination trials are essential for effective learning. Statistics textbooks typically fail to incorporate these components. As a result, students commonly master computational skills but gain little conceptual understanding of the statistics they compute.

Comprehending Behavioral Statistics remedies these omissions with three innovations:

• eyeball-estimation, a technique for assessing a distribution and quickly predicting the approximate magnitude of a statistic;
• eyeball-calibration, massed practice in estimating the characteristics of a distribution; and
• progressive cumulative review, chapter sections that develop students' ability to discriminate between new concepts and those presented in previous chapters.

These techniques are the results of more than 20 years spent helping my own students to visualize statistical concepts. They were made widely available for the first time in the first edition of Comprehending Behavioral Statistics. Students find these techniques actively engaging, easy, and fun. I am gratified by responses from students and teachers around the world who have written comments such as "I expected to hate statistics, but I loved your book -- especially the eyeball-estimation" and "I've been using your text for the last three years and I think it's a terrific book. It really helps to dispel some of the anxiety that students have about statistics, which is one of my goals for the course."

To reap these benefits, the busy teacher need not rethink the structure of the statistics course; the core structure of Comprehending Behavioral Statistics is consistent with traditional texts. Eyeball-estimation, eyeball-calibration, and progressive cumulative review techniques are formatted in the text for the instructor's flexibility and ease of use.

The second edition of Comprehending Behavioral Statistics has benefited from feedback offered to me by numerous instructors who have used the first edition. In addition, I have implemented a process I call the "student sieve": a line-by-line evaluation designed to screen out minute stumbling blocks in the text. While using the book, 50 students marked lines they had to reread to understand. By collating the 50 sets of markings, I have gained a focused view of the text from the student perspective, which enabled me to clarify the precise spots that students found troublesome.

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Eyeball-estimation

Eyeball-estimation techniques enable students to predict, without the use of a calculator or statistical tables, the approximate magnitude of statistics. Sections of the text that present eyeball-estimation skills are flagged with an eyeglass symbol.

Eyeball-estimation is not a substitute for accurate computation; Comprehending Behavioral Statistics is thorough in its treatment of computation skills. Students benefit from eyeball- estimation, however, for these reasons:

• Students who eyeball-estimate are actively involved. They inspect the data and decide for themselves the approximate magnitude of a reasonable answer.
• Eyeball-estimation cultivates genuine understanding of statistical concepts. The ability to make an educated guess is better evidence of comprehension than is the ability to compute a result.
• Following eyeball-estimation, computation has an element of excitement because it provides immediate feedback on the accuracy of the estimate.
• Eyeball-estimation is quick. A beginning student can eyeball-estimate a standard deviation in about 15 seconds. Computation would take the same student about 15 minutes. A class hour is ample time for eyeball-estimation and discussion of more than a dozen standard deviations. Students remain actively involved throughout the discussion because they provide the eyeball-estimations in each case.
• Eyeball-estimation engages students regardless of their level of mathematical sophistication. With eyeball-estimation, a classroom discussion of the standard deviation is comprehensible to inexperienced students, who can practice fundamentals such as locating an inflection point and estimating its distance from the mean. The same discussion is challenging for mathematically sophisticated students, who can practice refining their awareness of the effects of skew on the standard deviation.
• Eyeball-estimation is a valuable skill. It enables students to spot mistakes immediately. Students trained in eyeball-estimation techniques estimate far more accurately than do students taught by traditional methods.

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Eyeball-calibration

Eyeball-calibration exercises provide massed practice, not only in eyeball-estimation, but also in direct recognition of the relationship between data and statistics. Eyeball-calibration examples are flagged an eyeglass-and-ruler symbol.

Eyeball-calibration is useful with or without eyeball-estimation. For example, Chapter 11 presents pairs of histograms and asks whether the independent-sample t test null hypothesis should be rejected. No quantitative estimation is required. Students learn to observe the degree of overlap of the distributions and to predict directly whether or not the null hypothesis should be rejected. Thus, they gain awareness of the magnitude of difference required for rejecting null hypotheses. Students also have the option of using these figures for eyeball-estimation practice in estimating the sample statistic, the magnitude of t, and t's approximate value.

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Progressive Cumulative Review

Students of statistics who do well on quizzes and midterm exams may nonetheless perform poorly on a cumulative final. Why? Because traditional statistics textbooks fail to incorporate practice in one of the most important skills: the ability to discriminate between procedures. The student who uses a typical text knows that all the problems in the t test chapter require t, all the problems in the ANOVA chapter require ANOVA, and so on. The student therefore gets no practice in deciding which test to use.

Comprehending Behavioral Statistics remedies this omission by including progressive cumulative review exercises. In each chapter, cumulative review exercises present, in random order, problems of the types found in that and previous chapters. Rather than compute, students are asked to state which null hypothesis is appropriate and to describe the characteristics of the appropriate statistical test.

Cumulative review exercises are progressive in that the complexity of required discriminations increases gradually with each successive chapter. In Chapter 10, for example, the student discriminates among three easy options: finding the area under a normal distribution, creating a confidence interval, or testing a hypothesis. The task becomes slightly more complex in Chapter 11, where the student must also discriminate between testing a hypothesis about the mean of one group or the means of two groups. This step-by-step pattern of slightly increasing complexity continues throughout the text. By the end of the course, the student has become proficient in making complex discriminations.

I began developing cumulative review exercises for use with my graduate students. The exercises were so effective that I started using them with sophomores more than ten years ago. My sophomores' performance on cumulative exams now surpasses that of the graduate students I taught prior to using cumulative review exercises.

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ESTAT Computer Simulation Package

ESTAT is the computer software designed to accompany Comprehending Behavioral Statistics. ESTAT (for ESTimating STATistics) is available in Windows and Apple Macintosh formats. Comprehending Behavioral Statistics can be used independently of computer software. Students who use ESTAT, however, will benefit from its innovations: eyeball-estimation exercises, eyeball-calibration exercises, and the most user-friendly computational package available.

ESTAT provides practice in eyeball-estimation and eyeball-calibration by generating and displaying data, inviting the student to eyeball-estimate a statistic, and then providing immediate feedback on the accuracy of the estimate. For example, in one of the standard deviation exercises, sdest, ESTAT displays a histogram and asks the student to eyeball-estimate the standard deviation. When the student clicks a button, the actual standard deviation appears in both graphic and numerical form. Another click and ESTAT produces a new histogram from a randomly generated infinite series of data sets. Context-sensitive help is always available via a click, as is a step-by-step tutorial.

Compared with typical homework, ESTAT exercises are more efficient and cultivate better comprehension. Students who use a traditional text to do standard deviation homework spend one to three hours calculating the standard deviations of about three distributions, perhaps six if they also use a workbook. They compute their answers and check the results in the back of the book, spending almost no time developing comprehension of the relationship between those standard deviations and their distributions.

By contrast, students who use the ESTAT sdest standard deviation laboratory, with its infinite stream of Monte Carlo histograms, spend about a minute on each cycle of observation, estimation, and feedback. In less than half an hour, students can encounter more than 15 distributions, and all of that time is spent developing comprehension of the relationship between those standard deviations and their distributions. Plenty of homework time remains for computation, which is now based on a solid conceptual foundation.

Comprehending Behavioral Statistics invites students to use ESTAT where appropriate with a prompt:

You may wish to use the ESTAT exercise "sdest" at this time.

For those who do not have access to computers, ESTAT-like exercises are also included in the Study Guide.

ESTAT also includes a statistical computational package that is the most user friendly available. ESTAT provides all relevant statistics automatically, freeing the student from the need to figure out how to ask the computer to display any statistic. For instance, if the data consist of three or more groups, ESTAT automatically displays an ANOVA. If the data consist of two groups, ESTAT automatically displays the independent-sample t; if the groups have equal numbers of observations, ESTAT also automatically displays the dependent-sample t, the correlation coefficient, and the regression equation.

Because statistics are displayed automatically, ESTAT elicits a decision process that is the reverse of the process required by other programs. Typical programs require students to decide which statistic to request from among many that might be available. With ESTAT, students decide which statistics to use from among a few that are automatically displayed.

As a result, ESTAT's computational package dispels anxiety for the beginning student whose grasp of statistical concepts is not yet secure. Typical computational packages escalate anxiety because any complexity of the computer interface drastically compounds the student's insecurity. Nothing is more discouraging than the failure to elicit an appropriate result from the computer, particularly when the student does not know whether to attribute that failure to unfamiliarity with the interface or to unfamiliarity with the statistics themselves. By contrast, students can immediately interact successfully with ESTAT. Its interface actively facilitates every task and elicits in students the desire to explore and master statistical concepts.

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Instructor's Flexibility in Using the Text

Comprehending Behavioral Statistics is organized so that the instructor may choose which of its innovations to use. For example, the eyeball-estimation material in the hypothesis-testing chapters is presented in optional sections at the ends of those chapters. It can easily be assigned, made optional for selected students, or omitted altogether.

A complete set of ancillary materials is available and includes these items:

• ESTAT eyeball-estimation and computation computer program, available in Windows or Apple Macintosh formats. (Comprehending Behavioral Statistics can be used with or without computer software.)
• Student Study Guide (including ESTAT-like exercises for students without access to computers).
• Instructor's Manual (250 pages, including a test bank with 1100 items).
• Computerized test bank (1100 items for DOS or Macintosh)

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Organization for the Convenience of Students

Comprehending Behavioral Statistics incorporates numerous features that enhance the student's learning and convenience:

• There are more than 400 accurately drawn figures (two to three times more than most textbooks).
• End-of-chapter exercises are graduated from simple to complex and include examples from journals.
• Definitions of statistical terms and symbols are given both in the margins of pages where they initially appear and in the Glossary at the back of the book.
• Most frequently used formulas and tables are reproduced on the inside covers.
• "Info notes," flagged with the international information symbol , give useful comments and cross-reference information.
• Statistical tables have colored edges for easy accessibility (Appendix A).
• A reference review of basic arithmetic is included (Appendix B).
• All statistical formulas are listed together for ready reference (Appendix
• Results of exercise subcomputations, not just final results, are given in the answers to exercises (Appendix D).

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What's New in the Second Edition?

The following is a summary of the major changes incorporated in the second edition of Comprehending Behavioral Statistics.

New material

• A new section presents a priori comparisons.
• A new section presents repeated measures ANOVA.
• Computer exploration exercises are now included in most chapters. These exercises can be used with any computer statistics package (SPSS, SAS, BMDP, etc.).
• A "Connections" section added at the ends of most chapters typically has four parts: a cumulative review of the text so far; a discussion of how the material in that chapter is reported in journal articles; detailed instructions for operating the Windows and Macintosh versions of both ESTAT and SPSS 6.1 Student Version, including annotated examples of SPSS output; and homework tips.

Substantially altered material

• The discussion of practical significance and effect sizes has been amplified substantially and distributed across all hypothesis-testing chapters. This material is illustrated more profusely here than in other textbooks.
• The discussion of statistical power has been simplified, expanded, and integrated into Chapters 9 and 12.
• Computations have been simplified wherever possible. For example, the ANOVA notation has been simplified , and the material on interpolation is now optional.
• Eyeball-estimation material for the hypothesis-testing chapters has been moved to optional sections at the end of each chapter.

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