This unique text on psychological statistics 1) provides the general rationale underlying many statistical procedures commonly used in psychology, 2) covers a wide range of topics—from the logic of statistical inference to multivariate analysis of variance, and 3) gives simple step-by-step instructions on how to access the relevant SPSS program. Each chapter presents a different procedure (e.g., t-tests, factor analysis, etc.), and briefly describes the basic concepts, purpose, and history necessary to understanding its strengths and limitations. A concrete example is used for each procedure, with the discussion of the SPSS output being directly linked to the underlying statistical model, so that readers can see how the interpretation of results follows from the nature of that procedure. Chapter topics include statistics, computers, and statistical packages; the t-test; single factor analysis of variance designs; completely randomized factorial designs; single factor repeated measures designs; split plot analysis of variance; chi-square analysis of frequency data; bivariate regression and correlation; multiple regression and multiple correlation; factor analysis; and multivariate analysis of variance. A reference guide for statisticians—to remind them of procedures learned earlier in their careers.

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Preface

I first began writing this book seven years ago to fill a need. I had been asked to initiate a half-year course on Computer Applications in Psychological Research, and planned to place much of the emphasis on data analysis. The prerequisite was a full-course Introductory Statistics course in which students learned the basis of probability theory, t-tests, single- and two-factor completely randomized design analysis of variance, and bivariate regression. I found when I looked for a textbook that would meet our needs, that there didn't appear to be anything suitable. There were traditional statistics textbooks that dealt with some of the more complex procedures that we wanted to cover like multiple regression and factor analysis, etc., manuals that focussed primarily on communicating with computer packages, or annotated manuals that by-and-large dealt with the simpler analytic procedures such as cross-tabs, tests of means, etc. What the course needed, however, was a textbook that showed students how to interact with SPSS, how to understand the output and how to interpret it, and, just as importantly, one that provided the fundamentals underlying the procedures. In my view, this required a mid-level statistics book that students could read and understand, without being bogged down in computational formulae and mathematical notation. I felt, however, that the textbook should also explain the procedures so that students could see the implications of their analyses. Many computer programs are very comprehensive and versatile, but I felt that it was best to instruct readers on the basics that they needed, on the assumption that they could experiment with the extensions after they understood the fundamentals.

This book has undergone a number of revisions (the first few versions dealt with the DOS version of SPSS), and unpublished copies have been used as the textbook since the beginning. Initially, I also required our students to purchase a more manual-type textbook, but it soon became apparent that the students had little need for that sort of book. Once they became familiar with the system, they learned how to make use of the Help files, or simply to experiment on their own. A more important need, it appeared, was a book that explained the basic procedures in a clear and coherent fashion.

Although the book was initially intended for a third-year honors-level course, I found that graduate students and colleagues also found it helpful. Students in my graduate class in Research Design claimed that they found it useful to read the relevant chapters in my book before taking on the textbooks that I had chosen for the course. They claimed that it helped to make the textbooks more readable. Colleagues have also noted that it has served to remind them of analytic procedures that they hadn't used in some time. Some members of other faculties and other universities similarly report that the book has been useful in their courses, and one reviewer of the penultimate manuscript suggested that the book would be useful for a graduate-level textbook in some departments.

My intention in writing this book was to keep it short and simple. Many statistical concepts are relatively straightforward, and I have attempted to provide simple explanations of the concepts and principles, wherever possible. On occasions, I have had to admit that further explanation was beyond the scope of the book, but I have tried to keep this to a minimum, and to point to clear sources for further study. I have presented some formulae where I thought it would help the description, but I have refrained, in general, from showing many equations with lengthy computational exercises. It seems that with computers able to do the majority of computations, attention to computational niceties is unnecessary. The one exception to this generalization is in the discussions of post hoc tests following an analysis of variance. There I have given worked out examples, and have referred tangentially to a computer program, post hoc, that I have that will perform these computations for you.

Readers of this book will find some elements that are generally not found in other books. In addition to instructions on how to perform the major analytic procedures in both SPSS 8.0 and SPSS 9.0, there are other elements that are unique. Each chapter has a brief history section on the technique and related issues. I believe this is useful to place the procedures into historical perspective. Students often miss the fact that analytic procedures are interrelated and that they evolve over time.

Chapter 1 presents a general and simple overview of different types of statistics, and uniquely, it seems presents among other things the computational formulae used in SPSS for measures of skewness and kurtosis. Chapter 2 reviews various forms of the t-test, showing the relation between the independent and paired t-test, and indicating how they relate to the Critical ratio. Chapter 3 presents a simplified discussion of the single-factor completely randomized design, discusses issues such as the percentage of variance accounted for, defining both w2 and n2 and showing the relation between the two (a unique feature), and explains the general rationale underlying post hoc tests of means. This is extended in Chapter 4 to a discussion of two-factor completely randomized design analyses of variance and the meaning and significance of both omnibus and partial n2 directing attention to the calculation of partial n2 showing its relevance to the concept of power. The interpretation of results is stressed as it is in many other books, but more is made of the importance of reporting and interpreting power estimates that are associated with the F-ratios. This is continued in the subsequent chapters dealing with analysis of variance since it would seem to be as valuable to report n2 and power estimates associated with each F-ratio as it is to report the alpha level. Chapter 5 presents the single factor repeated measures analysis of variance (and by implication the randomized blocks design). A novel feature of this chapter is that is presents both the univariate and multivariate approaches to the analysis of such data, discussing the assumptions underlying each, and their relative merits and shortcomings. Split-plot analysis of variance is considered in Chapter 6, again from both the univarirate and multivariate perspectives. Issues associated with tests of simple main effects are discussed in some detail, and differences between the SPSS approach to tests of means and standard textbook approaches are indicated. Chapter 7 considers the chi-square analysis of categorical data. A unique feature of this chapter is its discussion of post hoc procedures to aid in the interpretation of a significant chi-square obtained from a table that is larger than 2 x 2. Most sources are silent on this, but the present chapter describes three different methods that might be followed, and discusses the advantages and limitations associated with each of them. Chapter 8 presents bivariate regression and correlation, showing the precise meaning of each. It also presents a number of tests of significance involving correlation coefficients that are not readily available in most textbooks. Chapter 9 is the largest chapter. It discusses the general logic underlying multiple regression and multiple correlation, and outlines the generality of this analytic procedure. It distinguishes between direct and indirect procedures in building an equation, and highlights the issues involved in the use of this equation. It discusses what a "prediction" equation means, and what it doesn't mean, and considers issues concerning the "best" predictor, and the interpretation of regression coefficients, showing the direct connection between a part correlation and a regression coefficient. In addition, the chapter deals with the issue of moderator variables and nonlinear relationships. Factor analysis is discussed in Chapter 10, with emphasis on basic factor theory, the principles of rotation, and the interpretation of solutions. Chapter 11 presents multivariate analysis of variance, and discusses the use and application of SPSS GLM and SPSS MANOVA. It shows how one might proceed to interpret a canonical variate, and some of the issues involved in this interpretation. A relatively unique feature of this chapter is the presentation of the formulae (with numerical examples) for the various multivariate tests of significance and their respective degrees of freedom.

Each chapter is preceded by a Table of Contents. This is provided to help the reader to see how the chapter is organized, and to emphasize the major elements and constructs involved in that chapter. I recommend to my students that they consider the chapter outline carefully before they start reading, and to think about the organization of the material. Of course, the Table of Contents for each chapter also helps someone to look up some specific aspect.

Many individuals have provided assistance and advice in the preparation of this book. This includes the many students who have used earlier versions (as well as this one) as the textbook in our course on Computer Applications in Psychological Research for the last eight years. Many have offered suggestions, comments and criticisms that have made their way into the final form presented here. Also, many of my colleagues have given me valuable feedback for which I express my sincere appreciation. These include Professor R. W. J. (Jim) Neufeld, with whom I have discussed many statistical issues, as well as Professors Ken McRae, Sampo Paunonen, and Tom Spalding, who have used earlier versions of the book in their sections of Computer Applications in Psychological Research. From pointing out ambiguities to offering editorial comment, they have offered moral support, advice, and/or suggestions that I believe have been of enormous benefit to the final product. Finally, I would like to thank the following reviewers for their helpful comments on the penultimate version of this book: Gerald Gibb, Embry-Riddle Aeronautical University; Leslie Gill, Eastern New Mexico University; Charles Halcomb, Wichita State University; and Miguel Quinones, Rice University.

Robert C. Gardner

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Prentice Hall
(2000)

ISBN 10: 013028324X
ISBN 13: 9780130283245

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