Preface to the Fourth Edition

This edition marks the first time that I have included detailed instructions for the use of IBM SPSS Statistics (SPSS, for short) in the text itself, and not merely in supplemental material on the web. Not every instructor wants to teach SPSS as part of his or her statistics course, but such a large proportion of my adopters, and would-be adopters, do incorporate SPSS instruction in their courses that I felt it would greatly enhance the usefulness of my text to add a section on SPSS to every chapter. To keep the text down to a manageable size, I had to modify the ABC section format that I have used since the first edition of this text, as described next.

The ABC Format

As in previous editions, Section A of each chapter provides the “Conceptual Foundation” for the topics covered in that chapter. In Section A, I focus on the simplest case of the procedure dealt with in that chapter (e.g., one-way ANOVA with equal-sized groups), and explain the definitional formulas thoroughly, so that students can gain some insight into why and how statistical formulas work the way they do. The emphasis is on the underlying similarity of formulas that look very different (e.g., it is shown that, in the two-group case, the MSW of a one-way ANOVA is exactly the same as the pooled-variance estimate in a two-group t test). In my experience, students learn statistics more easily when statistical formulas are not presented as arbitrary strings of characters to be memorized, or even just looked up when needed, but rather when the structures of the formulas are made clear (e.g., the sample size usually appears in the denominator of the denominator of the formula for the one-sample t test, which means that it is effectively in the numerator—so, making the sample size larger, with all else remaining the same, will increase the size of the t value). Some instructors may prefer an approach in which concepts are explained first without reference to statistical formulas at all. I don't feel I could do that well, so I have not attempted that approach in this text. However, I believe that all of the formulas in this text can be made understandable to the average graduate (or above-average undergraduate) student.

Section A has its own detailed summary, followed by exercises that help ensure that students grasp the basic concepts and definitional formulas before moving on to the complications of Section B. Section B, “Basic Statistical Procedures,” presents the more general case of that chapter's procedure and includes computational formulas, significance tests, and comments on research design so that students will be equipped to analyze real data and interpret their results. In addition to the basics of null hypothesis testing, Section B also includes supplementary statistical procedures (e.g., confidence intervals, effect sizes), and information on how to report such statistical results in the latest APA format, usually illustrated with an excerpt from a published journal article. Section B ends with a thorough summary and a variety of exercises so that students can practice the basic computations. Moreover, these exercises often refer to exercises in Section A of that chapter, or exercises from previous chapters, to make instructive comparisons (e.g., that a one-way RM ANOVA can be calculated on the same data that had been used to illustrate the computation of a matched t test).

In previous editions, Section C presented “Optional Material” that was usually more conceptually advanced and less central to students' needs than the topics covered in Sections A and B. In this edition, the former Section C material that was most relevant to the chapter has been incorporated in Section B, or in some cases in a separate section labeled “Advanced Material,” which does not appear in all chapters. The more specialized material from the previous C sections will be included in new supplements that I am preparing for each chapter, which will eventually be made available on the web. The new C Sections explain how to use SPSS to perform the statistical procedures in the B sections they follow. I have included some little-known, but useful, options that are available only by using a Syntax window (e.g., obtaining simple main effects from the two-way ANOVA procedure). I have also included explanations of SPSS's most important data management tools (e.g., Split File, Recode), spread across several C sections and illustrated in terms of the procedures of the chapter in which each is introduced.

One key reason I have included these new C sections is that SPSS often uses idiosyncratic symbols and terms that disagree with the ones I use in my text (and most similar texts I've seen). These new sections give me the opportunity to fully integrate a description of the results of SPSS analysis with the concepts and procedures as they are explained in Sections A and B. Moreover, note that all of the C sections have their own exercises that are based on a single data set (100 cases, 17 variables), which provides continuity from chapter to chapter. For those adopters who felt that my earlier editions overly emphasized hand calculations, the incorporation of exercises that are meant to be solved by SPSS (or a similar statistical package) should provide some welcome balance. The data set, called “Ihno's Data,” can be downloaded as an Excel spreadsheet from my own statistics web page: http://www.psych.nyu.edu/cohen/statstext.html

The Organization of the Chapters

This edition retains the basic organization of the previous editions, including my personal (and sometimes idiosyncratic) preferences for the ordering of the chapters. Fortunately, adopters of the previous editions reported no difficulty teaching some of the chapters in a different order than they appear in this text. The main organizational choices, and the rationale for each, are as follows. At the end of Part One (Descriptive Statistics), I describe probability in terms of smooth mathematical distributions only (mainly the normal curve), and postpone any discussion of probability in terms of discrete events until Part Seven (Nonparametric Statistics). In my experience, a presentation of discrete mathematics (e.g., combinatorics) at this point would interrupt the smooth flow from the explanation of areas under the normal distribution to the use of p values in inferential parametric statistics.

I also postpone Correlation and Linear Regression until after completing the basic explanation of (univariate) inferential statistics in terms of the t test for two independent samples. I have never understood the inclusion of correlation as part of descriptive statistics, mainly because I have never seen correlations used for purely descriptive purposes. More controversial is my decision to separate the matched (or repeated-measures) t test from the (one and) two independent-sample tests, and to present the matched test only after the chapters on correlation and regression. My reasoning is that the conceptual importance of explaining the increased power of the matched t test in terms of correlation outweighs the advantage of the computational similarity of the matched t test to the one-sample t test. However, the students' basic familiarity with the concept of correlation makes it reasonable to teach Chapter 11 (the matched t test) directly after Chapter 7 (the two-sample t test), or even just after Chapter 6 (the one-sample t test).

The unifying theme of Part Two is an explanation of the basics of univariate inference, whereas Part Three deals with the different (bivariate) methods that can be applied when each participant is measured twice (or participants are matched in pairs).

Part Four of the text is devoted to the basics of analysis of variance without the added complications of repeated measures. Moreover, by detailing the analysis of the two-way between-groups ANOVA before introducing repeated measures, I am able to describe the analysis of the one-way RM ANOVA in terms of factorial ANOVA. Part Five introduces repeated-measures ANOVA, and then includes a separate chapter on the two-way mixed design. Part Six introduces the basic concepts of multiple regression, and then draws several connections between multiple regression and ANOVA, in terms of such procedures as the analysis of unbalanced factorial designs, and the analysis of covariance.

Finally, Part Seven of the text begins with a demonstration of how the basics of probability with discrete events can be used to construct the binomial distribution and draw inferences from it. More complex inferential statistics for categorical variables are then described in terms of the chi-square test. What had been the last chapter (i.e., 21) in all of the previous editions, Ordinal Statistics, has been removed from the printed text and placed on the web, in order to make room for some new material (e.g., Mediation analysis).

Users of the third edition may notice the absence of two major topics that had been contained in C sections: Three-Way ANOVA, which had been in Chapter 14, and MANOVA, which had been in Chapter 18. All of this material, plus a section on three-way mixed designs, is contained in a separate chapter (Chapter 22), which will be available only on the web.

A Note About the Use of Calculators

To get the most out of this text, all students should be using a scientific or statistical calculator that has both the biased and unbiased standard deviations as built-in functions. This is a reasonable assumption because, in recent years, only the simplest...