Transcript
Page 1: Straightforward Statistics for the Behavioral Sciencesby James D. Evans

Straightforward Statistics for the Behavioral Sciences by James D. EvansReview by: Karl L. WuenschJournal of the American Statistical Association, Vol. 91, No. 436 (Dec., 1996), pp. 1750-1751Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2291607 .

Accessed: 14/06/2014 06:44

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journalof the American Statistical Association.

http://www.jstor.org

This content downloaded from 185.44.77.125 on Sat, 14 Jun 2014 06:44:22 AMAll use subject to JSTOR Terms and Conditions

Page 2: Straightforward Statistics for the Behavioral Sciencesby James D. Evans

1750 Journal of the American Statistical Association, December 1996

Statistical Analysis of Nonnormal Data J. V. DESHPANDE, A. P. GORE, and A. SHANUBHOGUE. New York: Wiley, 1995. viii + 240 pp. $40.95.

It is now well recognized that the normal distribution is more of an exception than the rule in a number of practical situations. The analyst is often confronted with processes (distributions) that are either unknown or at least are known to be far from being normal. Situations like these re- quire a clear understanding and a careful analysis. Because most statistical methods are for the normal distribution, it is useful to have a collection of statistical procedures that are suitable in the context of nonnormal dis- tributions. Statistical Analysis of Nonnormal Data will prove valuable in this regard.

The authors state in the preface that "three kinds of methodologies are available for analysis of data arising out of random variables that may not follow the normal distribution. The first type consists of nonparametric methods (see Lehmann (1985) or Hollander and Wolfe (1973)). There are also the methods for analysis of discrete data (e.g. Fleiss (1981) or Upton (1978)). Then there are methods appropriate for specific non-normal distri- butions in areas such as reliability, life testing (e.g. Nelson (1982), Mann, Schafer and Singpurwalla (1974)). The purpose of the present book is to combine these various aspects." The authors' "aim is three-fold (i) Make available in one place nonparametric methods and methods of discrete data analysis. (ii) Introduce methods appropriate for some simple, specific con- tinuous, non-normal distributions of interest in newly emerging areas of survival analysis and reliability. (iii) Provide computer programs for ready use."

There are 13 chapters in this 240-page book:

1. Preliminaries 2. Study of a Single Population 3. Comparison of Two Populations 4. Comparison of Several Populations 5. Rank Correlation and Regression 6. Nonparametric Tests for Some Designed Experiments 7. Standard Discrete Distributions 8. Analysis of Data with Two Responses per Unit 9. Analysis of Data with Three Responses per Unit

10. Models for Life Data 11. The Exponential and Related Distributions 12. Nonparametric Methods for Censored Data 13. Analysis of the Competing Risks Set-Up.

This is not a theory book; the focus is mainly on how to apply various in- ference methods. In this spirit the book is similar to the book by Hollander and Wolfe (1973). Each procedure is introduced in the context of a "prac- tical" situation and illustrated with a numerical example. Calculations for the examples are done by hand and shown in a step-by-step manner-a feature that will be particularly beneficial for self-learners. The authors also provide a computer program package that can be used to perform the calculations.

In keeping with aims (i) and (ii), many standard statistical inference procedures, both parametric and nonparametric, are discussed with a fair amount of detail. It should be noted that some of the materials are not com- monly found in textbooks. Examples include the Gore test for hypothesis of quasi-symmetry or uniform asymmetry (pp. 142-143), the Gore and Shanubhogue test for no difference between the main plot treatments and the subplot treatments in a split-plot experiment (pp. 98-99), Maritz's test for the intercept of a linear regression line (pp. 76-78), Bowker's test for mirror-image symmetry (pp. 139-140), Stuart's test for marginal symme- try (pp. 141-142), and the Bagai-Deshpande-Kochar test for stochastic dominance of one competing risk over another (pp. 206-207). Chapters 8 and 9 cover analysis of data in contingency tables and also contain materi- als usually not found in textbooks. These include discussions on testing the hypothesis of conditional independence and the hypothesis of complete, marginal, and conditional symmetry. Section 4 in Chapter 10 includes tests of exponentiality against positive aging based on cumulative total time on test statistic and on Deshpende's test. The discussions in Chapter 13 about various problems in the analysis of the competing risks setup are also noteworthy.

The authors have done a good job of putting together a collection of both parametric and nonparametric procedures useful for nonnormal data. Here are some suggestions to make the book more beneficial to users. First, add more exercise problems at the end of each chapter. Second, mention exact tests when one is available. A discussion of exact tests and the related details would be helpful, particularly if this were to be used as a textbook. It is true that having and using the exact distribution tables is a bit cumbersome, but students often find the experience useful, and in many

cases this leads to a better understanding of the concepts. Also, commercial software packages could be used (or referred to) to perform the more popular exact tests. Third, it seems more logical to interchange Chapters 10 and 11. The material on the exponential and related distributions (now Chap. 11) should precede the material on dealing with models for life data (now Chap. 10). Fourth, in Section 10.2, mention that the graphical procedures, in general, are called "Q-Q" plots. It would also be useful to have a short section on nonparametric goodness of fit methods, say in Chapter 2, and this could include a general discussion of the Q-Q plots. Fifth, a discussion on other interesting "one-sided" alternatives could be included in Chapter 4. For example, a substantial amount of literature now exists in the area of "comparing treatments with a control"; some of these could be mentioned (see, e.g., Gibbons and Chakraborti 1992, chap. 11). Sixth, the topic of multisample problems with censored data needs to be discussed. Finally, it would be better if the authors would use a commercially available Windows-based statistics software package (such as Minitab for Windows). Granted that no package will do everything that the user needs to do (at least not directly) such a move would add to the value of the book, as a number of students and users would be expected to be familiar with such a package. Windows-based software with a spreadsheet data interface is more user-friendly than a DOS-based command-oriented package. The point is that we need to spend more time teaching and learning the concepts with the aid of the software and less time learning the software itself.

Other minor comments include the usual typographical errors (e.g., Jonckheere is mispelled; "computations" on p. 238) and some omissions in presentation (e.g., on p. 6, Y, has the binomial distribution with parameters n and F(c), provided F is continuous). Ties appear to be handled a little differently from the usual practice for the sign test. For rank tests, no clear guidelines are given for ties. For example, in the Jonckheere test, the U statistic is defined to handle ties implicitly, but no mention of ties is made for the Kruskal-Wallis or the Wilcoxon-Mann-Whitney tests (although the example indicates they are broken by the usual midrank method). Fi- nally, discussions of the following topics would be useful: the continuity correction for the normal approximation to the sign test (p. 28), Lilliefor's test for normality, estimation of the intercept of a regression line, logrank test for censored data, and robustness of various procedures. Also useful would be more thorough reviews of some of the pertinent literature and guidelines for when to use which procedures (e.g., only the Deshpande test of scale homogeniety is mentioned, although several others are available; see Tsai, Duran, and Lewis 1975 for a review and some comparisons).

If this book were to be adopted as a text for a one-semester course, it would be useful to have some guidelines about which topics should be covered first and in what order. Even though no serious mathematical preparation is necessary, in my opinion the students will need to have at least a statistical methods course to fully appreciate the material.

In conclusion, Statistical Analysis of Nonnormal Data deals with prob- lems in an important area of statistics and will be useful to teachers, stu- dents, and practitioners.

Subha CHAKRABORTI University of Alabama-Tuscaloosa

REFERENCES

Gibbons, J. D., and Chakraborti, S. (1992), Nonparametric Statistical In- ference (3rd ed.), New York: Marcel Dekker.

Hollander, M., and Wolfe, D. A. (1973), Nonparametric Statistical Meth1- ods, New York: Wiley.

Tsai, W. S., Duran, B. S., and Lewis, T. 0. (1975), "Small-Sample Behavior of Some Multisample Nonparametric Tests for Scale," Journal of the American Statistical Association, 70, 791-796.

Straightforward Statistics For the Behavioral Sciences James D. EVANS. Pacific Grove, CA: Brooks/Cole, 1996. xxii + 600 pp. $63.95.

In many ways, Straightforward Statistics for the Behavioral Scienzces is typical of many textbooks written for teaching introductory applied statis- tics to undergraduate psychology students not greatly skilled in mathemat- ical concepts. The topics include basic descriptive statistics, t-tests, simple analyses of variance, and simple nonparametric tests. There is no separate chapter on probability. The author successfully strove to keep focused on fundamental topics and to review elementary topics when building on them later in the text. Each chapter is followed by numerous exercises and questions testing the student's understanding of the material; solutions and answers to odd-numbered questions can be found in an appendix. The book also includes an appendix presenting the basics of using Minitab and Mystat to compute many of the statistics covered in the text.

This content downloaded from 185.44.77.125 on Sat, 14 Jun 2014 06:44:22 AMAll use subject to JSTOR Terms and Conditions

Page 3: Straightforward Statistics for the Behavioral Sciencesby James D. Evans

Book Reviews 1751

Introductory statistics textbooks typically start out by defining basic statistical concepts. This book starts by attempting to convince students that learning statistics has great practical value to them. To the extent that the text is successful in so convincing the students, we should expect them to be more highly motivated to study a topic that many of them find, at least initially, boring.

I am of the opinion that teaching the basics of research design should precede teaching statistics, even though in the typical psychology curricu- lum a course in statistics is a prerequisite to a course in research design and methodology. I typically spend a day or two at the beginning of the semester teaching the very basics of research design to provide the stu- dents with the conceptual framework within which the subsequent ma- terial on statistics will fit. Straightforward Statistics does a good job of presenting the basics of research design prior to initiating instruction in statistics. Continuing the emphasis on using statistics in research, the au- thor illustrates each new statistical procedure with data from an actual or a hypothetical behavioral study. One nice feature often missing in introduc- tory texts is that following computation of each analysis, the author shows the reader how to write a summary statement of the sort that one would find in a research journal (using the style of the American Psychological Association).

Instructors in statistics sometimes joke about students' mistakes. For example, some students confuse the values of variables with the variables themselves (e.g., they may respond "female" or "male" rather than "sex" or "gender"). The experienced and effective instructor anticipates these mistakes and takes action to prevent or correct them. To me the most dis- tinctive feature of Straightforward Statistics is that the author has taken special steps in the text to help students with a number of the same mis- takes that I have, often with great frustration, observed my students make.

I was unable to find in Straightforward Statistics what I would consider serious errors. Of course there was the occasional typographical error, and the strict grammarian may notice several split infinitives. The introductory student wants to be told "the simple truth." The instructor who knows that the truth is not so simple may attempt to present it with more complexity than the introductory student is able to handle, qualifying every statement to the point that the students conclude that the instructor does not know what he is talking about. Alternatively, the instructor may tell a "little white lie," a simplification that technically is not true but that captures the essence of the concept in a way that will be useful to the introductory student. Many of what some sophisticated readers may consider to be errors in Straightforward Statistics may be considered more appropriately as such "little white lies." Here are two examples: First, the author asserts (p. 28) that a "statistically significant" result is one that is reliable in the sense that "it is likely to recur if the original study is repeated." One certainly could quibble with this; in domains where research is typically low in power, the most likely result of an attempted replication would be a type II error, but the introductory student is unlikely to appreciate such an argument, at least early in the course. Second, the author states (p. 77) that "in a skewed distribution the median is always somewhere between the mode and the mean." It is not difficult to show that this statement is not true, but would it help the introductory student to explain for which types of distributions it is true and for which it is not?

Some readers may find "errors" in this text that in fact are better de- scribed as differences of opinion. For example, some psychologists opine that scale of measurement is a critical dimension to consider when de- ciding which statistical analysis is appropriate; others opine that scale of measurement (especially the distinction between ordinal data and interval data) is of not much, or not any, importance in making such decisions. The latter group may be expected to be uncomfortable with Straightfor- ward Statistics, in which scale of measurement plays a central role in such decisions. In fact, the author asserts that even the calculation of a mean requires that one assume interval scale data.

I would recommend a look at Straightforward Statistics to instructors worried that their present textbook is too difficult for their introductory students to understand. Basic concepts are explained in simple language and the explanations are repeated later in the text, in the style of a patient instructor who has become accustomed to teaching students who have difficulty with the topic. However, I would not recommend the book to the instructor who would prefer to use a text that thoroughly covers the details and controversial issues of the statistical procedures commonly used in the behavioral sciences; Straightforward Statistics is simply not designed to fill that niche.

Karl L. WUENSCH East Carolina University

Growth Curves Anant M. KSHIRSAGAR and William Boyce SMITH. New York: Mar- cel Dekker, 1995. viii + 359 pp. $135.00.

Kshirsagar and Smith provide us with a new entry in the rather short list of recent textbooks on the analysis of growth curves (Diggle, Liang, and Zeger 1994; Goldstein 1979; Jones 1993; Lindsey 1993). Chapter 1 presents motivating analyses of several interesting biomedical case studies, complete with SAS PROC GLM code, including a comparison of classical split-plot analysis of variance and multivariate analysis of repeated mea- sures. Chapters 2 and 8, the heart of the text, introduce the balanced growth curve model of Potthoff and Roy (1964) and Grizzle and Allen (1969) with origins in the earlier work of C. R. Rao and C. G. Khatri. This classical Gaussian model, central to the authors' developments, requires all subjects to have complete data measured at the same times and modeled by polyno- mials of the same degrees, and to possess constant covariance matrices. A thorough understanding of matrix algebra and classical multivariate anal- ysis will assist the reader's study of these two chapters. Testing of general linear hypotheses, construction of Scheffe-type simultaneous confidence intervals, and proper choice of within- and between-subject contrasts are discussed, with emphases on Wilks' likelihood ratio and exact and ap- proximate F tests. The authors provide SAS PROC IML, REG, and GLM programs that implement the matrix approach of Potthoff and Roy sys- tematically and discuss an alternative two-stage formulation.

Unfortunately, the rigor of Chapters 2 and 8 does not extend to other chapters, in which several generalizations are developed. Chapters 3-5 in- clude variants of seemingly unrelated regressions, exchangeable errors, multivariate outcomes at each measurement occasion, time-dependent co- variates, and sums of profile models. Chapter 6 discusses sphericity tests and model selection using quasi-predictive likelihood, as well as a nonpara- metric multiple comparisons procedure (Zerbe and Murphy 1986). Chapter 7 gives generalizations that accommodate incomplete, unbalanced data, generalized estimating equation approaches (with further details given in Chap. 10), and an interesting motivation of the EM algorithm. How- ever, these treatments appear to lack adequate detail. Chapter 9 intro- duces Bayesian approaches, and Chapter 10 discusses kernel-based and rank-based methods. Randomization tests and nonlinear models are not discussed. The bibliography, though not comprehensive, provides many interesting references not found in other growth curve texts.

In summary, Growth Curves is an excellent reference text to guide statis- tics graduate students and professionals in their study of this active re- search area.

Gary ZERBE University of Colorado Health Sciences Center

REFERENCES

Diggle, P. J., Liang, K.-Y., and Zeger, S. L. (1994), Analysis of Longitudinal Data, New York: Oxford University Press.

Goldstein, H. (1979), The Design and Analysis of Longitudinal Studies, London: Academic Press.

Grizzle, J. E., and Allen, D. M. (1969), "Analysis of Growth and Dose- Response Curves," Biometrics, 25, 357-381.

Jones, R. H. (1993), Longitudinal Data With Serial Correlation: A State- Space Approach, New York: Chapman and Hall.

Lindsey, J. L. (1993), Models for Repeated Measurements, New York: Ox- ford University Press.

Potthoff, R. F., and Roy, S. N. (1964), "A Generalized Multivariate Analysis of Variance Model Useful for Growth Curve Problems," Biometrika, 51, 313-326.

Zerbe, G. O., and Murphy, J. R. (1986), "On Multiple Comparisons in the Randomization Analysis of Growth and Response Problems," Biomet- rics, 42, 795-804.

Survival Analysis: A Practical Approach Mahesh K. B. PARMAR and Machin DAVID. New York: Wiley, 1995. x + 255 pp. $45.

This book is written by two authors who work at the Medical Research Council Cancer Trials Office in Cambridge and have had much real ex- perience with clinical trials in which the endpoint is an observed time to an event. In comparison to many other books written on survival analysis, this book's approach to teaching survival analysis is practical and offers medical and health care researchers and neophyte medical statisticians a completely useful reference that will provide real help and expert guidance in conducting their work.

This content downloaded from 185.44.77.125 on Sat, 14 Jun 2014 06:44:22 AMAll use subject to JSTOR Terms and Conditions


Recommended