Reviews of Books and Teaching Materials

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Handbook of SAS DATA Step Programming.

Arthur Li. Boca Raton, FL: CRC Press, xxi + 253 pp., $59.95 (H), ISBN: 978-1-4665-5238-8.

The Handbook of SAS DATA Step Programming is a short book addressing a number of useful topics related to the DATA Step in SAS. It mainly deals with data manipulation in DATA Step although a few procedures related to data such as PROC SORT also appear in the text. Throughout the book, each topic is presented with example code, which helps the reader to better comprehend the topic. The handbook is divided into 10 chapters roughly of equal length. Chapters 1 and 2 are introduction to the rest of the book. Chapter 1 makes a good attempt to familiarize the reader with SAS and Chapter 2 shows the reader how to create datasets using conditional statements such as If-Then-Else or SELECT structures. Those with some familiarities with SAS can skip these two chapters.

Chapters 3–6 form the main body of the book which needs to be read in sequence. Chapter 3 focuses on Data Step including RETAIN, SUM, and conditional processing, that is, processing only a portion of a dataset. This chapter also presents other topics of interest such as detecting the end of file and format conversion. Additionally, we see some debugging techniques which will come handy when there is either syntax or a logical error in the SAS code. I would like to add that when dealing with high-level (third generation of) computer programming languages, there is a third category of errors called run-time errors. Examples include attempting to take the square root of a negative number or reading data from a file that does not exist. However, the fourth generation of languages such as SAS handle run-time errors differently. Chapter 4 is concerned with the processing of data with repeated observations per subject using the By-Group processing. One will also see, through some examples, a few applications of this structure such as identifying duplicates in a dataset. Furthermore, conversion of datasets from long format to wide format is presented using By-Group and without the use of arrays in this chapter.

As is the case frequently, if a part of a set SAS codes needs to be repeated a number of times (known or unknown), there would be a need for some kind of looping structure. The author nicely presents several looping structures and the difference (s) between these structures in Chapter 5. Other topics covered in this chapter include implicit and explicit loops, nested loops, and some applications of these structures (generating samples with and without replacement, for example).

A very important structure in computer programming is the use of arrays which allow one to access data repeatedly without having to read in such data over and over. This topic is covered in Chapter 6. Caution has to be taken when implementing arrays in a program to avoid having out-of-bound errors. A few interesting topics are presented in this chapter which include DIM, HBOUND, LBOUND, IN, and OF functions. The chapter is extended considering multi-dimensional arrays at the end. The remaining chapters, namely 7–10 can be read in an arbitrary order.

Chapter 7 discusses the situations where data come from different sources and need to be combined vertically or variables come from different sources and data need to be combined horizontally. One easy and popular method (if applicable) is concatenation. One-to-one reading or merging of datasets and match-merging are among the topics presented here.

Reading and writing to external files is another important process and comes handy frequently. These topics are covered in Chapter 8. The chapter also shows how to read from or write into external text files using specific formats. Additionally, the process of reading data where the fields in each record are of different types is presented in this chapter.

Most if not all programming languages provide the users with a number of more frequently used and popular built-in functions or routines. SAS offers a large set of such routines. In Chapter 9, the reader learns about the built-in CALL (functions) and CALL routines (equivalent to Procedures in other languages). A short list of these routines along with some examples is given in this chapter.

Finally, Chapter 10 introduces some PROC statements dealing with datasets. The list includes SORT, COMPARE, TRANSPOSE, Transpose-By-Group, some options related to this routine, and also the OPTIONS procedure. The examples in this chapter are very interesting to read.

In sum, this short book covers a number of introductory SAS topics dealing with DATA Step. It is not a comprehensive book on the topic, but covers a good number of topics attractive to SAS users. The strength of the book is a simple and straight-to-the-point approach taken by the author. Examples and a few exercises appearing at the conclusion of each chapter are very helpful in understanding the topics. It is a good source as supplement to a textbook or a statistics course using SAS. It does not require any prior exposure to SAS although it is always helpful to have some background on the topics. All of the code is written and explained very efficiently. Anyone interested in the topic will find this handbook very easy to follow. Solutions to the exercises along with SAS programs appearing in the book, also data sets used in the book, and pdf presentation slides can be found at: http://www.crcpress.com/product/isbn/9781466552388.

Morteza Marzjarani

Saginaw Valley State University (retired)

Optimal Experimental Design With R.

Dieter Rasch, Jürgen Pilz, Rob Verdooren, and Albrecht Gebhardt. Boca Raton, FL: Chapman & Hall/CRC, 2011, xix + 325 pp., $109.95 (H), ISBN: 978-1-4398-1697-4.

I was asked to review this book and its associated R package, OPDOE, because of my interest in the field of optimal experimental design. I was excited by the prospect of a new R package that could be used to generate optimal designs and perhaps serve as a useful companion to books in optimal design such as Atkinson, Donev, and Tobias (2007) or Goos and Jones (2011). Unfortunately for me, after agreeing to provide the review I learned that neither the book nor the software has much to do with what I think of as optimal design. With a few exceptions, the package focuses on two tasks: (1) generating classical designs and (2) determining sample sizes for those designs. In the words of the authors, “by offering R-programs for the construction of experimental design and the determination of the minimum sample size needed for some precision, we hope that even experimenters with limited knowledge about the theory of experimental designs are able to improve the efficiency of their experimentation by using these programs.” So, misnomer aside, this is still an admirable goal. Has it been met? In my view, the book is far too theoretical, and the software too limited and difficult to use, to be useful to experimenters with limited knowledge of design.

Chapter 1 (Introduction) provides a brief overview of empirical research, the basics of design, and an introduction to block designs. Chapters 2–5 constitute Part I: Determining the Minimal Size of an Experiment for Given Precision. Chapter 2 (Sample Size Determination in Completely Randomized Designs) covers sample size determination for estimation and hypothesis testing for means, variances, and proportions in one- and two-sample problems. Chapter 3 (Size of Experiments in Analysis of Variance Models) covers sample size determination for one-, two-, and three-way layouts with fixed, random, and mixed effects in crossed, nested, and mixed classifications. Chapter 4 is titled Sample Size Determination in Model II of Regression Analysis. By Model II, the authors mean that both the predictor(s) and the response variable are random, so this section is really about sample size determination for estimation and testing of a correlation coefficient. Chapter 5, on Sequential Designs, covers Wald’s sequential likelihood ratio test, sequential tests for means and proportions, and sequential selection procedures for identifying a best population.

Part II, the Construction of Optimal Designs, consists of Chapters 6–8. Chapter 6 is titled Constructing Balanced Incomplete Block Designs. Here, the intent of the software is to produce the smallest balanced incomplete block design (BIBD) that exists given the number of treatments v and the block size k < v. Chapter 7 (Constructing Fractional Factorial Designs) covers 2^{p − k} and 3^{p − m} (regular) fractional factorial designs. Given a list of confounded effects, a function is given that will identify the minimal complete sets of confounded effects for a given number of factors. Surprisingly, there is no example provided where a design is actually constructed using an OPDOE function. Chapter 8 (Exact Optimal Designs and Sample Sizes in Model I Regression) treats optimal design, but only for one-dimensional polynomial and nonlinear models.

The final two chapters make up Part III on Special Designs. Chapter 9 (Second-Order Designs) covers central composite designs, Doehlert designs (though I am not sure why), D-/G-optimum CCDs (though completely impractical due to sample size requirements), and how to compare designs using the determinant criterion. Chapter 10 (Mixture Designs) touches very briefly on simplex lattice designs, simplex centroid designs, and extreme vertices designs (all unconstrained). Although the chapter refers to the use of an R program to construct these designs, there is no example and the name of the function is not given.

The most useful parts of the book are Chapters 2 and 3 involving sample size determination for one-, two-, and three-way layouts. Here, the book is fairly exhaustive in that it considers virtually all combinations of crossing, nesting, and fixed versus random effects scenarios. In particular, sample size routines have been developed for tests of fixed effects for the following designs (A≻B indicates that factor B is nested within factor A):

Table

The R functions described focus on sample size for testing of fixed effects only, which seems a limitation. Unfortunately, I was not able to reproduce the examples in the book.

I was also drawn to the chapter on balanced incomplete block designs. The idea of providing the smallest BIBD for a given number of treatments and block size seemed useful, until I experimented with the function. My first call, for five treatments with a block size of two, was successful. But after that, I ran into problems with my other calls, for example, 10 treatments with block sizes of 3, 4, and 5; interestingly, I received a different error message in each of these cases. Additionally, some other functions, such as “design.centralcomposite,” were simply not yet present.

I am in no way on R “expert,” and I had difficulty getting the package to load. The website directions did not work for me, either on a Mac or on a Windows machine. However, things went smoothly using the package installers from the menus in R or R Studio. Once up and running, I realized that there was a paucity of documentation available—both online and in the book—regarding the OPDOE R functions. Apparently, documentation has been largely relegated to future development.

To give some flavor as to the level of the writing and to where the book falls on the applied/theoretical scale, consider the following from page 220:

Definition 7.8

In an s^p factorial experiment with a prime s > 1, we can identify the s^p treatment combinations with the points (x₁, x₂, …, x_p) of an EG(p, s) (see Definition A.11). Any (s − 1)-flat (with s − 1 points) of the EG(p, s) is defined by (a₀ + a₁x₁ + a₂x₂ + ⋅⋅⋅ + a_px_p) = 0; a_i ∈ GF(s) (see Definition A.7). By keeping (a₀, a₁, a₂, …, a_p) constant and varying a₀ over the elements of GF(s), we generate s parallel (having no point in common) p-flats, called a pencil P(a₁, a₂, …, a_p). P(a₁, a₂, …, a_p) divides the s^p treatment combinations into s − 1 degrees of freedom.

In summary, the book does not succeed as a textbook in design and it does not succeed as a manual for OPDOE. The R package OPDOE is useful, mostly, for sample size determination for analysis of variance studies and sequential design. The R functions provided for design construction are either problematic (e.g., for BIBDs) or not particularly useful in practice (e.g., for fractional factorial designs, exact optimal designs, CCDs, and mixture designs).

Christopher J. Nachtsheim

University of Minnesota

The Signal and the Noise: Why So Many Predictions Fail—But Some Don’t.

Nate Silver. New York, NY: The Penguin Press, 2012, 534 pp., $27.95 (H), ISBN: 978-1-594-20411-1.

I was pleased to be invited to review The Signal and the Noise: Why So Many Predictions Fail—But Some Don’t by Nate Silver as Mr. Silver, the proprietor of the New York Times’ FiveThirtyEight political blog and the developer of the Player Empirical Comparison and Optimization Test Algorithm (PECOTA) for forecasting Major League Baseball player performance, and I have many common interests—specifically statistics applied to problems in sports and politics. Furthermore, Silver and his book have received a great deal of attention outside the statistics community; recently, he served as a member of the roundtable on ABC’s Sunday morning news show This Week with George Stephanopoulos. An opportunity to carefully review this book would give me a chance to see for myself what is motivating this attention.

The 454 page body of the book is followed by 55 pages of notes and citations from a wide variety of sources; the copious endnotes provide an indication that this book will have more weight and depth than many (most) of the recently published wave of mathematics/statistics/analytics books targeted toward the general public. In his introduction, Silver provides a historical perspective on the massive and growing amount of information that is available to us and the impact these data have on scientific and public discourse. I particularly appreciated his straightforward admission that all prediction is subjective; this is the first of several instances in which the author explains a concept that may be obvious to statisticians but not so to many outside of our discipline. Silver carefully outlines how the book will proceed: “The first seven chapters diagnose the prediction problem while the final six explore and apply Baye’s [sic] solution.”

In Chapter 1: A Catastrophic Failure of Prediction, the author focuses on prediction in financial markets with an emphasis on the 2008 collapse of the stock market. His explanation of how unrealistic predictions/expectations by all parties led to the housing crash and ensuing recession is cogent and straightforward; this chapter reads as though it were written by a lucid economist. However, in attempting to make a point about the forecasted and actual 5-year default rates for collateralized debt obligation tranches, Silver uses circular displays that visually exaggerate the extent of the difference, neglecting that most people cannot easily gauge the relative differences in the areas of two circles. His discussion of what can be learned from this series of events and the distinction he makes between the concepts of accuracy and precision at the end of the chapter are well done, but I do wish at this point he had discussed how an accurate forecasting model of market behavior will cease to provide accurate forecasts once the public becomes aware of the model and alters its behavior (he does address this issue in a later chapter).

Silver turns his attention to prediction and politics in Chapter 2: Are you Smarter than a Television Pundit? He discusses Philip Tetlock’s analysis of personality traits that coincide with rates of accuracy in political predictions made by experts. The discussion of why foxes are superior to hedgehogs (think Tolstoy’s The Hedgehog and the Fox) with regard to prediction can be seen as analogous to concepts espoused by several forecasters such as Winkler and Makridakis (1983) in The Combination of Forecasts. The chapter concludes with a discussion on why television shows prefer to feature hedgehogs as guests and how to take a fox-like approach to forecasting.

In Chapter 3: All I Care About is W’s and L’s, Silver returns to what first brought him to prominence—prediction in sports with an emphasis on baseball. He discusses his development of the PECOTA (Player Empirical Comparison and Optimization Test Algorithm) system that projects performance of major league baseball players on the basis on comparable major league players, baseline forecasts, and a career-path adjustment to account for maturation/aging. The author uses his experience as a backdrop for a discussion of the integration of model-based predictions and subjectivity, which he strongly advocates.

Silver continues to make his case for hybridizing model-based predictions and subjectivity in Chapter 4: For Years You’ve Been Telling Us that Rain is Green. As an example of the relative accuracy of modern weather forecasting, he cites the National Hurricane Center’s forecast that the path of Hurricane Katrina would likely take the storm directly through New Orleans with almost 5 days’ advance notice. The author provides a brief history of weather forecasting, links much of the recent improvement to increases in computational power with an appropriate reference to Moore’s Law, and explains chaos theory within the context of the difficulty in forecasting weather. Ultimately he again returns the notion of integration of model-based predictions and subjectivity.

Silver discusses the difficulties associated with predicting earthquakes and uses this discussion to make a clear distinction between predictions and forecasts in the aptly named Chapter 5: Desperately Seeking Signal. In the context of earthquakes, the author classifies “a definitive and specific statement about when and where an earthquake will strike” as a prediction and “a probabilistic statement, usually over a longer time scale” as a forecast. He also provides a clear discussion of the power-law distribution and how it can be used to estimate the frequency of earthquakes of a particular magnitude that will occur in a region. This chapter also provides the author with an opportunity to return to the concepts of signal, noise, and overfitting. He refers to overfitting, correctly in my opinion, as “the most important scientific problem you have never heard of.” Here, Silver’s message is that what one disregards and what one retains are equally important when forecasting.

The topic of Chapter 6: How to Drown in Three Feet of Water, is economic forecasting. Here, Silver emphasizes the need for consideration of margin of error in forecasts and focuses on the role of forecasters in the public’s misunderstanding of the imprecise nature of forecasts. I wish the author would have expanded his discussion to include the role of the general public in this misunderstanding; it is difficult for me to understand how a rational person who hears that the forecasted crest of a swollen river is slightly under flood stage can casually believe that a flood cannot possibly happen. At least some of the responsibility must be shouldered by the public, who should be realistic about the nature of forecasts and understand that forecasts of complex systems such as weather and economies are not deterministic and cannot be expected to be error-free. Silver also uses this chapter to underscore the distinction between correlation and causation. Most importantly in my opinion, this is the chapter in which the author takes a stand against mindless mining of data without theory and explains how this approach often (usually?) leads to the interpretation of noise as signal.

In Chapter 7: Role Models, Silver makes points about the risks inherent in extrapolation and the relationship between extrapolation and achievable forecast precision. In this chapter, the backdrop is prediction of outbreaks, epidemics, and pandemics. Here, the author revisits the idea that the act of forecasting can render the forecast less accurate, as can happen when the forecast of an outbreak leads to various preventive measures, as well as the idea that the act of forecasting can improve the accuracy of the forecast, as can happen when media coverage of a medical condition increases public awareness of the associated symptoms and leads to a higher frequency of diagnoses of the condition. He also discusses the important trade-off between simplicity and sophistication in models.

As Silver promised in his book’s introduction, Bayes’ theorem is the focus of the final six chapters. In Chapter 8: Less and Less and Less Wrong, the author uses suspected marital infidelity and mammograms to explain conditional probability and Bayes’ theorem intuitively, and he segues smoothly into a discussion of false positives. In Chapter 9: Rage Against the Machines, he reviews the argument that computers and software alone cannot be expected to produce forecasts superior to those that incorporate human insight; he does this within the context of chess matches between computers and Grand Masters. Poker provides the setting for Chapter 10: The Poker Bubble; in this chapter Silver makes an analogy between learning curves and the relationship between effort and accuracy of forecasts, eventually arguing that by being less focused on results, one may produce more accurate forecasts. In Chapter 11: If You Can’t Beat’em, Silver addresses the difficulty of predicting financial markets and he reviews the efficient market hypothesis and the limitations of small samples. Chapter 12: A Climate of Healthy Skepticism finds the author turning to the debate over the existence of global warming to underscore the importance of scientific skepticism. He provides an interesting discussion of Scott Armstrong’s critique of the Intergovernmental Panel on Climate Change’s global warming forecasts. While engaging, this discussion would have been greatly enhanced by coverage of the debate published in several issues of Interfaces between Armstrong, Green, and Soon (2008) and Amstrup et al. (2009) over the decision to list polar bears as a threatened species. Finally, Silver reflects on how our perspective and confusing the unfamiliar with the improbable can blind us to possibilities of future events in Chapter 13: What You Don’t Know Can Hurt You; the attack on Pearl Harbor in 1941, the terrorist attacks of 9/11, and the potential for future terrorist attacks serve as the setting for this chapter. Throughout each of these final six chapters the author repeatedly returns to his ongoing discussion of Bayes’ theorem.

The Signal and the Noise: Why So Many Predictions Fail—But Some Don’t is very good at what it does. In each chapter, Silver smartly reviews an important statistical concept that is often misunderstood by the general public, and he does so within the context of a recent issue that most readers know well. The book is well organized, well written, coherent, and engrossing, and it is far superior to most books on statistics and mathematics that have been written for the general public.

How can a well-trained statistician benefit from reading Silver’s book? Although the statistical principles covered in this book are familiar to most professional statisticians, the examples Silver uses and the ease with which he uses them to elucidate important and often misunderstood concepts are invaluable. Many who teach statistics at the undergraduate and perhaps master’s level could make use of the examples and clear, cogent, and engaging explanations. I certainly will integrate material from this book into the introductory business statistics courses I teach, and I will also consider assigning the book to students in these classes as extra reading to improve their numeracy.

James J. Cochran

Louisiana Tech University

Statistical Graphics Procedures by Example—Effective Graphs Using SAS.

Sanjay Matange and Dan Heath. Cary, NC: SAS® Publishing, xii + 357 pp., $53.95 (P), ISBN: 978-1-60764-762-1.

At first glance, it seems odd to find a text of more than 330 pp. devoted to three SAS® procedures that are focused not on analytics but on creating visualizations. However, a careful reading shows just how many details there are in the SAS graphic procedures that need to be discussed. Sanjay Matange and Dan Heath of SAS provide an in-depth look at the PROC SGPLOT, PROC SGPANEL, and PROC SGSCATTER procedures in this text that could equally serve as a teaching instrument or a quick tutorial for producing high-quality visuals within the SAS system. The text is easy to read and serves as a useful resource for individuals who need to add analytics to their data visuals or those who wish to use options to create the most professional visualization possible in SAS.

The text is laid out into 16 chapters and starts with a general introduction of data-based visualizations and an overview of the text. Chapter 2 gives a description of each procedure involving the basic syntax and utilization of each of the three procedures. Chapter 3 then gives a brief description of the different graph types available, and while much of the focus is on commonly used visuals (scatterplots, histograms, boxplots, bar charts, etc.) there is also early discussion of domain specific visuals (such as vector plots or step plots). Early on, the authors provide a nice resource in the form of a table that illustrates exactly which graph types can be combined within each of the procedures. This visual serves as an early indication of the complexity and possibility of layered visuals that the SG procedures can produce.

Chapter 4 brings readers into the basics of creating each of these plots with easy to recognize and access SAS code. Chapters 5, 6, and 7 look at bivariate association style plots first focusing on two quantitative metrics, followed by one quantitative versus one categorical, and finally two categorical variable visuals. At the book's half-way point, things switch over from general ‘‘how to make this style of graph’’ to ‘‘how to make a more professional or appealing graph.’’ Chapter 8 deals with topics such as legends and insets that help to explain technical aspects of visuals better, while Chapter 9 deals with annotations and attributes which help the reader to understand the message being conveyed by the visual.

After dealing with paneling of graphs in Chapter 10 and creating scatterplot matrices in Chapter 11 the book hits its real stride with Chapters 12 and 13 (arguably the most valuable in the text). Chapter 12 delves into specific visuals commonly used in the health and life sciences and provides terrific examples (with code) of a Forest Plot for meta-analysis and an Adverse Event Timeline for drug development studies. Similarly, Chapter 13 provides business and other industry style graphs such as Stock Plots and Social Network Graphs. The book ends with the last three chapters devoted to style guides, ODS, and exporting graphics which all focus on getting these visuals out of SAS and into some other reporting mechanism.

It is clear from the book's layout that the authors wished to have an example-based reference style text for those working with SAS and wanting to have a go-to resource for creating stunning professional visuals. However, there is also a secondary avenue for this kind of text, while the text is not written for newcomers to the SAS system, this text would make an excellent supplement to an introductory course on SAS coding. For instructors in statistics and biostatistics who are being asked to design courses that introduce SAS coding to students not majoring in the statistical sciences, one issue is in teaching an effective course and an introduction into programming to individuals who have a limited statistical background. The examples in this text are clear enough and the content focused enough that it might be possible to use many of these examples to illustrate the nuances of SAS coding without spending much time on discussing analytics. Instructors could create examples that deal with data importing, managing, and cleaning while simultaneously teaching code that provides meaningful output and do so without having to spend time discussing statistical theory. There has been a growing call for such coursework for students in public health, health information management, informatics, and other areas.

The text does have some room for improvement; the authors point out early on that a limitation in the text is the use of grayscale visualizations. That point comes across multiple times in the text when the reader is faced with an excellent graphic and wonders how it could be made better with color. While the use of color would likely cause a major increase in the cost of the text, it might seem like a good idea for Matange and Heath to explore a color e-book version of the text with enhanced visualizations. This may be especially helpful for programmers who wish to copy and modify code that is in the text. Also, the text uses a variety of examples but generally refers to the same SAS datasets over and over again. In addition to a traditional index, the authors may want to consider an example index so that readers who see a particular appealing visualization can explore other visuals that were created in other places in the book with the same dataset.

Jason Brinkley

East Carolina University

Statistical Theory: A Concise Introduction.

Felix Abramovich and Yaácov Ritov. Boca Raton, FL: Chapman & Hall/CRC Texts in Statistical Science, 2013, xv + 224 pp., $69.95 (H), ISBN: 9781439851845.

This book is designed to serve as the textbook for a one-semester statistical theory course for advanced undergraduates in statistics, and upon inspection it shows itself to be a refreshing presentation of the required topics. Those of us who have taught such a course for many years, using texts such as Casella and Berger (2002) supplemented by classics such as Stuart and Ord (1999) or Lehmann and Casella (1998), understand the frustration in trying to cover so much important material in a single semester. Several years ago, the department opened its first-year graduate course to upper-level undergraduates and non-Ph.D. students, requiring a modification of presentation, resulting in an ongoing quest for appropriate textbooks. “Undergraduate” texts such as Hogg, McKean, and Craig (2012), while at about the right mathematical level, also have too much material to cover in-depth. And of course the numerous, almost popular-level books are just not at the right level, despite including calculus-based approaches; see, for example, Navidi (2010) or Hogg and Tanis (2010). Having generally had good experiences with books with the CRC imprint, in hope and trepidation I opened Abramovich and Ritov's text.

It is going to raise many an eyebrow to see topics such as likelihood, sufficiency, minimal sufficiency, completeness, and the exponential class of distributions presented primarily in the introduction! This approach works, however, and provides an important way of thinking to the student when covered in this manner. Shock is good in some cases. After an expert statement of what statistics is, and the introduction of some canonical examples that are used throughout the text, we are immediately introduced to likelihood and sufficiency. The authors’ explanation of minimal sufficiency and completeness is quite insightful and constructive. They conclude their introduction with a concise discussion of the exponential class, including a curved exponential example.

Point estimation is presented in Chapter 2, beginning with maximum likelihood estimation (MLE) (including the nonregular case) and the method of moments. We are then introduced to mean squared error as a goodness of estimation measure, preparing the reader for chapter 7 that covers squared-error loss and decision theory. The authors present a good discussion of the decomposition into bias and variance. This raises the point of unbiasedness, which then leads to Fisher information and the information inequality. They present a good discussion and several examples of Rao-Blackwellization, which illustrate the point, and which make the subsequent Lehmann–Scheffé theorem easy to follow.

Confidence sets are covered beginning with a nice discussion, leading to the additive-type intervals before pivots are introduced. Although I prefer to teach hypothesis testing first, which provides the constructive likelihood ratio test inversion methodology, outside of asymptotic techniques we tend to resort to pivots as well, so this is not a limitation. Abramovich and Ritov do an excellent job with simultaneous confidence regions and the Bonferroni methods, a topic that is not commonly covered given the press of subject matter in competing texts.

The hypothesis testing/critical region problem is introduced well, with motivation provided by error probability analysis. They gently present the Neyman–Pearson lemma, although I was surprised they did not use the generalized version with the randomized test function to handle the discrete case; in fact, test functions were not mentioned. P-values, the power function, most powerful tests, the likelihood ratio tests, and the difficulty in finding uniformly most powerful tests were well explained. The proof of the distribution of the p-value under H₀ was left as an exercise for the reader (but with solution in Appendix B). The chapter contains good examples, and concludes with an adroit exposition on sequential Wald testing.

The authors handle asymptotic analysis in Chapter 5 by introducing three modes of convergence of sequences of random variables, the weak law of large numbers (including Khinchin), and consistency. For motivation, they provide several examples of distributional convergence, including Poisson, exponential, and extreme value distributions, before presenting the iid central limit theorem, and the Berry–Esseen bound for finite variance problems. After handling the plug-in theorem and asymptotic normality of MLE, they provide a good discussion and nice examples for the Wald and Wilks tests/confidence intervals. They address the geometry of confidence regions in the multiparameter case for exact and asymptotic tests, as well as goodness-of-fit tests.

The next two chapters address Bayesian analysis and elements of statistical decision theory. The Bayesian philosophy itself is well presented, as are the necessary topics such as choice of prior, calculation of posterior, point estimation/credible sets, and hypothesis testing. The examples are good. The decision theory chapter covers loss function optimality, risk, admissibility, minimaximality, etc. Many motivating concepts are explained using Bayesian illustrations, Bayes’ estimators, and rules (tests). As in most treatments of decision theory, the choice of loss function remains that of the decision maker.

The final chapter on linear models is a handy collection of results, intuition, and examples of use of the standard linear model. In it, Abramovich and Ritov concisely develop the least-square solutions and, with an appropriate distributional assumption, the MLE for β and σ_ϵ², Fisher information/Cramer–Rao lower bound, confidence intervals for the coefficients and predictions, etc. They consistently provide geometrical insights and excellent examples. The chapter concludes with a brief overview of one-way and two-way analysis of variance.

Part of the implicit “fine print” of this book is that the first month of material is presented in Appendix A, which includes some basic probability theory, random variables, functions of random variables, distribution theory, univariate parametric families, and some linear algebra projection theory applied to statistics. The second appendix contains solutions to selected exercises in the text, from the good collection of exercises at the end of each chapter. Offered without solution are many thought questions scattered throughout the text.

Overall, there are some quirks, as there would be if any of us wrote such a book. For example, the authors disclaim use of measure theory, but in their introduction for minimal sufficiency they have no qualms about presenting an equivalence class explanation. This, like measure theory, will likely lose most engineers. Similarly, some of their treatment of the Hat projection matrix uses geometric concepts from linear algebra; this works, but it is a bit more rigorous than the rest of the text. Most of the multivariate versions of the topics are asterisked as more advanced. They do not present almost sure convergence, but they do use convergence in pth mean. They do not present the Rao (Score) test. And, although I do not begrudge another author's notation, their moment notation uses the “backward” μ₂ = E(Y²), versus the aesthetically superior (in our opinion) μ₂ = μ′₂ − μ′²₁. Their distributional notation is fine with andf_Y(y; θ).

As teachers of theoretical statistics, we can use a new approach, which this text offers. The book does not aspire to be a compendium of applied techniques, nor a presentation of all the important theoretical developments in these last few centuries. It will be a helpful resource for teachers of mathematical statistics who are looking for an outline of teaching material and useable depth. Their material attains a workable syllabus, which can be easily augmented with the teacher's preferred emphasis. This volume will make a solid contribution to any theoretical statistics instructor's collection due to its convenient size, its scope of coverage, judicious use of examples, and clarity of exposition.

John A. Dobelman

Rice University

Understanding Advanced Statistical Methods.

Peter H. Westfall, and Kevin S. S. Henning. Boca Raton, FL: CRC Press, 2013, xxv + 543 pp., $79.95 (H), ISBN: 978-1-4665-1210-8.

This book is designed to replace the prevailing conventional two-course sequence for many academic majors that consists of elementary statistics followed by advanced research methods. Its primary audience is upper-division undergraduates and graduate students from any major area of study. The book emphasizes applications and has a wealth of examples from the social and economic sciences, biological and medical sciences, and physical and engineering sciences. A previous course in statistics is not necessary. The authors claim it can also serve as the text for a lower-division course to satisfy a mathematics general education requirement. The prerequisites are algebra, functions and graphs, and familiarity with spreadsheet software such as Microsoft Excel (the use of dedicated statistical software is encouraged but not required). Calculus is used but is not a prerequisite; the book employs a self-contained “just-in-time” approach to explain mathematical topics such as derivatives and integrals when discussing continuous distributions and expected value, and optimization when discussing maximum likelihood.

The book is similar in approach to Rice (2007) but integrates this approach more intensely throughout the text. The authors’ motivation for writing the book is to remove the gap in understanding that they claim often exists between the first elementary statistics course and the advanced research methods course, with the gap in understanding caused primarily by a formulaic approach to sophisticated topics in the latter course. This book contains just as many formulas as other statistics texts, but with intuitive, engaging, insightful, and irreverent explanations (“We have the famous historical figure R. A. Fisher to blame for the pv ⩽ 0.05 rule of thumb, which we call extremely ugly because it is so overused and abused by researchers”) the authors strive mightily to part the curtain that hides the fundamentals of statistical thinking from most students. The authors take very seriously the word Understanding in the book’s title.

The book has 20 chapters that cover the usual topics, and more, in an undergraduate/graduate math stat text; it is suitable for a fast-paced semester course offered to serious students. The “and more” refers to the strong emphasis throughout the book on thoughtful applications in a wide variety of disciplines. To support this emphasis, each chapter has a generous number of exercises that extend the chapter content and illustrate discipline-specific applications; end-chapter vocabulary lists and formula summaries are also included for each chapter. Chapter 1 is the most important chapter in the book; it explains the statistical science paradigm and the authors’ DATA/data approach, Nature → Design and measurement → DATA, that contrasts with the more conventional population/sample model. Briefly, DATA include all possible values that could be produced by the process (not the population) being studied, while data denote the values observed in a particular study. While on the surface the difference appears to be only semantic, there is a real difference resulting from the authors’ model produces data approach as opposed to the traditional data produces model.

After Chapter 1 the book has several chapters on probability; the topic coverage is focused on those aspects of probability models and distributions useful for statistics as opposed to counting rules and individual probability calculations. Simulation is emphasized as a way to understand processes, therefore there are no probability distribution tables in the text. In addition, Bayesian methods are presented before the more traditional frequency methods; Bayes’ theorem is presented in terms of distributions instead of the usual two-event approach.

The coverage of mathematical statistics is extensive and benefits from a substantial effort by the authors to explain the intuition motivating the procedures and the correct interpretation of specific results. They use a clever town/mountain lion analogy to clarify the correct interpretation of a frequentist confidence interval and devote an entire well-written chapter to illustrate and illuminate the subtleties in the logic of hypothesis testing and the meaning of p-values.

A companion Web site at http://www.understandingadvancedstatisticalmethods.com/ has a wealth of material useful for the instructor and students. Included are sample quizzes, midterm exams, final exams, text figures, data files, and computer code (R and SAS).

In summary, the text represents a successful effort by the authors to advance and improve the statistics education paradigm for courses offered to upper-level undergraduate and graduate students. For two reasons, it is not appropriate as a text for a lower-division class. (1) Beyond what could be considered preliminary chapters there are no “stand alone” chapters; since each chapter depends on the previous chapter throughout the book, its use at the lower division would require a significant effort on the part of the instructor concerning what chapters/parts of chapters to include and omit. A “road map” at the companion Web site suggesting one or more options for lower-division use would be of great assistance to an instructor. (2) The academic maturity and quantitative expertise of many students enrolled in a lower-division course may not be sufficient to appreciate and implement the insight and subtleties provided throughout the text. I can imagine a situation late in the course, where many students still do not understand the meaning of the “model produces data” approach introduced in Chapter 1. At the lower division, a more appropriate text written in the same spirit would be De Veaux, Velleman, and Bock (2012).

Thomas W. Reiland

North Carolina State University

When to Use What Research Design.

W. Paul Vogt, Dianne C. Gardner, and Lynne M. Haeffele. New York, London: The Guilford Press, 2012, xxi + 378 pp., $43.00 (P), ISBN: 978-1-4625-0353-7.

As indicated by the title When to Use What Research Design, the book provides thoughtful guidelines on how to choose research designs and their associated research methods. I congratulate the authors for writing the book with the clear organization, high accessibility of contents, and complete coverage of various designs and methods. It will be an excellent reference to various levels of readers: graduate students, teachers, and researchers in applied fields, such as social science, education, nursing, and marketing, who are trying to decide what methods to use to carry out a research project.

Starting with a general introduction on “Designs, Sampling, and Ethics,” the book is organized into three parts with each part consisting of six chapters, corresponding to the six design themes, that is, survey research, interviews, experiments, observational research, archival research, and combined designs. Part I on designs addresses the question of “given my research problem, which of the six designs shall I use?” by carefully comparing and weighting advantages and disadvantages of each design. Regardless of the design to be employed, it is crucial to determine “who should I study, and how many of them?” This question, along with numerous subsidiary questions, is addressed in chapters of Part II on sampling. At the intersection of designs and sampling, ethical issues emerge saliently. Part III discusses ethical issues, problems, and choices in turn for each of the six design themes. The three parts—Design, Sampling, and Ethics—are a complete integration and a sort of “design package” that assist researchers to collect data. Besides the clear organization with structured chapters as described above, there are two main points I found extremely useful about this book.

First, the book has high accessibility of contents. Many chapter headings and subheadings are written as questions and answers. A summary table is provided at the end of each chapter. As researchers are puzzled by some specific questions, they are able to quickly locate succinct answers in a bullet list (main points) by referring to the summary table of each chapter. If further detailed explanations are needed, readers can dip into chapters where extensive interpretation is provided for each bullet in the summary table. In addition, a comprehensive glossary is provided at the end of the book, covering complete aspects of the definitions that are relevant to selecting research designs and methods.

Second, there is limited number of existing texts on research designs that have such complete coverage of various research designs, including basic methods of collecting evidence: surveys, interviews, experiments, observations (participant and naturalistic), archival research (data and textual archives), and combinations of these methods. For each of the research designs, overall guidance and succinct summary of critical questions relevant to research designs are provided so that readers can quickly obtain big pictures about when to use what research designs. Readers with big pictures in mind, however, are expected to refer to more advanced texts that are specialized in certain research designs for further study. For example, the authors spend 1.5 pages (i.e., pp. 173–174), clearly stating the motivation of applying the technique called propensity score matching in studies under quasi-experimental designs with nonequivalent groups, followed by a persuasive example. Details on various matching methods (such as close neighbor matching, kernel matching, radius matching, etc.) and other applications of propensity scores (such as stratification, regression adjustment, etc.), however, are not fully discussed due to “so many questions, so little time.” This problem is apparently realized by the authors. At the end of each chapter, further readings at different advanced levels are suggested, including popular textbooks such as Dillman et al. (2009) and Groves et al. (2009) for survey design, Spradley (1979) and Mishler (1986) for interview, Shadish, Cook, and Campbell (2002) for experiments and quasi-experiments, etc. Helpful texts are recommended at all levels of readers’ expertise.

In summary, this book is a rich resource and readers will find many opportunities to gain useful insights and suggestions to undertake actions and start new research into ways of integrating it with teaching. The book does contain a lot of interesting material (examples) that can enrich a lecture course and deepen the reader's understanding of research designs, so that it definitely belongs to the shelf of every serious student/teacher/researcher in the field who are interested in designing research and conducting associated research methods. The book provides very useful guidance, supplementary material for graduate students, teachers, and researchers to quickly obtain big pictures on when to use what research design. Further readings on specific research designs are recommended.

Yan Li

University of Maryland at College Park