2003 Royal Statistical Society 0039–0526/03/52235

The Statistician (2003)52, Part 2, pp. 235–255

Book reviews

Books for reviewIf you would like to review a book, and thereby to retain it for your collection, please contactthe Book Reviews Editor, whose details can be found by clicking on ‘books currently available’in the information about The Statistician on the Royal Statistical Society’s Web site:

http://www.rss.org.uk/publications/

Reviews in this issueBedford, T. and Cooke, R. Probabilistic Risk Analysis: Foundations and Methods, p. 236Blossfeld, H.-P. and Rohwer, G. Techniques of Event History Modeling: New Approaches to

Causal Analysis, p. 236Cabrera, J. and McDougall, A. Statistical Consulting, p. 238Chung, K. L. A Course in Probability Theory, p. 239Diggle, P. J., Heagerty, P. J., Liang, K.-Y. and Zeger, S. L. Analysis of Longitudinal Data, p. 239Greenfield, T. (ed.) Research Methods for Postgraduates, p. 240Healy, M. J. R. Matrices for Statistics, p. 241Hsiao, C., Morimune, K. and Powell, J. L. (eds) Nonlinear Statistical Modeling, p. 241McCulloch, C. E. and Searle, S. R. Generalized, Linear, and Mixed Models, p. 242Millard, S. P. and Krause, A. (eds) Applied Statistics in the Pharmaceutical Industry, with Case

Studies in S-Plus, p. 243Morgan, B. J. T. Applied Stochastic Modelling, p. 244Mort, D. Sources of Non-official UK Statistics, p. 244Myers, R. H., Montgomery, D. C. and Vining, G. G. Generalized Linear Models with Applica-

tions in Engineering and the Sciences, p. 245Parmigiani, G. Modeling in Medical Decision Making: a Bayesian Approach, p. 246Pesarin, F. Multivariate Permutation Tests: with Applications in Biostatistics, p. 247Redner, S. A Guide to First-passage Processes, p. 247Serfling, R. J. Approximation Theorems of Mathematical Statistics, p. 247Sheskin, D. The Handbook of Parametric and Nonparametric Statistical Procedures, p. 248Shorack, G. R. Probability for Statisticians, p. 249Sijtsma, K. and Molenaar, I. W. Introduction to Nonparametric Item Response Theory, p. 249Sprott, D. A. Statistical Inference in Science, p. 250Titterington, D. M. and Cox, D. R. (eds) Biometrika: One Hundred Years, p. 251Weaver, J. H. Conquering Statistics: Numbers without the Crunch, p. 252Weichselberger, K.Elementare Grundbegriffe einer AllgemeinerenWahrscheinlichkeitsrechnung,

vol. I, Intervallwahrscheinlichkeit als Umfassendes Konzept, p. 253Wright, D. B. First Steps in Statistics, p. 254

236 Book Reviews

Probabilistic Risk Analysis: Foundationsand MethodsT. Bedford and R. Cooke, 2001Cambridge, Cambridge University Pressxviii + 394 pp., £37.50ISBN 0-521-77320-2

This book has developed from a Master of Sci-ence level course at Delft University of Technol-ogy. Three of the 18 chapters were co-authored byother writers. Although it contains about 60 pagesdescribing distribution theory, and both Bayesianand classical methods of inference, it is aimed atgraduates who already have a good knowledge ofprobability and statistics. Most chapters end with acollection of exercises whose solutions will be madeavailable to bona fide teachers.

After the historical and motivating material, anda suitably compact account of the knowledge thatis assumed, the meat of the book—‘System analysisand quantification’—begins in Chapter Six. Diverseapproaches are suggested for how to make an assess-ment of the chance that some system with inter-acting components will fail. Applications describedinclude reactors, security systems, river barriers,protection from fire risk and computer software.As well as statistics and probability, the specific de-sired background includes competence in Booleanalgebra, but it is plain that a good general mathe-matical training is expected. Throughout the book,the places of precise definitions of different modesand causes of failure, and of logical ways of combin-ing information from several sources, are illustratedwith genuine data.

The appearance and lay-out are very attractive,although I would have preferred that some ratioshad been displayed as a numerator above a denom-inator, rather than make repeated use of ‘/’. Thedifferent symbols used for AND and OR gates aremuch too similar. Typographical errors and minorslips are few in number. Among them, it is Allais towhom the credit for exercise 2.4 belongs (and choiceC1 should offer 1 million dollars); the formula inexercise 2.6 is not the answer to the problem stat-ed; the definition (page 64) of partition is wrong;Fig. 6.6 has all its labels missing; the entry ‘3’ in thenetwork in Fig. 15.1 should be ‘1’. There are manyacronyms but no index for easy reminder of whatthey stand for: this is very irritating.

The second edition of a book on the same broadsubject, Wilson and Crouch (2001), has recentlybeen published. Although Wilson and Crouch(2001) is far more concerned with medical andoccupational risks than the book under review, andis avowedly much less mathematical, it is surprisinghow little ground the two have in common. Neitherbook mentions any work by the authors of the oth-

er: indeed, although both books have extensive bib-liographies, only a handful of items appear in both.This prompts the fears that two schools address-ing the same important area are developing almostindependently, and that the benefits of the moreabstract approach are not widely appreciated.

Often, the main purpose of risk analysis is tosuggest actions to reduce risk. The present bookdescribes how the public’s perception of risk canbe important in galvanizing action, and how theopinions of different experts can be combined. Itnotes the difficulties of finding agreement onobjective measures of the benefits of risk reduction,and the importance of the base rate participationwhen seeking to quantify risk. Without offering patsolutions to difficult practical and ethical issues, itprovides a readable mathematical framework with-in which these serious matters can be discussed. Itcan be recommended both for any specialist courseon this subject and as a good source of practicalapplied probability in general.

ReferenceWilson, R. and Crouch, E. A. C. (2001) Risk–BenefitAnalysis. Cambridge: Harvard University Press.

John HaighUniversity of Sussex

Brighton

Techniques of Event History Modeling:New Approaches to Causal Analysis, 2nd ednH.-P. Blossfeld and G. Rohwer, 2002Hillsdale, Erlbaumx + 310 pp., £32.50ISBN 0-8058-4091-5

This second edition is an attempt by the authors toprovide an updated introductory account of model-ling event history data since Blossfeld and Rohwer(1995). The objectives of this edition are the sameas before:

(a) to demonstrate the usefulness of event his-tory models in uncovering or mapping outpossible causal relationships;

(b) to introduce the reader to the statistical pack-age TDA (‘transition data analysis’), which isused to analyse the examples presented;

(c) to supplement Blossfeld et al. (1989), whichI have not read.

The book comprises 10 chapters and an appen-dix. Chapter 1 opens with a general introductionto event history data, providing examples from thesocial science field. This is followed by a brief outlineof the material that is covered in later chapters. An

Book Reviews 237

illuminating discourse on observation plans (cross-sectional, panel and event history, in that order) andtheir progressing importance in arriving at poten-tial causal interpretations and relationships is nextpresented. The chapter ends by defining statisticalterms such as transition rate, survivor function andcumulative hazard rate and showing their connec-tions to one another.

Chapter 2 introduces the basic terminology forevent history modelling. Concepts such as transi-tions, states, episodes, censoring and multistate andmultiepisode processes are all mentioned. The waythat event history data need to be organized andanalysed in TDA is covered in detail.

Chapter 3 concentrates on nonparametricmethods (life-tables, Kaplan–Meier curves and thelog-rank test) used for describing and comparingsurvival curves for the special case of single-episodedata (possibly with competing risks). I was a lit-tle disappointed that no explicit mention was maderegarding the danger of overinterpreting survivalcurves. It would have been useful to have a para-graph advising the reader to be careful when inter-preting a survival curve, especially when examiningthe right-hand side of the survival curve or lookingat the fine details of the curve, as this informationcan be unreliable and inaccurate. (The overall sur-vival pattern is more reliable!)

Also, I disagree with the authors when they sug-gest that one method of comparing survivor func-tions to determine whether they are statisticallysignificantly different is to calculate ‘confidence in-tervals for each of the survivor functions and thencheck if they overlap or not’. I would never advo-cate such an approach for formal assessment, butinstead I would recommend constructing an appro-priate test statistic (i.e. their second suggested meth-od), such as the log-rank statistic. Besides, is not theconfidence band for the difference in survivor func-tions (in the case of two curves) more appropriatethan separate confidence bands for each of the sur-vivor curves? Finally, no mention was made aboutthe potential insensitivity of the log-rank test forcurves that cross.

Exponential transition rate models, piecewiseconstant exponential models and exponential mod-els with time-dependent covariates are introducedin Chapters 4, 5 and 6 respectively, with each ofthese chapters naturally building on and extendingthe previous one. The material that is covered inthese chapters is interesting and, I believe, essentialfor appreciating and understanding the more com-plex event history models that are used regularly inthe literature. Additionally, the examples presentedthere illustrate quite clearly the flexibility of thesemodels to cope with time constant and time-vary-ing covariates, multiple destinations (i.e. competing

risks models) and multiple episodes data, and fur-thermore demonstrate the versatility of the TDApackage. My only qualm was that the authors couldand should have explicitly defined the terms exo-genous and endogenous, rather than assuming thatthe reader (though probably a social scientist andthus already familiar with these terms) knew theirmeanings.

Chapter 7 discusses parametric models (such asthe Weibull, the Gompertz, the log-logistic, the log-normal and the Sickle models) for duration data,which unfortunately I found rather repetitive. Itcould have been written more concisely. In Chap-ter 8, two graphical approaches to assessing theparametric assumption for the models described inChapter 7 are discussed. The first is based on trans-formations of survivor functions (e.g. complemen-tary log-survival curves) and the second is based onresiduals.

Chapter 9 describes the very important Cox semi-parametric approach to modelling event historydata. Topics such as stratification and assessing theproportional hazards assumption (both graphicallyand analytically) are addressed. However, it wouldhave been useful for the authors to discuss morefully the extensions of the Cox model for survivalanalysis data to data sets with multiple events ofthe same type or different types, i.e. I would haveliked to see the authors address more fully the is-sues regarding extending the Cox proportional haz-ards model to models that take into account theintraunit correlation. Discussions of the frailty andmarginal approaches (Therneau and Grambsch,2000; Andersen and Gill, 1982; Wei et al., 1989;Prentice et al., 1981), robust variance–covariancematrices and multiple timescales would have beenappreciated.

The final chapter concludes the book by address-ing issues to do with model (mis)specification. Theissue of unobserved heterogeneity (due to omittedcovariate information) and the topic of fitting para-metric mixture models to account for this unex-plained heterogeneity are critically covered in themajority of this chapter. In the discussion sectionother aspects of model specification (e.g. definingthe state space) are also briefly summarized.Appendix A provides basic information on the TDApackage.

Modelling of event history data is a very activearea of research in medical and social science. Thisbook is written for the social scientist (reflecting theauthors’ area of research), but all the ideas that areintroduced in it can easily be translated to otherareas of research. Overall, this book appears to haveaccomplished, at least, the first two of its aims. Thethird aim of being a supplement to Blossfeld et al.(1989) is difficult for me to judge, as I have not read

238 Book Reviews

it, and therefore the details (technical or practical)that I found lacking in this second edition may haveappeared there. I would recommend this book tosocial science researchers who are interested in eventhistory modelling and those researchers who are in-terested in using the TDA package. The topics andexamples that are covered would be accessible andrelevant to this readership.

ReferencesAndersen, P. K. and Gill, R. D. (1982) Cox’s regression

model for counting processes: a large sample study.Ann. Statist., 10, 1100–1120.

Blossfeld, H.-P., Hamerle, A. and Mayer, K. U. (1989)Event History Analysis. Hillsdale: Erlbaum.

Blossfeld, H.-P. and Rohwer, G. (1995) Techniques ofEvent History Modelling. Hillsdale: Erlbaum.

Prentice, R. L., Williams, B. J. and Petersen, A. V.(1981) On the regression analysis of multivariate fail-ure time data. Biometrika, 68, 373–379.

Therneau, T. M. and Grambsch, P. M. (2000)ModelingSurvival Data: extending the Cox Model. New York:Springer.

Wei, L. J., Lin, D. Y. and Weissfeld, L. (1989) Regressionanalysis of multivariate incomplete failure time databy modelling marginal distributions. J. Am. Statist.Ass., 84, 1065–1073.

Brian D. M. TomMedical Research Council Biostatistics Unit

Cambridge

Statistical ConsultingJ. Cabrera and A. McDougall, 2002New York, Springerxii + 390 pp., £62.50ISBN 0-387-98863-7

There now seems to be a burgeoning little indus-try of statistical consulting texts; the authors of thisbook cite 12 other references on the subject. Thisbook uses two approaches to the subject. In partone a broad approach is taken, putting statisticalconsulting in its historical and contemporary con-text, before looking at methodological issues andthe life-cycle of a project. This sets the scene for parttwo, which consists of 20 case-studies set into threegroups. Each group represents a level of complexityof analysis and design. They start with basic χ2- andt-tests, analyses of variance and regression mod-els. They then move on to logistic regression, timeseries and factorial designs. In the final group, mixedeffects models, multivariate exploratory techniques,recursive partitioning and classification and regres-sion trees are covered. There are appendices con-taining an outline of a statistical consulting course,fairly solid introductions to the SAS and S-PLUSprograms and technical descriptions of probabilitydistributions, statistical tests and power calcula-tions.

This book covers much ground and is clearlyaimed at maintaining undergraduates’ awareness ofhow to apply the techniques that they are learn-ing. More than anything, it should encourage themto think flexibly rather than to try to design everyproject so that it is another chance to apply theirfavourite statistical test. The breadth of areas andtechniques covered can feel a little overwhelming,but then this is a reflection of how real world sta-tistical consulting can feel. Achieving this breadthmust represent a large amount of work by the au-thors. Given this breadth it is a book that reallyrequires a teacher or lecturer to guide the studentthrough it. The outline course at the back of thebook gives a useful and realistic plan to do this. Byassigning each of the three groups of cases-studies toan undergraduate year it is fairly easy to see how thisbook could see a student through their undergradu-ate course. This would achieve the highly desirablegoal of helping to keep the student’s mind clearlyfocused with regard to the applied, coal-face, end ofstatistics. At the same time the concise descriptionsof statistical techniques should provide an effectivereinforcement of what is being taught on the restof the course. The structure could just as easily beapplied to a three-term post-graduate course.

One of the book’s greatest strengths is its chap-ter on communication; although whole books havebeen written about this subject, e.g. Derr (2000), thissuccinct little chapter gives one of the best intro-ductions to report writing and graphics that I havecome across. I hesitate to raise the issues of gram-mar and style, partly because my own will probablybe scrutinized in the light of my comments. How-ever, there are just a couple of pages of sensibleadvice that many undergraduates and new gradu-ates could profit from following. On the subject ofgraphics, again following the advice of the two orthree pages may lead to more students producinggraphs that not only look impressive but also areproperly annotated and so can be understood.

With its wealth of Web sites, the availability of da-ta sets and broad coverage this would make a goodrecommended text-book for a graduate or post-graduate degree course with an emphasis on appliedstatistics. Its expense (unless the publisher intendsto produce a paperback version) may be justified ifit proves to be the student’s companion throughoutthe course.

ReferenceDerr, J. (2000) Statistical Consulting: a Guide to Effec-tive Communication. Pacific Grove: Duxbury.

James TigheOxleas National Health Service Trust

London

Book Reviews 239

A Course in Probability Theory, 3rd ednK. L. Chung, 2001San Diego, Academic Pressxviii + 420 pp., £39.95ISBN 0-12-174151-6

The first edition of Chung’s classicCourse in Proba-bility Theory appeared in 1968, the same year as thethird edition of Feller’s Introduction to ProbabilityTheory and Its Applications. Both books have beengreatly influential, but in different ways. WhereasFeller stressed both theory and applications,Chung’s intention was to write a mathematics book.He says,

‘Although many notions of probability theoryarise from concrete models in applied sciences,recalling such familiar objects as coins and dice,genes and particles, a basic mathematical text(as this pretends to be) can no longer indulge indiverse applications, just as nowadays a coursein real variables cannot delve into the vibrationsof strings or the conduction of heat’.

Some idea of the coverage of the book can begleaned from the list of contents: 1, ‘Distributionfunction’; 2, ‘Measure theory’; 3, ‘Random variable,expectation, independence’; 4, ‘Convergence con-cepts’; 5, ‘Law of large numbers, random series’;6, ‘Characteristic function’; 7, ‘Central limit the-orem and its ramifications’; 8, ‘Random walk’; 9,‘Conditioning, Markov property, martingale’; ‘Sup-plement on measure and integral’ (new); ‘Gener-al bibliography’; ‘Index’. Despite the relationshipbetween random walks and stochastic processes,there is no mention of birth–death or branchingprocesses. Although martingales are regarded ‘asan essential tool’, the serious study of Markov pro-cesses, etc., is deferred to a subsequent course onstochastic processes.

The two earlier editions of the book presupposeda certain mathematical maturity of the student.Professor Chung has found, however, that manystudents from departments such as statistics, opera-tions research and electrical engineering have need-ed to take a prerequisite course on abstract measureand integral theory. The defining addition in thisnew edition is a largely self-contained supplementon these topics.

Chung first taught a course based on this book,entitled ‘Advanced probability’, in 1966 at StanfordUniversity. The back cover says,

‘Since its publication by Academic Press [nearly35 years ago], tens of thousands of students havetaken a probability course using this classic text-book . . . . It has been used successfully at over75 universities since its initial publication.’

One reason for its long-standing popularity is itsflexibility. A short course built around Chapters 2–4 with selections from Chapters 5 and 6 and theearly parts of Chapter 9 is one suggestion made bythe author. Another suggestion, for mature math-ematicians, is to ‘begin with Chapter 3, go at onceto Chapter 5 with a few glances at Chapter 4, skimthrough Chapter 6, and take up the remaining chap-ters seriously’.

If you or your department already have an earlieredition of this book, then consider buying a bookon measure theory instead of this new edition. Ifyou do not already have access to Chung’s Coursein Probability Theory, then try to ensure that thereis a reference copy in your departmental library.

Freda KempUniversity of St Andrews

Analysis of Longitudinal Data, 2nd ednP. J. Diggle, P. J. Heagerty, K.-Y. Liangand S. L. Zeger, 2002Oxford, Oxford University Pressxvi + 380 pp., £40.00ISBN 0-19-852484-6

‘Longitudinal studies are rare, other than amongchildren, and it is wrong to think that a cross-sectional view . . . can be a substitute, at leastover a long period . . . ’ (Rosenbaum, 1988).

This is a timely update of the authors’ first bookon the analysis of longitudinal data. The aim ofthis book is to describe statistical models for theanalysis of longitudinal data and to update the cur-rent literature in this area. A recurring theme is thecomparison of longitudinal data with that collectedcross-sectionally. The statistical level of understand-ing is that of a post-graduate student in statistics.A strong emphasis is on applications for both thebiological and the health care sciences. Indeed, mostof the data sets are in the public domain.

The book is organized into 14 chapters plus anappendix detailing statistical concepts. The firstthree chapters give an overview of the subject.Indeed, the first sentence states that the definingcharacteristic of longitudinal data is that measure-ments are made repeatedly over time. This is in con-trast with cross-sectional data where observationsare measured once. The authors make an interestingstatement saying that longitudinal data can be col-lected either prospectively (examining subjects overtime) or retrospectively (via historical records). Myexperience is of the former. Longitudinal data re-quire special statistical models as it is assumed thatobservations that are made over time are correlated.

What I tend to do when faced with repeated mea-

240 Book Reviews

surements is to collapse the data into one or twosummary measures according to Matthews et al.(1990). This approach is commented on briefly inChapter 1. I was surprised that there was no refer-ence to Matthews et al. (1990), as it is so well known.I guess that it is a function of how the approachto longitudinal data analysis has changed over thelast decade. Matthews et al. (1990) argued for thesimplicity of summary measures, an approach thathas my sympathy. However, the analysis of repeatedmeasurements has moved forwards since then andit is this that I now focus on.

Chapter 2 discusses design considerations withparticular reference to sample size calculations. Forcross-sectional studies five characteristics are need-ed to calculate sample size. These are the type I errorrate, clinically worthwhile difference, type II errorrate, measurement variation and drop-out rate. Forlongitudinal data two other things should be takeninto consideration, namely the number of repeatedmeasurements per person (this they say may be lim-ited by study costs) and the degree of correlationbetween the repeated measures. The authors sug-gest that estimates of correlation may be availablefrom the literature. I doubt this and imagine myselfhaving to resort to guesswork. Examples of samplesize calculations are given for both continuous andbinary response data (assuming a type I error of 5%and type II error of 20%).

Chapter 3 discusses how to explore longitudinaldata graphically. This is a natural starting-point forany study (longitudinal or not) and I found it a mostuseful reference. Tukey (1977) brought this back in-to fashion. The next few chapters discuss the generallinear model for longitudinal data. One of the prob-lems highlighted by the authors concerns sources ofrandom variation. Three such sources are outlined,namely random effects, serial correlation and mea-surement error. The authors discuss different mod-els for taking into account the variations outlined,including combinations of all three. The followingchapters discuss special cases of longitudinal dataand include binary response data, random-effectsmodels and methods for categorical data. All thechapters give data examples as well as the detailedtheoretical treatise. There is more on sample size es-timation taking into account more than two groups.

Chapter 13 discusses the problems of drop-outs.This must be more a problem in longitudinal datawhen compared with a cross-sectional study. Theymake a nice distinction between purely missing dataand data measured intermittently. The latter posemore problems statistically as a wider variety ofnon-response patterns need to be considered. A sim-ple method to handle drop-outs is to analyse onlycomplete data sets (this could be wasteful ofdata). An alternative method is to take the last ob-

servation forwards, which is used routinely in thepharmaceutical industry. If patients show improve-ment over time, this technique has the advantage ofa conservative effect of treatment. This is a strongargument in its favour. However, the authors donot advocate this method of handling missing data,though they fail to justify their case. They prefer,instead, a random-effects model, arguing that a pa-tient’s pattern of responses is likely to depend onmany characteristics (observed and not observed).The unobserved characteristics are included in anymodel as random effects and modelled as such. Forme this is the best chapter of the whole book. Itseems that there is much research to be done in thisarea. Missing values are not so much a problem ifyou adopt the approach of Matthews et al. (1990)of summary measures.

Is there anything missing? Bootstrapping is notcovered though I expect that this is a novel fieldthough I did note some correspondence on ALL-STAT recently re bootstrapping. Perhaps a historyof longitudinal measurements could have been con-sidered. There is also scant reference to statisticalsoftware. The authors argue that the software needsto catch up with the theory first and I accept this.

It is a long time since I undertook my post-gradu-ate course in statistics. At the time methods for han-dling longitudinal data were in their infancy. I wish Ihad had this book then. It is excellent in all respects.What I need now to use the methods effectively isan appropriate training course. I recommend thisbook without reservation.

ReferencesMatthews, J. N. S., Altman, D. G., Campbell, M. J.

and Royston, P. (1990) Analysis of serial measure-ments in medical research.Br.Med. J., 300, 230–235.

Rosenbaum, S. (1988) 100 years of heights and weights.J. R. Statist. Soc. A, 151, 276–309.

Tukey, J. W. (1977) Exploratory Data Analysis. Read-ing: Addison–Wesley.

Alan S. RigbyUniversity of Sheffield

Research Methods for Postgraduates, 2nd ednT. Greenfield (ed.), 2002London, Arnoldxiv + 270 pp., £29.95ISBN 0-340-80656-7

This soft cover book consists of 42 chapters div-ided into 10 parts. There are 28 authors, most ofwhom are from the UK, but two are from Australiaand one is from the USA. The diverse backgroundsof the authors, and the editor’s presentation style,facilitate a light, refreshing, yet lively flavour to this

Book Reviews 241

serious subject. The book aims to provide post-graduates with a concise, but thorough, referencetext for research methods. Chapters on creativity,use of the Internet and software packages are newto this edition.

An introduction forms part I, in which researchplanning, time management, documentation, wordprocessing tips and ethics are discussed. Part IIcovers writing research proposals, funding andother support for research. ‘Tools of research’, partIII, presents topics on information technology, soft-ware, library services and the Internet. Part IV dis-cusses creativity tools, including creative problemsolving, software and Web sites for creativity. PartV, ‘Research types’, addresses specific types ofresearch, such as randomized trials, laboratory andindustrial experiments, agricultural experimentsand survey research.

‘Measurement’, the largest section, is the topicof part VI, and ‘Analysis’ makes up part VII. ‘Spe-cial tools’, part VIII, first provides an introductionto mathematical models and then discusses the top-ics of deterministic models, stochastic models andsimulation, and, lastly, optimization. Part IX, ‘Pre-sentation’, gives valuable tips on writing, graphicdisplay, oral presentation and Internet home pageconstruction. The subjects of part X are protect-ing and exploiting technology, intellectual propertyrights and career opportunities. I feel that part V,‘Research types’, is the section that could be mostexpanded, to enhance the next edition.

The main strength of the book is the extent towhich it provides a vast interdisciplinary coverageof topics that compose the elements of research. It isbacked by an abundance of references for focuseddetailed study of specific topics. The emphasis onthe Internet and software are additional strengths.A minor weakness is that part V is a little succinct.It could be lengthened, so that the discussion in-cludes additional types of research. The index con-sists of only four pages, but it is adequate. Overall,I am impressed by the richness of this book as a re-source for post-graduate research, and I consider itan essential guide for post-graduates. The authors’aims have been achieved. I highly recommend it foruniversity library purchase.

Mark A. BestEastview

Matrices for Statistics, 2nd ednM. J. R. Healy, 2000Oxford, Clarendonx + 148 pp., £22.99ISBN 0-19-850702-X

Michael Healy’s Matrices for Statistics has been inprint since 1986. This greatly rewritten new edition,

like its predecessor, aims to give users of statisticalmethods involving matrices an understanding of theunderlying matrix theory while avoiding aspects ofthe theory that they are unlikely to meet.

Chapter 1 is introductory. A useful feature is theindex of terminology with section references withwhich it ends. Determinants, inverse matrices andthe concepts of linear dependence and rank are thetopics in Chapters 2, 3 and 4 respectively. Simulta-neous equations and generalized inverses are stud-ied in the context of least squares problems inChapter 5. Chapters 6 and 7 move on to linear spac-es and to quadratic forms and eigensystems. Thefinal chapter is new. It contains a miscellany of top-ics that have been suggested by readers of the firstedition; these include direct sums and products,vectorizing, matrix calculus, matrices with complexelements and quadratic forms in normal variates.

There are two appendices, on matrix calculation(including precision of results) and on matrix algo-rithms. The index is short yet adequate.

This new edition is deliberately less concise thanthe earlier one. Some material that was formerlygiven in the form of exercises for the reader is nowdiscussed in the text. There remain many student ex-amples; although there is no formal ‘Answers’ sec-tion in the book, many of the examples lead thereader towards their solutions.

This is a widely used text, suitable for statisti-cians, life scientists, behavioural scientists and en-gineers, that has been brought up to date and mademore easy to read for non-mathematicians.

Freda KempUniversity of St Andrews

Nonlinear Statistical ModelingC. Hsiao, K. Morimune and J. L. Powell(eds), 2001Cambridge, Cambridge University Pressxviii + 452 pp., £65.00ISBN 0-521-66246-X

The Cambridge series ‘International symposia ineconomic theory and econometrics’ aims

‘to provide refereed journal-quality collectionsof research chapters of unusual importance inareas of currently highly visible activity withinthe economic profession’.

This is the 13th volume in the series. It is dedicated toTakeshi Amemiya and contains 16 papers inspiredby his work on topics as diverse as dependent vari-ables, discrete choice, non-linear estimation, paneldata and simultaneous equation models.

242 Book Reviews

The book begins with a unification of the treat-ment effect literature and the latent variable litera-ture by J. J. Heckman and E. J. Vytlacil. Chapter 2,by N. E. Savin and A. H. Würtz, compares the prop-erties of hypothesis tests for limited dependent vari-able models using

(a) critical values based on first-order asymptot-ic approximations and

(b) critical values calculated by bootstrapping.

Simulation estimation of sample selection modelsis L.-F. Lee’s topic in Chapter 3. A new approachto the attrition problem in longitudinal studies ispresented by K. Ryu in Chapter 4. The next threepapers, by F. Goto, by J. L. Powell, and by Y.Nishiyama and P. M. Robinson, are all concernedwith semiparametric estimation problems.

In Chapter 8, C. F. Manski studies bounds onrelative risks and attributable risks by using aux-iliary distributional information. The selection ofregressors in a regression model is a long-stand-ing research topic; D. McFadden’s contribution tothis book is to show that prescreened least squar-es is equivalent to direct estimation by non-linearleast squares. T. E. MaCurdy presents a new es-timation method for regression and simultaneousequations that uses the second and higher momentsof the disturbances. In Chapter 11, T. W. Andersonand L. You prove that the existence of the secondmoment is sufficient for weak convergence of thestandardized spectral distribution when the processconsists of independent and identically distributedvariables.

Unit root tests are studied by H. Lütkepohl,C. Müller and P. Saikkonen and by K. Morimuneand M. Nakagawa in Chapters 12 and 13. A sim-ultaneous switching autoregressive model for theanalysis of financial time series data is developed asa generalization of the Tobit model by N. Kunitomoand S. Sato. The last two chapters, by T. Lancasterand by S. J. Yhee, J. B. Nugent and C. Hsiao, dealwith problems arising in the analysis of panel data.

The book ends with Takeshi Amemiya’s curricu-lum vitae and an index. These papers form a worthytribute to him on the occasion of his 65th birthday.

Freda KempUniversity of St Andrews

Generalized, Linear, and Mixed ModelsC. E. McCulloch and S. R. Searle, 2001New York, Wileyxxii + 326 pp., £70.50ISBN 0-471-19364-X

I very much enjoyed reading this excellent book.The book is written for graduate statistical and

mathematical students, and for practising statis-ticians; it can be very useful for statisticians in dif-ferent environments and with different levels ofexperience.

In Chapter 1, the basic ideas of fixed and ran-dom factors, and mixed models are introduced. Itgives a brief discussion and definition of generalizedmodels, the generalized linear model (GLM) andthe generalized linear mixed model (GLMM). If allparameters are considered as fixed then the model isa GLM. If the model includes fixed and random ef-fects then the model is a GLMM. In addition, a fewexamples from clinical trials are presented to give abetter understanding of different models with fixedor random effects. There is also a brief descriptionof the analysis for such models.

Chapters 2 and 3 introduce all the main ideasin the remainder of the book, using the two sim-ple contexts of one-way classification and linear re-gression. Chapter 2 deals with data which are eithernormally or Bernoulli distributed. Chapter 3 coverssimple regression, i.e. regression with a single pre-dictor. For a simple linear regression, the restrictiveassumptions that y is a linear function of a predic-tor x is only a crude approximation or the first stepin a more detailed analysis. Sometimes, it is for onlya short interval of time that y is a linear function ofx; over the entire range of time, the relationship canbe non-linear. In some cases, we must transform yand/or x before the linearity assumptions are meteven approximately. A different approach would beto model some known function of the mean of y aslinear in x. Maximum likelihood (ML), as an esti-mating method, and likelihood ratio techniques areintroduced for both balanced and unbalanced data.The authors suggest that these first three chapters,with a minimum of emphasis on generality of re-sults and notation, together with some additionalmaterial, can be used for a one-semester Master’scourse.

Chapter 4 describes the general ideas of linearmodels (LMs). First, the general model and its no-tation are introduced; then an LM for fixed effectsis discussed. The maximum likelihood method isused to estimate the vector slope β at the same timeas the variance. Using this method, there are manysolutions, but none of them is unbiased for β. Theimpracticality of that solution for β is avoided withthe introduction of an estimable function of β. TheML estimator of the estimable function is unbiasedand based on the sufficient statistics; it is a uniformminimum variance unbiased estimator. Examplesof one-way and two-way classifications are present-ed with the following linear hypothesis tests: likeli-hood ratios, t-tests and confidence intervals.

In Chapter 5, ‘Generalized linear models(GLMs)’, a brief discussion that GLMs can han-

Book Reviews 243

dle probit or logistics regression, Poisson regression,log-linear models for contingency tables, variancecomponents estimation from analysis-of-variancemean squares and many other similar problems ispresented. The building of GLMs is considered withrespect to the following three aspects: the distribu-tion of data, the function of the mean that will bemodelled as linear in the predictors and the predic-tors. A review of tests of hypothesis such as likeli-hood ratio tests, Wald tests and associated confi-dence intervals is presented. Quasi-likelihood as aninferential method which works as well or almostas well as ML, but without having to make specificdistributional assumptions, is discussed at the endof this chapter.

Chapter 6 is an extension of Chapter 4. Thestarting model in Chapter 4 is an LM with fixedeffects whereas in Chapter 6 the random effect isadded inside the model. This model is called a lin-ear mixed model (LMM). A brief description of thegeneral nature of longitudinal data in connectionwith LMMs is given. The estimation of fixed ef-fects for known and for unknown variance (matrix)is presented and discussed; next the prediction ofrandom effects for known and unknown variance isshown. The analysis-of-variance estimation of vari-ance components and restricted ML for balancedand unbalanced data are presented at the end ofthis chapter.

Chapter 7 gives an extension of the longitudi-nal data modelling that is introduced in Chapter 6.The following models for both balanced and unbal-anced data are examined: models for uncorrelat-ed subjects; models that are uncorrelated betweenand within subjects; models that are uncorrelatedbetween and autocorrelated within subjects; mod-els that are correlated between but not within sub-jects. A generalized estimating equation model ispresented at the end of this chapter.

The use of random effects is not restricted toLMMs. How should the random effects be incorpo-rated in non-linear models? To answer this question,the GLMM is introduced in Chapter 8. This chap-ter explores the consequences of adding randomfactors and studies estimation by ML. The follow-ing topics are covered: marginal versus conditionalmodels; other methods of estimation such as gen-eralized estimating equations; penalized quasi-likelihood; conditional likelihood and tests ofhypothesis such as likelihood ratio tests, asymptoticvariances, Wald tests and score tests.

Chapter 9 deals with three different but interre-lated methods of prediction: best prediction, bestlinear prediction and LMM prediction (best linearunbiased prediction). Because these methods do notall require the same assumptions, the assumptionsrequired are discussed separately.

In Chapter 10, the authors identify some of thecommon methods that are used for likelihood cal-culation and maximization: the EM algorithm forML and for restricted ML; the Newton–Raphsonmethod for LMMs; numerical quadrature (Gauss–Hermite quadrature and likelihood calculations);Markov chain Monte Carlo algorithms; stochas-tic approximation algorithms for GLMMs. In ad-dition, they mention and give references to somecurrent research topics.

Chapter 11 discusses the topic of non-linearmixed models. The GLMMs are a proper subsetof non-linear mixed models. Two examples (agri-culture and pharmacokinetic models) are presentedand discussed.

I would certainly recommend this book. It is defi-nitely worth havingGeneralized ,Linear, andMixedModels as a part of your library.

Lada MitchellNovartis Pharma

Basel

Applied Statistics in the Pharmaceutical Industry,with Case Studies in S-PlusS. P. Millard and A. Krause (eds), 2001New York, Springerxvi + 514 pp., £79.95ISBN 0-387-98814-9

This book aims to give a general guide to statisticalmethods that are used in the pharmaceutical indus-try, and to show how to use the S-PLUS softwarepackage to implement these statistical methods.

There are 19 chapters which are organized toreflect the natural sequence of drug development:preclinical studies, early studies in humans, threephases of clinical trials (phases II, III and IV) andmanufacturing or production. With 32 contributorsto the book, from a wide variety of backgrounds(North American and European researchers fromacademic institutions and industry) it is not sur-prising that each chapter has a very different nar-rative. Thankfully, however, most chapters have acommon structure that helps to orientate the read-er. Each chapter contains an introduction to thetopic, including the relevant statistical theory andregulatory considerations, followed by workedexamples that illustrate the analysis and interpre-tation of each statistical problem. There is also anappendix to each chapter that describes all relevantS-PLUS programming code.

Overall, the book meets its aim, covering a widerange of statistical methodology and dealing withmany situations that are encountered in pharma-ceutical statistics. The authors should be congratu-

244 Book Reviews

lated for showing how S-PLUS can be used in eachsituation although some readers may not like thereliance on user-written functions to do this. Also,there are some situations that are either not ide-ally suited to S-PLUS (Gibbs sampling in samplesize re-estimation) or rely on output from other sta-tistical software (use of NONMEM output in anexample of Monte Carlo simulation), or cannot cur-rently be implemented in S-PLUS (the continualreassessment method, a Bayesian-based dose esca-lation rule). Although most areas are covered insufficient statistical detail, I would have expectedbinary and survival data to be covered in thepower and sample size section, which is restrictedto the non-central t-distribution. Nevertheless, thestrength of the book is in the detail of the examplesthat illustrate the power of S-PLUS in interactiveanalysis and its ability to display graphical resultsin innovative and revealing ways. I particularly likedthe examples showing the use of multipanel graphsand contour plots. Therefore, the book succeeds intempting this died in the wool SAS user, and nov-ice to S-PLUS, to try S-PLUS in more situations,especially given the useful Web site, which covers allexamples in the book and allows users to downloadS-PLUS programming code easily.

I would recommend this book to any pharma-ceutical statistician who wishes to explore alterna-tive software for interactive data analysis andvisualization. It may also be useful as a teachingtext for potential medical statisticians because ofthe numerous real life worked examples and theirsoftware solutions.

Nigel BrayshawDeal

Applied Stochastic ModellingB. J. T. Morgan, 2001London, Arnoldxxii + 242 pp., £19.99ISBN 0-340-74041-8

Modelling is fun to do. I hope that we all know thesatisfaction in finding a suitable model to explainthe patterns in an interesting set of data. In appro-priate places, the model itself can shed light on theunderlying mechanisms which give rise to the data.

The author’s enthusiasm for his subject shinesthrough this book. There are plenty of interestingexample data sets, many from the field of wildlifestudies and ecology, with others from many fieldsand an intriguing example of inflorescence patternsof strawberry plants, which is a topic I had nevergiven any thought to before. Many of these exam-ples have arisen from the author’s own consulting

activities, and the impetus for the book seems tocome from these experiences and from courses runat the University of Kent and at Pfizer.

The book covers much ground in quite a shortspace. The full table of contents can easily be foundon the Web, so I shall not give it here. The mainthemes are the use of likelihood methods and simu-lation. There is a very elegant presentation of the useof profile likelihoods and likelihood ratios to definemultiparameter confidence regions. The simulationtheme runs through many major areas, includingrandomization tests, bootstrapping, the EM algo-rithm and Bayesian analysis.

Data sets and code for MATLAB® and S-PLUSare supplied on the book’s Web page. Each chapterhas a good set of exercises.

In conclusion, I like this book and strongly rec-ommend it. It covers many of my favourite topics.In another life, I would have liked to have writtenit, but Professor Morgan has made a better job ofit than I would have done.

Tim AutonProtherics

Macclesfield

Sources of Non-official UK Statistics, 5th ednD. Mort, 2002Aldershot, Gowerxii + 358 pp., £67.50ISBN 0-566-08449-X

This fifth edition in seven years confirms the con-tinuing search and demand for statistics of all kinds.Minimal information of almost 900 sources fromover 400 organizations carries with it telephone con-tact numbers, Web site addresses and indications ofwhether some or all of the information is free. Thestructural format of the information and the com-prehensive index assist the user to identify, clearlyand quickly, possible sources. However, unlike theguide that is produced for National Statistics, theinformation is limited and rarely carries the samplesize details of surveys.

Delving into the detail of the index revealed afew errors both of classification and of referencing.It was surprising to find only one reference to Walesthough information about Wales can be found fromthe sources indexed under ‘Region’.

This book will continue to be a valuable pointerboth to data sources and to organizations. Marketresearchers will find it a handy reference to be keptclose to hand. Libraries should stock this book forstudents who are always on the lookout for odd sta-tistical series. The addition of a compact disc con-taining the current information, with a means of

Book Reviews 245

updating the information between editions, wouldbe a great advantage for serious researchers.

Ed Swires-HennessyLocal Government Data Unit—Wales

Cardiff

Generalized Linear Models with Applicationsin Engineering and the SciencesR. H. Myers, D. C. Montgomery andG. G. Vining, 2002New York, Wileyxiv + 342 pp., £66.50ISBN 0-471-35573-9

This book aims to present an introductory treat-ment of generalized linear models (GLMs), for stu-dents who already know the basics of regression,model fitting and statistical inference procedures.The authors’ stated aim is to make the book acces-sible to a wide audience, including engineers andscientists as well as statisticians, and to present boththe theory and its application. In accordance withthis aim, the book includes a wide range of illustra-tive examples, many end-of-chapter exercises basedon real data and illustrations of the use of popularstatistics software (MINITAB, SAS and S-PLUS)to fit the models that are discussed.

The detailed contents of the book are, perhaps,not exactly what we would expect from the title.This is not in itself a bad thing, but potential read-ers and users should be aware of what they will find.After a brief introductory chapter, there is an exten-sive chapter on linear regression models, and an-other on non-linear regression. As in the rest of thebook, this material is written with clarity and enthu-siasm, and with a good balance between theory andapplication. Any comprehensive book on GLMsmust contain some material on what one might call‘non-generalized’ linear models, which are after allspecial cases of GLMs and which provide crucialbackground for the models that are discussed later;however, these two chapters make up almost a thirdof this book.

The middle third of the book, roughly, containsthe central core material on GLMs. This begins witha chapter on logistic and Poisson regression: mod-els, approaches to inference, ways of dealing withoverdispersion and many interesting and reward-ing examples. After that, the authors move on tothe general definition of GLMs, illustrated princi-pally by examples using the gamma distribution.

The final third of the book deals with moreextensions and further applications. There is achapter on generalized estimating equations, withexamples of their use in longitudinal studies and

in split-plot experiments. The final chapter coversa selection of more advanced topics, including as-pects of experimental design, simulation studies ofthe properties of inference procedures (includingthe situation where the link function is misspecified)and generalized additive models.

This is a book with both strengths and weak-nesses. On the positive side, the authors achieve awriting style that is at once clear and enthusiastic.Their use of examples shows that these techniquesand ideas have real practical value. Yet theory is notneglected; the balance between theory and appli-cation seems just right for the intended audience ofgraduate level statisticians, scientists and engineers,and on the European side of the Atlantic it wouldperhaps be appropriate for some advanced under-graduate courses as well.

On the negative side, there were some omissionsthat rather surprised me. I rather expected to seesomething on ordinal response data, and/or on log-linear models. These are both areas where theinterpretation of GLM analyses can be tricky. (How-ever, no book in this wide and still developingarea could cover everything.) I was also rather dis-appointed with the way that the computer exampleswere used and presented. The book is certainly notfree of misprints, and there are several in the data ta-bles. Any reader wanting to work through the exam-ple analyses for themselves would need to key in thedata (because they do not seem to be available on alinked Web site), work out in some cases where themisprints are and work out for themselves actual-ly how to run the analyses in SAS or S-PLUS. Thebook’s publicity materials and preface both prom-ise rather more than the book actually delivers interms of computer guidance and illustration. For in-stance Chapter 5 (on the general family of GLMs) issaid to contain ‘several illustrations . . . employingboth SAS PROC GENMOD and S-PLUS’, whilein fact all the numerical results come from SAS,and the use of S-PLUS seems to be limited to pro-ducing various diagnostic plots. (Indeed S-PLUS isnever explicitly mentioned in the chapter.) Gener-ally, apart from a brief comparison of SAS PROCLOGISTIC and PROC GENMOD in logistic regres-sion, there is no mention of the strengths and weak-nesses of different statistical packages for the an-alyses described.

Finally, the book shows some inconsistencies indetail. For example, the very last section of the chap-ter on logistic and Poisson regression (Chapter 4)introduces the idea of classification (CLASS) vari-ables in SAS, by referring back to a previous exam-ple where they could have been used but were not. Infact, the SAS output in that example makes it clearthat a CLASS variable was used; indeed the out-put might make little sense to a reader who did not

246 Book Reviews

already know what such a creature was. (In pass-ing, I should note that the authors clearly do nottake the view that marginality constraints in fac-torial models are essential.)

In summary, this is a useful and interesting book,with some flaws. It provides a valuable reference andpractical advice, and could provide support for ataught course; but a reader who is new to the sub-ject, working through the book on their own, mighthave some difficulties. I recommend it for librarypurchase.

Kevin McConwayThe Open University

Milton Keynes

Modeling in Medical Decision Making:a Bayesian ApproachG. Parmigiani, 2002Chichester, Wileyxiv + 268 pp., £45.00ISBN 0-471-98608-9

Published in Wiley’s ‘Statistics in practice’ seriesthis book is primarily aimed at students and prac-titioners of biostatistics. For practitioners who areinvolved in medical decision-making, this bookprovides a glimpse of the challenges in the use ofquantitative modelling in decision-making. Forstatisticians, this book offers challenging statis-tical problems encountered in medical decision-making.

The book has two parts: part I, ‘Methods’ andpart II, ‘Case studies’. Part I has three chapters. Thefirst chapter is on ‘Inference’, wherein fundamen-tals of Bayesian inference are discussed with exam-ples. The topics discussed here include conditionalprobability, specificity, sensitivity, Bayes factors,odds, nomograms, conditional independence, pri-or and posterior probabilities and predictive values.Examples from medical diagnosis, genetic counsel-ling and chronic disease modelling are used as illus-trations for some of the methods introduced. Thesecond chapter is ‘Decision making’. This chaptercontains fundamentals of Bayesian decision theoryand foundations of expected utility theory. Amongthe topics that are discussed in this chapter are quan-tifying the value of health outcomes to individualsby using utility theory, decision-making in healthcare, the Bayesian approach to prediction andexpected utility, statistical decision theory and lossfunctions. The third chapter in part I is ‘Simulation’,which includes discussions on Markov chain Mon-te Carlo methods, using simulation for prediction,calculating expected utility, probabilistic sensitivityanalysis and searching for strategies.

In part II there are three chapters also. Chap-ter 4 illustrates the use of Bayesian meta-analysisin developing probability distributions on the mag-nitude of the effects of a medical treatment. Thecase-studies in this chapter include an overview ofclinical trials of adjuvant tamoxifen for women withbreast cancer and clinical trials about treatments formigraine headache. Chapter 5 is on ‘Decision trees’.The modelling of multistage decision problems byusing decision trees is illustrated in this chapter witha case-study of axillary lymph node dissection, asurgical procedure that is commonly used in earlybreast cancer. ‘Chronic disease modelling’ is thetitle of Chapter 6. A decision model exemplifyingthe type of multicomponent approaches that areneeded to address complex decisions in chronic dis-ease modelling is presented, using a study of theappropriate frequency of examinations in screeningfor breast cancer.

Most of the examples used in the book are fromresearch papers in which the author of this bookis one of the authors. The prerequisite for readingthis book is exposure to elementary statistics andprobability. No claim is made about the book be-ing self-contained and readers are referred to orig-inal papers and other books for mathematical de-tails. This may be discouraging for an uninitiatedreader though the author has tried his best to presentcomplex material in a readable fashion.

There are quite a few typographical errors andduplications of words, and also mistakes in cita-tions. The typographical mistakes are not alwaystransparent; for example, ‘Uncertainly’ should be‘Uncertainty’ (page 189), ‘chromic’ should be‘chronic’ (page 195) and ‘spend’ should be ‘spent’(page 200). The references to ‘Feinleib (1977)’ (page5), ‘Oddoux et al. (1998)’ (page 19), ‘Weinstein et al.(1979)’ (page 31), ‘van Hout et al. (1994)’ (page 108),‘O’Hagan et al. (2000)’ (page 108) and ‘Wiener et al.(1979)’ (page 256), inter alia, are either missing orneed correction. On page 105, 12th line, the mean-ing of the sentence ‘Generate . . . if the first is not toD’ is not clear.

The book will be useful to research students inbiostatistics as it contains case-studies and also dis-cusses the use of Bayesian inference techniques inmedical decision-making. The statistical problemsarising in the various case-studies are challenging.Since the case-studies that are discussed are topical,the book is a welcome addition to any undergrad-uate library in statistics as it gives a flavour of thedifficulties that are encountered in medical decision-making.

Ravi SreenivasanUniversity of Mysore

and University of Sheffield

Book Reviews 247

Multivariate Permutation Tests: with Applicationsin BiostatisticsF. Pesarin, 2001Chichester, Wileyxxviii + 408 pp., £55.00ISBN 0-471-49670-7

Most practising statisticians take a particular inter-est in techniques of data analysis that promise to beof broad applicability. Permutation testing is onesuch technique that has become much more wide-spread since software to implement the requiredintensive computations has been developed. Meth-ods of permutation testing for univariate problemsare reasonably well understood and covered exten-sively in the literature. Applying permutation teststo multiple end points is the subject of this text byPesarin. The general approach that is proposed hereis to apply a suitable permutation test to each indi-vidual component of the multivariate problem, andthen to combine the individual inferences.

Much of the material here has not been pub-lished before and largely represents the author’s ownresearch on this subject. Accordingly, many for-mal proofs and derivations are included, and for afull understanding of the results a reasonably highlevel of statistical and mathematical knowledge isrequired. As well as descriptions of the author’smethods, there are descriptions of applications tovarious biostatistical problems, but this is not themain thrust of the book. Despite the author’s claimsthat the book will be of interest to practitioners (andalso to undergraduate students), my feeling is that itwill in fact be of value mainly to graduate studentsand researchers who have an interest in permutationtesting and in nonparametric methods.

The first six chapters of the book introduce somegeneral principles of permutation tests and also theauthor’s methods for multivariate problems. Chap-ters 7–12 describe some general and some specificapplications of the methodology. Software to im-plement some of the methods that are described inthe book is available via the Internet, and Web siteaddresses are given in the introduction to the text.

In summary, this is a book for the specialistreader.

L. W. HusonGNB Limited

Chislehurst

A Guide to First-passage ProcessesS. Redner, 2001Cambridge, Cambridge University Pressx + 312 pp., £55.00ISBN 0-521-65248-0

The first-passage problem (called also the first-cross-

ing or first hitting time problem) is among the mostchallenging problems in stochastic processes. Thepresent book provides a unified account of modelsof complex random phenomena that are describedby stochastic processes and are such that it is ofprimary importance to know the behaviour of thesystem until some special event occurs, e.g. failure,ruin or reaching a critical value. Any such a situ-ation leads to a specific first-passage problem. Theaim of the author is to use a moderate mathematicalbackground and to present as much as possible ofthe material that has accumulated in this area.

The author treats a variety of models: discretemodels such as random walks and continuous mod-els based on diffusion-type processes. Let us listthe titles of the chapters: 1, ‘First passage funda-mentals’; 2, ‘First passage in an interval’; 3, ‘Semi-infinite system’; 4, ‘Illustrations of first passage insimple geometries’; 5, ‘Fractal and nonfractal net-works’; 6, ‘Systems with spherical symmetry’; 7,‘Wedge domains’; 8, ‘Applications to simple reac-tions’.

Each chapter consists of sections dealing with aparticular model (mostly from physics, in particu-lar from electrostatics and current flows in resistornetworks) and a first-passage problem followed bythe solution. The author provides hints about thederivation of the formulae or solutions and makescomments on their use in particular cases. Amongthe mathematical tools that are widely used arerecursive relations, the Laplace transform, partialdifferential equations, generating functions and as-ymptotic analysis of functions. It seems that, to un-derstand deeply the content of the problems and theresults, the reader needs good knowledge in severalfundamental branches of mathematics. The style ofthe author is clear and encouraging.

Graduate and post-graduate students in someareas of physics and chemistry can benefit greatlyfrom reading and using this book. Perhaps research-ers in the area will find this book useful in theirwork, either as a reference source or as a source ofideas and techniques that can help them to studyother complicated phenomena under randomness.

Jordan StoyanovUniversity of Newcastle

ApproximationTheoremsofMathematicalStatisticsR. J. Serfling, 2002New York, Wileyxiv + 372 pp., £59.50ISBN 0-471-21927-4

This volume is a paperback version of Serfling’sbook from 1980. No changes (that I could spot)have been made to the contents. A range of standard

248 Book Reviews

approximate and asymptotic results in mathemati-cal statistics is presented in this text-book aimed atstudents with some experience in probability theoryand mathematical statistics.

Notation, various types of convergence, limittheorems and other tools from probability theoryand analysis are introduced in Chapter 1. Chapter 2concerns sample statistics and their asymptotic rep-resentations. Transformations of normal statistics,vectors and multivariate vectors are discussed inChapter 3. Chapter 4 considers asymptotic theoryin parametric inference. Chapter 5 studies U-statistics, and Chapter 6 von Mises differentiablestatistical functions. Chapters 7, 8 and 9 reviewM-estimates, L-estimates and R-estimates respec-tively. Asymptotic relative efficiency is discussed inChapter 10.

The strength of this book is that it covers mostclassical asymptotic results without using advancedmathematics. The weaknesses are examples andexercises: the examples neither seem to clarify thetheory nor to illustrate the applicability of the ap-proximate results to practical situations, and theexercises consist mainly of completing proofs ofthe results that are covered in the book. How-ever, supplemented with extra examples and exer-cises, this could be a good, if rather expensive,course book for students with no background inmeasure theory.

Pia Veldt LarsenUniversity of Southern Denmark

Odense

The Handbook of Parametric and NonparametricStatistical Procedures, 2nd ednD. Sheskin, 2001Boca Raton, Chapman and Hall–CRCxxxii + 982 pp., £93.00ISBN 1-58488-133-X

The author’s aim in writing this book is

‘to provide researchers, teachers, and studentswith a comprehensive reference book in the areasof parametric and nonparametric statistics’.

The envisaged readership is wide—people frommathematics, statistics, the biological and the socialsciences, business and education. The reader is toldthat

‘The Handbook of Parametric and Nonparamet-ric Statistical Procedures is designed to be usedby those who have a basic familiarity with de-scriptive statistics and experimental design . . .although it is not a prerequisite’.

To remedy any deficiencies that the reader mayhave, Sheskin provides a lengthy introductory chap-ter giving an overview of statistics at the level of afirst-year service course. The chapter is strong on‘how’. There are no proofs, but there are some inter-esting heuristic discussions, e.g. on parametricversus nonparametric procedures. This introduc-tory material has been extended from 29 to 37pages and now contains illustrative computationsconcerning the variance, skewness and kurtosis. Itis followed by an outline of the wide range of in-ferential statistical tests and measures of correla-tion and association that are described in the book.The chapter ends with guidelines and decision tablesconcerning the choice of appropriate procedures.These have been revised to accommodate the addi-tional material in the book.

The 26 chapters in the earlier edition havebecome 32. The additional ones are as follows:the single-sample test for evaluating populationskewness; the single-sample test for evaluatingpopulation kurtosis; the Kolmogorov–Smirnovgoodness-of-fit test for a single sample; theKolmogorov–Smirnov goodness-of-fit test for twoindependent samples; the Moses test for equal vari-ability; the van der Waerden normal scores test fork independent samples. Over 70 procedures are nowcovered.

The underlying philosophy is based on hypothe-sis testing using classical (non-Bayesian) methods.I am glad that this new edition contains a 15-pageoverview of computer-intensive methods; althougha good set of references is provided, I would not,however, call the coverage in this addendum ‘com-prehensive’. There is also some material on pointestimation, confidence intervals and correlationalresearch. Multiple regression is treated under theheading of measures of association and correlation.The focus throughout is on small data sets—mod-ern methods of analysing large data sets with manyregressors (generalized additive models, generalizedlinear models, etc.) are not covered.

The following standard format is provided for thegreat majority of the tests: I, hypothesis statementand background information; II, example; III, state-ment of the null versus the alternative hypotheses;IV, test computations; V, interpretation of the testresults; VI, additional analytical procedures for thetest and/or related tests; VII, additional discussionof the test; VIII, additional examples illustratingthe use of the test; IX, an addendum about one ormore related tests not discussed in VI; references;end notes.

The appendix of tables at the end of the booknow contains three more. It would be helpful tohave the tables on an accompanying diskette. In-deed it would be useful to have the whole book

Book Reviews 249

made available on a compact disc, particularly if onetried to adopt the author’s suggestion of using thebook as a text-book in undergraduate and graduatecourses.

This book is a useful and comprehensive com-pendium of the type of material that was the main-stay of courses in applied statistics before the adventof the specialized packages that have been writtenfor today’s powerful computers. Even if students areno longer doing all their calculations by hand, how-ever, they should still be familiar with the modusoperandi of their computations. If yours is a depart-ment in a new institution that has not inherited astatistical library from the 1980s, then this bookwith its carefully prepared and clearly written con-tent would be a wise investment. And, if your de-partment is not new, still try to add it to your librarycollection but, because of its weight and the flexi-bility of its binding, make sure that it is kept in thereference-only section.

Freda KempUniversity of St Andrews

Probability for StatisticiansG. R. Shorack, 2000New York, Springerxviii + 586 pp., £55.00ISBN 0-387-98953-6

Students of statistics in the UK are unlikely toconsider this a text that is suitable for their needs(despite the author’s inclusion of ‘highly statisti-cal optional’ chapters on asymptotics via empiri-cal processes and asymptotics via Stein’s approach).And few UK lecturers in statistics will feel ableto devote enough lecture hours to enable this tobe a suitable course text at any undergraduate orgraduate level. The book was written and has beenused for graduate probability classes (more than85 hours) at the University of Washington inSeattle. Three or more hours per week on proba-bility theory is a large amount of time in the UKcontext, where courses in applied statistics providevery strong competition in nearly all taught Masterof Science statistics programmes.

The author claims, nevertheless, that ‘There is athin self-contained textbook within this larger pre-sentation’. The first five chapters cover the mea-sure theoretic material that is needed later in thebook. Chapter 6, on topology and Hilbert spaces,is ‘presented only for reference’. Chapters 7–9 usestatistical theory to introduce some basic prob-ability concepts, including distribution functions,quantile functions, conditional expectation and sta-

tistical distribution theory (in matrix notation whereappropriate).

The presentation of probability theory begins inearnest in Chapter 10—from here on a ‘pick-and-mix’ approach to ways of presenting material is pos-sible. Chapter 10 deals with the weak and stronglaws of large numbers, the law of the iterated log-arithm, the strong Markov property, martingalesand maximal inequalities. Convergence in distribu-tion, Brownian motion and characteristic functionsare the leading topics in Chapters 11–13. Centrallimit theorems have already been developed inChapter 11 via Stein’s method; they reappear inChapter 14 using characteristic function methods.Infinitely divisible and stable distributions are stud-ied in Chapter 15. The highly optional Chapters 16and 17 are on asymptotics via empirical processesand asymptotics via Stein’s approach. Martingalesreceive coverage in depth in Chapter 18. Chapter 19is on convergence in law on metric spaces. Theappendix covers the gamma and digamma func-tions and maximum likelihood estimation.

Galen Shorack comments that it is his hope ‘thateven those well versed in probability theory willfind some new things of interest’ here. Although Iam very doubtful about the possibility of using thisbook as a course text in the UK, I would like to seeit in the hands of lecturers giving probability cours-es, on the principle that the lecturer’s understandingof what he is teaching should be more mature thanthe level of understanding that he or she is trying toimpart.

Freda KempUniversity of St Andrews

Introduction to Nonparametric Item ResponseTheoryK. Sijtsma and I. W. Molenaar, 2002Thousand Oaks, Sageviii + 168 pp., £18.99ISBN 0-7619-0813-7

This book is volume 5 in the series ‘Measurementmethods for the social sciences’ and is aimed at stu-dents and researchers in the social and behaviouralsciences rather than at statisticians. An elementaryknowledge of statistics is assumed.

The presentation concentrates on the design andanalysis of tests to determine certain properties of asingle latent characteristic such as an attitude or anability. The emphasis is on situations where partic-ipants are required to respond to a series of items,usually presented in ascending order of difficulty,and each item is scored 1 for a correct response

250 Book Reviews

and 0 for a nil or an incorrect response. The pro-posed nonparametric methodology is focused onthe total score attained. Extensions of this 0–1dichotomy to totals of scores for each item on ascale from 0 to p (> 1) are considered in the finaltwo chapters.

A strength of the book is the care that is takenby the authors, obvious enthusiasts for the meth-ods that they are expounding, to point out the dif-ficulties in choosing and deciding the order ofpresentation of items to be included in experimentsto investigate single latent characteristics such asarithmetic ability, verbal ability or attitudes towardsa controversial subject such as abortion. Manyof the points are illustrated by fully workedexamples.

Two aspects of the presentation are less helpfulto users than they might be. The first is the ab-breviation of names of 13 of the most commonlyused terms to initials. Thus, an item response func-tion becomes an IRF and an item response test anIRT. Given this information you might or mightnot guess what an NIRT is, but I had to refer sever-al times to the list of (so-called) acronyms in theappendix before readily recalling that IIO meantinvariant item ordering. Use of such jargonby consenting adults regularly working in thearea may have merits, but it is not helpful tonewcomers.

The second shortcoming concerns the orderingof some of the material. In particular, I found muchof that on scalability in Chapter 3 impossible tounderstand until I had read Chapter 4. The brief‘theoretical side-step’ on the topic on page 36 doesnot explain how to compute the scalability coeffi-cients that are used in Chapter 3—that is only ex-plained in Chapter 4.

The authors justify their emphasis on the inves-tigation of one latent characteristic at a time onthe grounds that this is what many researchers ineducation and psychology do. Although there maybe good reasons to use this approach I would havethought that often the simultaneous investigationof two or more latent traits, and how they relateto each other, would be a more fruitful field ofexperimentation. However, within the constraintsimposed the methods described in this monographare clearly useful.

In summary, the book is a good introduction forsocial scientists to important practical aspects ofitem response analysis and may also prove a use-ful reference for statisticians who are interested in,but have no specialist knowledge of, this type ofinvestigation.

P. SprentWormit

Statistical Inference in ScienceD. A. Sprott, 2000New York, Springerxvi + 246 pp., £48.00ISBN 0-387-95019-2

Many undergraduate and post-graduate pro-grammes in statistics expect students to carry outan extensive and examinable project in applied sta-tistics in their final year. Professor Sprott has hadmany years’ experience teaching at the University ofWaterloo, Ontario, and at the Centro de Investiga-cion en Matematicas, Guanajuato, Mexico. Someof his students have become statistical innovators;many are now statistical practitioners. This book isespecially suitable for the latter group of students.

It has a slightly old-fashioned air, with its use ofrelatively small data sets (many drawn from medicalresearch) and its avoidance of reference to any sta-tistical computer package. Nevertheless it is aheadof much current statistical practice with its empha-sis, not so much on using sample information toobtain estimates, their marginal distributions andtheir optimal properties, but instead on methodsfor separating sample information into componentsthat address different aspects of an investigation.For example, the division of the sample informationfor a Poisson model with t = Σn

i=1 yi and assumedmean nθ is given as

f.yi; θ/ = ∏ θyi e−θ

yi!

≡[

.nθ/te−nθ

t!

]·[

t!∏yi!

∏(1n

)yi]

,

where the first factor enables (marginal) inferencesabout θ to be made, whereas the second factor is themultinomial consequence of the Poisson model; ifthe data cast doubt on the multinomial distribu-tion, then the Poisson model and consequently theinferences about θ from the first factor are also indoubt.

Professor Sprott begins with a discussion ofrepeatable experiments in Chapter 1. In Chapter 2he describes at length, with many examples, the useof the likelihood function and relative likelihood.Chapters 3 and 4, on the division of sample infor-mation, form the core of the book. Conditional like-lihood, marginal likelihood, pivotal likelihood andprofile likelihood all receive attention. The next fourchapters contain material on estimation statements,tests of significance, the location–scale pivotal mod-el and the Gauss linear model. Notes and referencesfor Chapters 1–6 appear at the end of Chapter 6;notes and references for Chapters 7 and 8 are at theend of Chapter 8.

Book Reviews 251

Maximum likelihood estimation is the topic inChapter 9. The author’s approach, unlike that ofBarndorff-Nielsen and Cox’s Inference and Asymp-totics, 1994 (section 8.4), is

‘to obtain a linear pivotal that is efficient whenassumed to have a N.0, 1/, t, or log F distribu-tion, that is, the resulting pivotal likelihood willapproximate the observed likelihood function’.

The chapter has notes and references and three ap-pendices; they are on degrees of freedom of log.f/,observed information of the profile likelihood andsymmetrizing the likelihood function.

Chapter 10 is on controlled experiments. It endswith a cautionary note concerning randomizationand random assignment. All the problems for stu-dents are contained in Chapter 11:

‘It seemed that putting them at the end of a givenchapter would limit and prejudge how they couldbe approached. In addition . . . [some] problemswould appear at the end of a number of chapters.’

There are no hints or solutions.The book is strong regarding the large number

of illustrative examples that use data from pub-lished scientific papers. The presentation of analyti-cal findings is taken seriously, with much emphasison the use of likelihood plots. For detailed treat-ments of generalized additive models, generalizedlinear mixed models, etc., a more specialized text isneeded.

This book is intended not only for class teach-ing at advanced undergraduate and post-graduatelevels but also as a reference text. Supervisors ofapplied statistics projects should ensure that theirstudents have access to it. It is as least as essentialfor their departmental libraries as books on ‘Statis-tical inference for scientific data using the packageXYZ’.

A. W. KempSt Andrews University

Biometrika: One Hundred YearsD. M. Titterington and D. R. Cox (eds), 2001Oxford, Oxford University Pressviii + 384 pp., £45.00ISBN 0-19-850993-6

Over its first 90 years, Biometrika essentially hadthree editors only. The first issue appeared inOctober 1901, and Karl Pearson, with early assis-tance from Weldon, Galton and Davenport, was incharge until his death in 1936. His son Egon oc-cupied the position for 30 years, David Cox served

from 1966 to 1991, but Mike Titterington is alreadythe third editor since Cox.

The first 216 pages of this celebration are areprint of papers that were commissioned and pub-lished as the first issue of the journal in 2001. Theintention was to describe the impact of Biometrikaacross diverse fields, and the choice of authors tomake these surveys is admirable. Cox offers a his-tory of the journal, Anthony Davison reviews itsinfluence on statistical theory, Anthony Atkinsonand Rosemary Bailey share the duties for experi-mental design and David Oakes assesses the paperson survival analysis. Peter Hall carries the torch fornonparametric statistics, Fred Smith covers sam-ple surveys and Howell Tong has sifted through thetime series work.

These accounts have plainly been constructedwith great diligence. Accepting the invitation to huntthrough a century of journal issues, and to assessthe influence of all papers in a given area, could nothave been a light decision. The authors have alsodescribed instances of interaction, when workbegun in Biometrika was further developed else-where, and vice versa, but about 80% of all paperscited have this journal as their origin.

There are gems tucked away among the scholar-ly accounts. Atkinson and Bailey offer evidence ofthe difficult personal relationships between Fisherand Karl Pearson to which Cox alludes. Davisonnotes Wilks’s prediction, when reviewing Jeffreys’sTheory of Probability, that it would persuade fewpractitioners to change their approach. Smithremarks that ways of obtaining without-replace-ment samples with probability proportional to sizewere described in the 1960s but were felt unusablebecause of their computational complexity, an ob-jection that no longer carries weight. He also pointsout that the journal has plainly not developed inone of the ways that its founders envisaged, thatof helping to make the evolutionist a sort of regis-trar-general for all forms of life: hardly any work onsampling in biology has appeared. Oakes describeshow Pearson himself, in the very first issue of thejournal, overlooked a trap in comparing the meanlifetimes of older and younger siblings. Hall spec-ulates on the future: that parametric and nonpara-metric techniques will

‘work in tandem, as aspects of a single method-ology for the quantification of information’.

He believes that the computer-associated develop-ments of the last 25 years have seen changes in non-parametric statistics that are comparable in impor-tance with changes in the second quarter of the lastcentury when the foundations of parametric statis-tics were laid down. Tong also looks to the future:he calls for developments in time series to be linked

252 Book Reviews

more closely with general work in stochastic pro-cesses. He also remarks that, in the list of 61 ‘break-throughs in statistics’ compiled by Kotz and John-son, seven appeared in this journal. That seems anhonourable proportion.

The rest of the book consists of reprints of10 papers, from the journal’s first 70 years, chosenas significant landmarks in statistics. Excluding themore recent work has meant that the papers select-ed have had time to demonstrate real impact onthe subject. (Contrast this perspective with that ofthe current 5-yearly research assessment exercises,which seek to judge the worth of research almostas soon as it has appeared.) Some long papers thatwere strong candidates on grounds of importancehave been omitted for brevity: Harold Hotelling oncanonical correlations, the series of papers asso-ciated with the Durbin–Watson test and KirstineSmith’s 1918 experimental design paper, ‘30 yearsbefore its time’, are among the unfortunates. Sevenof the papers selected come from 1950–1971, nicelycomplementing the two neighbouring quarter-centuries picked out by Hall as important for otherreasons.

Egon Pearson’s perspective on the interactionsbetween his father, Fisher and Gosset, and Mau-rice Quenouille’s short paper, that developed thejackknife which he had introduced elsewhere, areboth included. So is Frank Yates’s thoughtful 1939design paper, full of real data and arguing that theobject of most agricultural experiments is the esti-mation of the magnitude of treatment effects, andtheir standard errors, not just testing for their ex-istence. Curiously, although Henry Daniels’s 1944paper on correlation appears here, I find no refer-ence to it in the seven commissioned surveys. Statis-tics within this journal is even broader than mighthave been supposed.

Because the entire contents of this book are al-ready available in Biometrika, albeit scattered, per-sonal sales may be limited. But libraries should beencouraged to acquire a copy, as many statisticianswill wish to read the authoritative overviews, orto have easy access to the older reprinted seminalpapers.

It is a happy academic tradition to publish aFestschrift to mark a significant birthday in the lifeof a distinguished scholar. Many such scholars con-tinue to publish valuable work long after being hon-oured in this fashion; and we can expectBiometrikaserenely to accept this present tribute, and to con-tinue its role in the development of statistical theoryand practice.

John HaighUniversity of Sussex

Brighton

Conquering Statistics: Numbers without the CrunchJ. H. Weaver, 2000Cambridge, Perseusxii + 236 pp., £12.99ISBN 0-7382-0495-1

This book left me with a disturbing thought. Eitherthere is or is not a worse way to begin learning aboutour subject than by reading Conquering Statistics.If there is, I fear for the readers of that book (orstudents in that course). If as I suspect there is not,perhaps I might save others a few hours and muchirritation.Conquering Statistics is intended to convey the

great ideas of statistics to a general audience. I likedthe selection of topics—samples, populations, prob-ability, variability, the normal curve, the law of largenumbers and statistical significance to name a few—but found the breeziness of the writing annoying,from the subtitle onwards. Sentences like

‘The real tragedy of [the neglect of statistics] isthat statistics, like broccoli, is a very good thingeven though both may have a slightly malodor-ous aftertaste’

(page 3) are fine in a Dave Barry newspaper columnbut become tiresome well before the end of a 248-page book. It is unfortunate that statistics is neglect-ed, but the book’s fabricated illustrations (qualitycontrol at the Zippy Cola Company, anyone?) willnot convince many of the tragedy. The conspicu-ous exceptions (some of the difficulties in estimat-ing the attendance at the 1995 Million Man Marchin Washington) prove the rule.

Add to the awkwardness of style many errors offact. Histograms are not ‘bar-charts’ even if theyhave bars (page 46). Subtracting the average scoreof the class from Bruno’s examination score anddividing by the number of students in the class doesnot tell you how many standard deviations abovethe mean Bruno was (page 64). The chance ofobtaining an even 50–50 split between heads andtails does not increase with the number of coin toss-es (page 71), as an exercise in one of Weaver’s citedreferences (Freedman et al., 1978) makes clear. Andso on.

Speaking of Freedman et al. (1978)—pick up acopy of that book, or another outstanding introduc-tory statistics text, to obtain an accurate expositionof the ideas mangled in Conquering Statistics. Ortry Gigerenzer’s (2002) Reckoning with Risk (pub-lished as Calculated Risks in the USA) for a gener-al interest introduction to statistical thinking. But,however you choose to conquer statistics, stay awayfrom Conquering Statistics.

ReferencesFreedman, D., Pisani, R. and Purves, R. (1978) Statis-

Book Reviews 253

tics, 1st edn. New York: Norton.Gigerenzer, G. (2002) Reckoning with Risk: Learningto Live with Uncertainty. London: Penguin.

Wesley D. EddingsJohns Hopkins University

Baltimore

Elementare Grundbegriffe einer AllgemeinerenWahrscheinlichkeitsrechnung, vol. I,Intervallwahrscheinlichkeit als UmfassendesKonzeptK. Weichselberger, 2001Heidelberg, Physicaxiv + 684 pp., £57.00ISBN 3-7908-1411-3

This book, currently unfortunately only available inGerman, provides a detailed presentation of inter-val probability. In the preface, two further volumesare announced which are currently in development.The second volume will mainly focus on conceptsof independence and conditional interval probabil-ity; the third volume will consider general samplespaces and basic theory of corresponding statisticalmethods. These two volumes will be very importantfor a complete and useful theory; I hope that theywill appear soon. This first volume introduces inter-val probability, with key concepts and motivationsclearly presented. A concise overview of some keyconcepts has been presented by the author in anEnglish language paper (Weichselberger, 2000).

Central to the theory is the following generali-zation of Kolmogorov’s axioms to interval-valuedprobabilities. For a σ-field A of random events ina sample space Ω, a set function p.·/ defined on Ais named a K-function (or K-probability or clas-sical probability), if it obeys the three axioms ofKolmogorov. Additional axioms for an interval-valued set function P.·/ are

(a) P.A/ = [L.A/; U.A/], ∀A ∈ A, with 0 L.A/ U.A/ 1, ∀A ∈ A,

(b) the set M of K-functions on A with L.A/ p.A/ U.A/, ∀A ∈ A, is not empty and

(c) infp∈Mp.A/ = L.A/ and supp∈Mp.A/ =U.A/, ∀A ∈ A.

An interval-valued set function which satisfiesaxioms (a) and (b) is called R-probability (for ‘rea-sonable’), or F -probability (for ‘feasible’) if it alsosatisfies (c). Straightforward properties of F -proba-bility, which do not need to hold for R-probabil-ity, are U.A/ = 1 − L.Ac/, ∀A ∈ A, U.∅/ = 0 andL.Ω/ = 1. The set M in (b) is called the ‘structure’of the R-probability field, which is a fundamentalconcept in this theory. In addition, an important

role is played by the concept called ‘prestructure’:any set J of K-probabilities is named a prestruc-ture of an F -probability field if infp∈J p.A/ =L.A/, ∀A ∈ A. Prestructures can be useful for cal-culations, and in situations where sets of classicalprobabilities are used without the properties ofa structure, e.g. as in many often used models inrobust (Bayesian) statistics.

After preparing for this theory in Chapter 1,which also includes a concise history of generalizedprobabilistic concepts with discussion of their mo-tivations, the main concepts are defined, togetherwith many interesting results in Chapter 2, for sit-uations where all interval probabilities of interestare actually determined. This chapter also includesa large section on decision-making under F -proba-bility, focusing on order relations for events in termsof F -probability, and including a detailed analysisof Ellsberg’s paradox and an interesting exampleon insurance, a natural area of application of in-terval probability, with differences between upperand lower probabilities related to risk averseness ofindividuals and profit margins of insurance com-panies. Although the main concepts presented inthis book are generally applicable, most of the de-velopment and presentation is with restriction tofinite sample spaces, on which the concept of R-probability coincides with Walley’s (1991) ‘avoidingsure loss’, and F -probability coincides with Walley’s‘coherence’. A main difference from Walley (1991)is that Walley explicitly generalized the subjectiveframework of de Finetti to allow for different buy-ing and selling prices for bets on an uncertain eventA and—presupposing minimax strategies—relatedL.A/ directly to the highest buying price for a beton A and U.A/ to the lowest selling price. Weich-selberger’s book explicitly does not build the the-ory from a particular interpretation of probabilitybut takes a fully axiomatic approach and studies allconsequences. Therefore it also allows for personalstrategies deviating from minimax.

Chapter 3 considers partially determined inter-val probability, where the interval probabilities arenot actually provided for all events. An interestingand relevant case appears with partial specificationswhich generalize the classical cumulative distribu-tion functions. Chapter 4 presents results which par-ticularly hold for finite sample spaces, to emphasizethis material before more general sample spaces areconsidered in the later volumes. There is detailedattention to linear optimization for identificationand construction of R- and F -probability fields.Classical statistical methods often build on a con-cept of equal probability for events, following the‘principle of insufficient reason’. This concept ofsymmetry is generalized, leading to important dif-ferences between ‘K equal probability’, which is suit-

254 Book Reviews

able in cases of physical symmetry, and ‘R equalprobability’, which is suitable in cases of epistemicsymmetry. The book ends with several appendices,presenting some further theory and a brief look atthe use of upper and lower density functions, whichprovide important methods for statistical models,to be discussed in more detail in the third volume.

This is an exceptional book which offers a widerange of new concepts and related theoreticalresults. The relevance of many of the concepts mayonly become apparent after a detailed study, whichis enabled by the careful descriptions and motiva-tions and clear examples. The timing of this bookis excellent, as many researchers in statistics andother fields, most noticeably perhaps artificial in-telligence, have been developing theory related togeneralized probabilities along these lines for sever-al years now (for example see www.sipta.org).This theory promises to play the same role for theseimportant developments as Kolmogorov’s workplayed for modern statistics and probability theory,so it is crucial that an English language version ofthis book becomes available soon, as well as Englishversions of the two further volumes that the authorhas announced.

ReferencesWalley, P. (1991) Statistical Reasoning with ImpreciseProbabilities. London: Chapman and Hall.

Weichselberger, K. (2000) The theory of interval-prob-ability as a unifying concept for uncertainty. Int. J.Approx. Reasng, 24, 149–170.

F. P. A. CoolenUniversity of Durham

First Steps in StatisticsD. B. Wright, 2002London, Sagex + 148 pp., £15.99ISBN 0-7619-5163-6

I frequently recommend introductory statisticsbooks to people who have diverse backgrounds andminimal statistics knowledge. In general these textstend to be longer than I would like them to be andusually I end up giving some of my introductory sta-tistics notes instead. On seeing that this book wasonly 147 pages long I felt that it was worth reviewingto see whether I would put it on my recommenda-tion list.

As there is no preface it is difficult to say to whomthis text is aimed. Instead I shall quote from theback cover. The text aims to offer a

‘. . . comprehensive introduction to the most com-mon statistical techniques taught on first yearresearch courses . . . ’.

The author aims to use his ‘. . . typical friendlyand humorous style’ using ‘real-life’ examples to

‘guide the student comfortably through their firstexperience of doing basic statistics at undergrad-uate or postgraduate level’.

So in summary it is aimed at students who are aboutto experience statistics for the first time and they willbe aided by the author’s informal approach.

The text covers summary statistics (central ten-dency and spread), graphical methods for lookingat data distributions (e.g. histograms and scatter-plots), random sampling, interval estimation,hypothesis testing, analysis of variance, simple lin-ear regression (and correlation), simple nonpara-metric methods (e.g. Wilcoxon) and contingencytables. In summary, this text seems to offer whatmost introductory texts offer with the exception ofprobability.

The author uses informal language to explain sta-tistical techniques. The two main approachesappear to be to motivate a technique by using anexample and then to lead the reader into the meth-odology or to explain the concepts of a techniqueand then again to use an example to lead the readerinto the methodology. Graphs and tables are usedextensively to illustrate the presentation of data andinterpretation. To illustrate some specific pointsboxes highlighted in grey are used with a detailedexample. All chapters end with a summary and exer-cises for the reader. Answers to the exercises are notgiven in the text but on the back cover it is statedthat these can be obtained from the publisher.

The author uses a variety of examples and ex-ercises that include real life situations, real life ex-amples and some imaginative examples. The reallife exercises and examples are primarily driven bythe author’s personal interests in psychology andperhaps in quantum physics. An example of animaginative example uses combinations of twopizza toppings to illustrate populations and sam-pling. There are five toppings so the population con-tains 10 possible pizzas. Simple random sampling isdescribed in the context of randomly selecting fromthe pizza population which appeared to be odd orimaginative as choosing a pizza is not really a ran-dom process. The author’s style is to use many ex-amples even when explaining one given technique.For example, to calculate the mean the authoruses the height of children and rainfall data, andfor the median he uses the height-of-children data,the rainfall data and salary data. For the mode (andproportions) he uses data from a question with cat-egorical response. So for three measures of centraltendency (the mean, median and mode) he uses fourdifferent examples.

Most statistical techniques that can be expected

Book Reviews 255

in a standard introductory text are presented. I wasconcerned that the normal distribution is given min-imal attention in favour of the use of t-tests for alltests involving continuous data. Several times thereader is referred back to Chapter 2 for the follow-ing sole explanation of the normal distribution.

“‘Bell-shaped” curves have a special place in sta-tistics, so it is worth briefly mentioning themhere. Figure 2.4 shows what is called a normaldistribution (sometimes called the Gaussiandistribution). It is shaped like one of those old-fashioned bells. In many of the statistical testscovered later in this book, it is assumed that theyfollow roughly this distribution. In reality mostdo not (Micceri, 1989).’

Another notable omission is the binomial dis-tribution. This is noticeable when the numbers fora single binary variable are tested for equality byusing the χ2-test. Such examples are usually natu-ral candidates for testing proportions using thebinomial distribution.

There are some errors in the text. For example theformula for an odds ratio is stated asAD/BD ratherthan AD/BC. This error is repeated in the accom-panying text and a nearby table. Another exampleis in Chapter 8: graphs of the data that are used toillustrate simple linear regression do not correspondfor one of the outlying points.

In summary the author tries to use everyday lan-guage to explain statistical methods by using differ-ent examples and introducing the algebra after this.The use of long (and sometimes complicated) exam-ples and the frequent change of examples does notmake the text flow naturally. Using a smaller num-

ber of simple examples and introducing some of thealgebra earlier could have helped the flow. Trying tokeep algebra out of the explanation and not alwaysusing standard notation is not good practice. Thiscould lead to the reader being at odds with otherstatistical texts if they should wish to learn more.

Before my final comments on the text I would liketo quote from the text:

‘Sometimes I read manuscripts where the authorstry to use the longest words possible, and presenttheir ideas in the most complicated manner. Theseare signs of poor writing.’

In applying this judgment to this text I wouldreplace ‘longest words’ with ‘longest examples’.

The aim of adding this text to my list of recom-mend texts for introductory statistics has not beenmet and hence I cannot recommend it. The authoraims to use many examples to help to explain themethodology, which is natural for this type of text,but this has not been achieved. Primarily this isbecause examples change frequently (including dur-ing an explanation of methodology) and can bemore difficult to understand than the methodology.It is also because examples may describe scenari-os that are not naturally associated with the statis-tics. A couple of other major points in not recom-mending this text are the lack of detailed discussionsabout the normal and binomial distributions, andmy concerns relating to the errors that I spotted(and those that I did not).

Saghir BashirSBTC

Cambridge