The Design and Analysis of Computer Experiments

Each chapter follows the same general format. A short introduction sets the stage, followed by methods involving binary or categorical responses. Then come methods for continuous responses, followed by a short section on methods for right-censored data. Each chapter has an appendix with mathematical derivations and a second appendix with computer programs (essentially SAS code for implementing the methods). Just about everything you would expect to find in a compilation of basic binary/categorical response and distribution-free methods is covered. Binomial, chi-squared, McNemar’s, sign, Wilcoxon signed-rank, Wilcoxon rank sum, Kruskal–Wallis, Friedman, Spearman rank correlation, Kendall’s tau, and Theil’s test for the slope are included. Point estimation of, and confidence intervals for, parameters based on distribution-free tests are also covered. The coverage is quite complete and includes some methods not often seen in other books. As the authors state in the Preface, “this is not a theorem-proof book.” However, what the authors consider “minimal mathematical statistics background” is actually quite substantial. Although the authors claim to introduce concepts intuitively, I found that the abundance of computational formulas overwhelmed any intuition. A unique feature of this book is inclusion of distribution-free methods for censored data. Each chapter has a section on censored data methods. However, these sections make up only a small portion of the book (about 15%), whereas the standard methods take up most of the book (about 85%). The only method presented for a single sample with censored data is the Kaplan–Meier estimate of the survival function. For two independent samples, Gehan’s Wilcoxon test and the less well-known Tarone and Ware test are covered. For paired samples, a sign test and a generalized signed-rank test are discussed. The methods of Tarone and Ware are extended to the case of multiple independent samples. Similarly, generalized signed-rank test methodology is extended to block designs. For the chapter on independence, correlation, and regression, a test for independence with censored data and the proportional hazards model are presented. The discussion of these censored data methods, although brief, is a nice addition. The chapter on block designs is very complete and covers material far beyond the usual Friedman test. The last chapter, on computer-intensive methods, appears to be an afterthought. Only six pages are given for the discussion of permutation and randomization tests and the bootstrap. In summary, Desu and Raghavarao have compiled a solid set of basic methods for binomial/categorical response data and distribution-free methods. The inclusion of methods for censored data is a plus, but these methods make up only a small portion of the book. Although the authors’ intent was “to introduce the concepts intuitively with minimal mathematical statistics background,” I found the intuition lost in the abundance of formulas. Additionally, those readers without a solid junior/senior-level grounding in mathematical statistics may find the book tough going.