Applied Statistics for Engineers and Scientists

This textbook was written through research to redesign the introductory statistics courses at Worcester Polytechnic Institute. The courses were redesigned and enhanced with funding from the National Science Foundation. Enhancements include the addition of new technologically advanced statistical techniques with an emphasis on the use of computers, the use modules that include labs and group projects and have an emphasis on active and interactive learning, and the use of cooperative group learning. Active and interactive learning is encouraged using scientiŽ c and engineering examples, discussion questions, exercises, miniprojects, and labs provided in each chapter of the book. Group cooperative learning is encouraged by several capstone projects throughout the book that require the application of multiple statistical topics. This book is very comprehensive in its coverage of applied statistical methods useful to engineers and scientists and includes the necessary introductory theory. The authors capture the students’ interest through the use of scientiŽ c and engineering examples and data, humor, and informative narratives. A humorous example is found in “Preface—To the Student,” where the authors use a pun about bias. An example of the narrative is the very clear analogy of the American judicial system to hypothesis testing. This analogy helps the student to understand the reasoning behind the strong conclusion in the alternative hypothesis. Although several professors and instructors I know have said they use this example in their courses, I have not seen this example written in many statistics textbooks. There are 2 prefaces, 15 chapters, and several appendixes in the book. The Ž rst preface describes the book to instructors, and the second gives tips on how to use the book for students. Each chapter begins with an interesting quote and a table listing the “knowledge” and “skills” that will be acquired by successfully completing the chapter. Chapter 1 is titled “Introduction to Data Analysis” and covers many topics including deŽ nitions of variation, stationary processes, data distributions, graphical techniques, methods for identifying variation, and gauge repeatability and reproducibility studies. The title of Chapter 2 is “Summarizing Data,” and it includes a deŽ nition of a variable, how to create and use a histogram, summary measures for location and spread, a deŽ nition of outliers, box-and-whisker plots, resistance, and trimmed means. Chapter 3, “Designing Studies and Obtaining Data,” introduces the student to controlled experiments (deŽ ning factors, levels, treatments, effects, etc.) and observational studies such as surveys. It also includes sampling concepts such as probability sampling, simple random sampling, stratiŽ ed random sampling, cluster sampling, sampling errors, and bias. Chapter 4 is titled “An Introduction to Statistical Modeling.” This chapter includes a deŽ nition of models, an introduction to probability, and a discussion of discrete and continuous random variables. The discussion of random variables includes expectation, probability distributions, and cumulative distribution functions. Chapter 5, “Introduction to Inference: Estimation and Prediction,” describes Center + Error (C+ E) models and includes Ž tting a model, estimating the mean, conŽ dence intervals on the mean, estimating a proportion, conŽ dence intervals on a proportion, conŽ dence intervals on two population means and proportions, tolerance intervals, and robustness. This is the Ž rst chapter that includes a capstone project that requires the students to utilize concepts from the Ž rst Ž ve chapters. In Chapter 6, “Hypothesis Tests,” a Ž ve-step procedure for hypothesis testing is given for tests on means and proportions. The authors also discuss the relationship between hypothesis testing and conŽ dence intervals and include a capstone project. Chapter 7, “The Relationship Between Two Variables,” introduces the notion of bivariate data. This chapter includes displaying and summarizing bivariate data and correlation and gives a thorough discussion of simple linear regression and instructions for another capstone project. Chapter 8 is titled “Multiple Regression.” The methods of multiple linear regression and analysis of variance (ANOVA) are described. Chapter 8 also includes an appendix of the vector-matrix formulation of the regression models. Chapter 9, “The One-Way Model,” deŽ nes the randomized block design, a one-way means model, residual analysis, formal and informal inference, data snooping, Bonferroni comparison, Tukey comparisons, the one-way effects model, and a capstone project. Chapter 10 is titled “The Factorial Model” and provides a thorough discussion of two-way means models, interactions, factorial effects models, ANOVA for factorial models and model comparisons and includes a capstone project. Chapter 11, “Distribution-Free Inference,” includes the following methods —the sign test, rank-based tests, permutation and randomization tests, and bootstrapping. An appendix on bias correction and acceleration formulas is also included. Chapter 12 is titled “2 Designs.” This chapter provides a thorough description of two-factor factorial designs, how to use them effectively, and their importance. Chapter 13, “2kp Designs and Their Role in Quality Improvement,” describes fractional factorial designs, including a discussion of confounding, aliasing, blocking and sequential experimentation and an introduction to Taguchi robust parameter design including the advantages and a critique. Chapter 14, “Response-Surface Methodology,” continues the topic of experimental design. This chapter provides an introduction to response surfaces and describes the geometry of second-order surfaces, the method of steepest ascent, and second-order designs such as the central composite design. This chapter also includes a capstone project and two appendixes on eigenvalues and eigenvectors and a multivariate calculus refresher. Chapter 15, “Statistical Process Control,” presents the “new quality philosophy,” control charts, and capability analysis. In particular, S X and R, S X and s control charts for individuals and p1 c, and u charts are covered. The capability indices Cp1 Cpk , and Cpm are introduced. Following the Ž nal chapter is the appendix that includes tables that are referenced and used throughout the text and a section with answers to odd-numbered questions. Each chapter contains discussion questions, a large number of exercises, a miniproject, and at least one lab project. References to key or cited literature are given within the chapter as a footnote. A data disk is provided with the book. The authors discuss the use of Minitab and SAS statistical software to support data analysis. In fact, the authors have written supplementary material to support this book. These supplementary materials were not provided for review, but the textbook states that these materials include SAS macros, Minitab Ž les for the text, and the Minitab Student Version, Release 12.0. I would recommend this comprehensive and innovative textbook for use in teaching statistics to engineers and scientists.