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More About This Textbook
Overview
This classic text provides a rigorous introduction to basic probability theory and statistical inference, with a unique balance of theory and methodology. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. This revision focuses on improved clarity and deeper understanding.
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Meet the Author
Raymond H Myers is currently Professor Emeritus of statistics at Virginia Tech. He received his Masters and Ph.D. from Virginia Tech in statistics and his BS in chemical engineering. His major areas of interest are linear models, design of experiments, and response surface methodology. He has authored or coauthored six statistics texts that were published in fifteen separate editions and in several foreign languages.
He has received numerous teaching awards and in 1985 he was selected “Professor of the Year” in the state of Virginia by the Council on the Advancement and Support of Education. He was elected Fellow of ASA in 1974. In 1999 he was given the Shewhart Award for lifetime contributions in statistics and quality control by the American Society of Quality.
Sharon L Myers is currently Professor Emeritus of mathematics and statistics at Radford University. She received her MS in statistics from Virginia Tech. Her areas of interest are statistical computing, regression analysis, and response surface methodology. She has coauthored three editions of “Probability & Statistics for Engineers & Scientists”. She was the assistant director of the statistical consulting center at Virginia Tech for 15 years and the director of the statistical consulting center at Radford University for 7 years.
Keying Ye, University of Texas at San Antonio
Table of Contents
Preface
1. Introduction to Statistics and Data Analysis
1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability
1.2 Sampling Procedures; Collection of Data
1.3 Measures of Location: The Sample Mean and Median
Exercises
1.4 Measures of Variability
Exercises
1.5 Discrete and Continuous Data
1.6 Statistical Modeling, Scientific Inspection, and Graphical Methods 19
1.7 General Types of Statistical Studies: Designed Experiment,
Observational Study, and Retrospective Study
Exercises
2. Probability
2.1 Sample Space
2.2 Events
Exercises
2.3 Counting Sample Points
Exercises
2.4 Probability of an Event
2.5 Additive Rules
Exercises
2.6 Conditional Probability, Independence and Product Rules
Exercises
2.7 Bayes’ Rule
Exercises
Review Exercises
2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
3. Random Variables and Probability Distributions
3.1 Concept of a Random Variable
3.2 Discrete Probability Distributions
3.3 Continuous Probability Distributions
Exercises
3.4 Joint Probability Distributions
Exercises
Review Exercises
3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
4. Mathematical Expectation
4.1 Mean of a Random Variable
Exercises
4.2 Variance and Covariance of Random Variables
Exercises
4.3 Means and Variances of Linear Combinations of Random Variables 127
4.4 Chebyshev’s Theorem
Exercises
Review Exercises
4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
5. Some Discrete Probability Distributions
5.1 Introduction and Motivation
5.2 Binomial and Multinomial Distributions
Exercises
5.3 Hypergeometric Distribution
Exercises
5.4 Negative Binomial and Geometric Distributions
5.5 Poisson Distribution and the Poisson Process
Exercises
Review Exercises
5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
6. Some Continuous Probability Distributions
6.1 Continuous Uniform Distribution
6.2 Normal Distribution
6.3 Areas under the Normal Curve
6.4 Applications of the Normal Distribution
Exercises
6.5 Normal Approximation to the Binomial
Exercises
6.6 Gamma and Exponential Distributions
6.7 ChiSquared Distribution
6.8 Beta Distribution
6.9 Lognormal Distribution (Optional)
6.10 Weibull Distribution (Optional)
Exercises
Review Exercises
6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
7. Functions of Random Variables (Optional)
7.1 Introduction
7.2 Transformations of Variables
7.3 Moments and MomentGenerating Functions
Exercises
8. Sampling Distributions and More Graphical Tools
8.1 Random Sampling and Sampling Distributions
8.2 Some Important Statistics
Exercises
8.3 Sampling Distributions
8.4 Sampling Distribution of Means and the Central Limit Theorem
Exercises
8.5 Sampling Distribution of S ^{2}
8.6 tDistribution
8.7 FDistribution
8.8 Quantile and Probability Plots
Exercises
Review Exercises
8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
9. One and TwoSample Estimation Problems
9.1 Introduction
9.2 Statistical Inference
9.3 Classical Methods of Estimation
9.4 Single Sample: Estimating the Mean
9.5 Standard Error of a Point Estimate
9.6 Prediction Intervals
9.7 Tolerance Limits
Exercises
9.8 Two Samples: Estimating the Difference Between Two Means
9.9 Paired Observations
Exercises
9.10 Single Sample: Estimating a Proportion
9.11 Two Samples: Estimating the Difference between Two Proportions
Exercises
9.12 Single Sample: Estimating the Variance
9.13 Two Samples: Estimating the Ratio of Two Variances
Exercises
9.14 Maximum Likelihood Estimation (Optional)
Exercises
Review Exercises
9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
10. One and TwoSample Tests of Hypotheses
10.1 Statistical Hypotheses: General Concepts
10.2 Testing a Statistical Hypothesis
10.3 The Use of PValues for Decision Making in Testing Hypotheses
Exercises
10.4 Single Sample: Tests Concerning a Single Mean
10.5 Two Samples: Tests on Two Means
10.6 Choice of Sample Size for Testing Means
10.7 Graphical Methods for Comparing Means
Exercises
10.8 One Sample: Test on a Single Proportion
10.9 Two Samples: Tests on Two Proportions
Exercises
10.10 One and TwoSample Tests Concerning Variances
Exercises
10.11 GoodnessofFit Test
10.12 Test for Independence (Categorical Data)
10.13 Test for Homogeneity
10.14 TwoSample Case Study
Exercises
Review Exercises
10.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
11. Simple Linear Regression and Correlation
11.1 Introduction to Linear Regression
11.2 The Simple Linear Regression Model
11.3 Least Squares and the Fitted Model
Exercises
11.4 Properties of the Least Squares Estimators
11.5 Inferences Concerning the Regression Coefficients
11.6 Prediction
Exercises
11.7 Choice of a Regression Model
11.8 AnalysisofVariance Approach
11.9 Test for Linearity of Regression: Data with Repeated Observations 416
Exercises
11.10 Data Plots and Transformations
11.11 Simple Linear Regression Case Study
11.12 Correlation
Exercises
Review Exercises
11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
12. Multiple Linear Regression and Certain Nonlinear Regression Models
12.1 Introduction
12.2 Estimating the Coefficients
12.3 Linear Regression Model Using Matrices
Exercises
12.4 Properties of the Least Squares Estimators
12.5 Inferences in Multiple Linear Regression
Exercises
12.6 Choice of a Fitted Model through Hypothesis Testing
12.7 Special Case of Orthogonality (Optional)
Exercises
12.8 Categorical or Indicator Variables
Exercises
12.9 Sequential Methods for Model Selection
12.10 Study of Residuals and Violation of Assumptions
12.11 Cross Validation, C_{p} , and Other Criteria for Model Selection
Exercises
12.12 Special Nonlinear Models for Nonideal Conditions
Exercises
Review Exercises
12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
13. OneFactor Experiments: General
13.1 AnalysisofVariance Technique
13.2 The Strategy of Experimental Design
13.3 OneWay Analysis of Variance: Completely Randomized Design (OneWay ANOVA)
13.4 Tests for the Equality of Several Variances
Exercises
13.5 Multiple Comparisons
Exercises
13.6 Comparing a Set of Treatments in Blocks
13.7 Randomized Complete Block Designs
13.8 Graphical Methods and Model Checking
13.9 Data Transformations In Analysis of Variance)
Exercises
13.10 Random Effects Models
13.11 Case Study
Exercises
Review Exercises
13.12 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
14. Factorial Experiments (Two or More Factors)
14.1 Introduction
14.2 Interaction in the TwoFactor Experiment
14.3 TwoFactor Analysis of Variance
Exercises
14.4 ThreeFactor Experiments
Exercises
14.5 Factorial Experiments for Random Effects and Mixed Models
Exercises
Review Exercises
14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
15. 2 ^{k} Factorial Experiments and Fractions
15.1 Introduction
15.2 The 2 ^{k} Factorial: Calculation of Effects and Analysis of Variance 598
15.3 Nonreplicated 2 ^{k} Factorial Experiment
Exercises
15.4 Factorial Experiments in a Regression Setting
15.5 The Orthogonal Design
Exercises
15.6 Fractional Factorial Experiments
15.7 Analysis of Fractional Factorial Experiments
Exercises
15.8 Higher Fractions and Screening Designs
15.9 Construction of Resolution III and IV Designs
15.10 Other TwoLevel Resolution III Designs; The PlackettBurman Designs
15.11 Introduction to Response Surface Methodology
15.12 Robust Parameter Design
Exercises
Review Exercises
15.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters
16. Nonparametric Statistics
16.1 Nonparametric Tests
16.2 SignedRank Test
Exercises
16.3 Wilcoxon RankSum Test
16.4 KruskalWallis Test
Exercises
16.5 Runs Test
16.6 Tolerance Limits
16.7 Rank Correlation Coefficient
Exercises
Review Exercises
17. Statistical Quality Control
17.1 Introduction
17.2 Nature of the Control Limits
17.3 Purposes of the Control Chart
17.4 Control Charts for Variables
17.5 Control Charts for Attributes
17.6 Cusum Control Charts
Review Exercises
18 Bayesian Statistics
18.1 Bayesian Concepts
18.2 Bayesian Inferences
18.3 Bayes Estimates Using Decision Theory Framework
Exercises
Bibliography
A. Statistical Tables and Proofs
B. Answers to OddNumbered NonReview Exercises
Index
Preface
Goals, Approach and Mathematical Level
The seventh edition emphasizes and illustrates the use of probabilistic models and statistical methodology that is employed in countless applications in all areas of science and engineering. There remains an important balance between theory and methodology that is featured in the text. We do not avoid the use of some theory but our goal is to let the mathematics provide insight rather than be a distraction. We feel that engineers and scientists are trained in mathematics and thus the providing of mathematical support when needed keeps the pedagogy from becoming a series of illustrated recipes in which the concepts are not understood and could never be applied or extended by the student except within very narrow bounds.
The text contains an abundance of exercises in which the methodology discussed is illustrated by the use of reallife scientific scenarios and data sets. The complete set of data files which accompany the text are available for download from the text companion website, located at our site. Though we attempt to appeal to engineers, the exercises are not confined to engineering applications. The student is exposed to problems encountered in many sciences including social sciences and biomedical applications. The motivation here stems from the fact that trained engineers are more and more becoming exposed to nontraditional settings, including areas like bioinformatics and bioengineering.
While we do let calculus play an important role but it should be noted that its use is confined to elementary probability theory and properties of probability distributions (Chapters 3, 4, 6, and 7). In addition, a modest amount ofmatrix algebra is used to support the linear regression material in Chapters 11 and 12. This is despite the fact that an "optional" section appears in Chapter 11 that includes the development of the multiple linear regression model with more substantive use of matrices. The student who uses this text should have completed one semester or two quarters of differential and integral calculus. An exposure to matrix algebra would be helpful but not necessary if the course content excludes the aforementioned optional section.
Content and Course Planning
The text is designed for either a one or two semester course. A reasonable curriculum for a one semester course might include Chapters 1 through 10. One may even choose to teach an early portion of Chapter 11 in order to introduce the student to the concept of simple linear regression. Chapter 1 is an overview of statistical inference, sampling and data analysis. Indeed, some very rudimentary aspects of experimental design are included, along with an appreciation of graphics and certain vital characteristics of data collection. Chapters 2, 3, and 4 deal with basic probability and discrete and continuous random variables. Chapters 5 and 6 cover specific discrete and continuous distributions with illustrations of their use and relationships among them. Chapter 7 deals with transformations of random variables. This chapter is listed as "optional" and would only be covered in a more theoretical course. This chapter is clearly the most mathematical chapter in the text. Chapter 8 includes additional material on graphical methods as well as an introduction to the notion of a sampling distribution. The t and F distributions are introduced along with motivation regarding their use in chapters that follow. Chapters 9 and 10 contain material on one and two sample point and interval estimation and hypothesis testing. The flexibility in a single semester course lies in the option of exclusion of Chapter 7 as well as teaching only a subset of the several specific discrete and continuous distributions discussed and illustrated in Chapters 5 and 6. There is additional flexibility involved in dealing with Chapter 9 where maximum likelihood and Bayes estimation are covered in detail. An instructor may decide to give only a cursory development of one or both of these topics. In addition, estimation in Chapter 9 includes new material on prediction intervals and tolerance intervals along with a thorough discussion on the distinction among them, with examples. Flexibility may be exercised here.Chapters 1117 contain ample material for a second semester of a twosemester course. Chapters 11 and 12 cover simple and multiple linear regression respectively. However, Chapter 12 contains new material that deals with special nonlinear models involved when one deals with nonnormal responses. As a result, logistic and Poisson regression are treated along with important practical illustrations. This in addition to new material in categorical variable regression again provides considerable flexibility for the instructor in his or her treatment of regression. The treatment of regression in this text is extensive and many special regression topics in Chapter 12 are selfcontained. Chapters 13 through 17 contain topics in analysis of variance, design of experiments, nonparametric statistics, and quality control.
Case Studies and Computer Software
As in previous editions there are many case studies that demonstrate statistical analysis of interesting reallife data sets. In most cases graphical techniques are used. These case studies are featured in two sample hypothesis testing, multiple linear regression, analysis of variance, and the analysis of 2level experimental designs. Where appropriate, the use of residual plots, quantile plots, and normal probability plots are described in the analysis. Computer output is used for illustration purposes for these case studies and for other examples in the text. In that regard both SAS and MINITAB are featured. We have always felt that the experience of reading computer printout is invaluable to the student even if the package or packages featured in the text are not what is used by the instructor. Exposure to more than one type of software can broaden the experience base for the student. There is certainly no reason to believe that the software in the course is that which he or she will be called upon to use in practice.
New To This Edition
Available Supplements
Acknowledgements
We are indeed indebted to those colleagues who reviewed the sixth edition and provided many helpful suggestions for this edition. They are: Ruxu Du, University of Miami; Nirmal Devi, Embry Riddle; Judith Miller, Georgetown University; Stephanie Edwards, Bemidji State University. We would like to thank personnel at the Virginia Tech Statistical Consulting Center. The consulting center was the source of many reallife data sets. In addition we thank Linda Seawell who worked hard in the typing and preparation of the manuscript.
RHM
SLM
KY