Applied Statistics for Engineers and Physical Scientists

Prentice Hall
Johannes Ledolter / Robert V. Hogg  
Total pages
December 2008
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This hugely anticipated revision has held true to its core strengths, while bringing the book fully up to date with modern engineering statistics. Written by two leading statisticians, Statistics for Engineers and Physical Scientists, Third Edition, provides the necessary bridge between basic statistical theory and interesting applications. Students solve the same problems that engineers and scientists face, and have the opportunity to analyze real data sets. Larger-scale projects are a unique feature of this book, which let students analyze and interpret real data, while also encouraging them to conduct their own studies and compare approaches and results.


This book assumes a calculus background. It is appropriate for undergraduate and graduate engineering or physical science courses or for students taking an introductory course applied statistics.


  • The solid organization presents information in a logical, easy-to-grasp sequence and provides early discussion on fundamental statistical concepts such as data collection, variability, randomization, and graphical representation of data.
  • Numerous exercises range from straightforward “drill” problems to more challenging problems that test conceptual understanding.
  • Comprehensive coverage on the design of experiments (Chapters 6 and 7) and regression (Chapter 8) gives students abundant exposure to these topics.
  • Thorough discussions include summarizing and interpreting data, basic probability and probability distributions, sampling distributions, and basic statistical inference.
  • Data sets are available in Minitab® and text formats. They are available for download from the Pearson data sets website at, or at

New to this Edition

  • Chapter 2 (Probability Models and Discrete Distributions) has been expanded to include Multivariate Distributions and theEstimation of Parameters from Random Samples.
  • Chapter 3 (Continuous Probability Models) now explores Simulation and the Distributions of Two or More Continuous Random Variables. In addition, Chapter 3 includes an Introduction to Reliability, which was presented later in the previous edition.
  • Projects at the end of every chapter apply the theoretical methods to the solutions of real world problems. Several projects describe how statistical studies were carried out, and give students the opportunity to analyze and interpret results. Other projects allow students to develop their own studies and compare their approaches to what was actually done.
  • Computer Software sections, which use Minitab, have been added to reflect advancements in statistical software, data analysis, and experimental design.
  • Additional Remarks are included at the end of each chapter. These sections elaborate on basic statistical concepts by sharing historical context. They are designed to be informative as well as fun and engaging for students.

Table of Contents

Chapter 1: Collection and Analysis of Information

1.1 Introduction

            1.1.1 Data Collection

            1.1.2 Types of Data

            1.1.3 The Study of Variability

            1.1.4 Distributions

            1.1.5 Importance of Variability (or Lack Thereof) for Quality and Productivity Improvement

1.2 Measurements Collected over Time

            1.2.1 Time-Sequence Plots

            1.2.2 Control Charts: A Special Case of Time-Sequence Plots

1.3 Data Display and Summary

            1.3.1 Summary and Display of Measurement Data

            1.3.2 Measures of Location

            1.3.3 Measures of Variation

            1.3.4 Exploratory Data Analysis: Stem-and-Leaf Displays and Box-and-Whisker Plots

            1.3.5 Analysis of Categorical Data

1.4 Comparisons of Samples: The Importance of Stratification

            1.4.1 Comparing Two Types of Wires

            1.4.2 Comparing Lead Concentrations from Two Different Years

            1.4.3 Number of Flaws for Three Different Products

            1.4.4 Effects of Wind Direction on the Water Levels of Lake Neusiedl

1.5 Graphical Techniques, Correlation, and an Introduction to Least Squares

            1.5.1 The Challenger Disaster

            1.5.2 The Sample Correlations Coefficient as a Measure of Association in a Scatter Plot

            1.5.3 Introduction to Least Squares

1.6 The Importance of Experimentation

            1.6.1 Design of Experiments

            1.6.2 Design of Experiments with Several Factors and the Determination of Optimum Conditions

1.7 Available Statistical Computer Software and the Visualization of Data

            1.7.1 Computer Software

            1.7.2 The Visualization of Data


Chapter 2: Probability Models and Discrete Distributions

2.1 Probability

            2.1.1 The Laws of Probability

2.2 Conditional Probability and Independence

            2.2.1 Conditional Probability

            2.2.2 Independence

            2.2.3 Bayes' Theorem

2.3 Random Variables and Expectations

            2.3.1 Random Variables and Their Distributions

            2.3.2 Expectations of Random Variables

2.4 The Binomial and Related Distributions

            2.4.1 Bernoulli Trials

            2.4.2 The Binomial Distribution

            2.4.3 The Negative Binomial Distribution

            2.4.4 The Hypergeometric Distribution

2.5 Poisson Distribution and Poisson Process

            2.5.1 The Poisson Distribution

            2.5.2 The Poisson Process

2.6 Multivariate Distributions

            2.6.1 Joint, Marginal, and Conditional Distributions

            2.6.2 Independence and Dependence of Random Variables

            2.6.3 Expectations of Functions of Several Random Variables

            2.6.4 Means and Variances of Linear Combinations of Random Variables

2.7 The Estimation of Parameters from Random Samples

            2.7.1 Maximum Likelihood Estimation

            2.7.2 Examples

            2.7.3 Properties of Estimators


Chapter 3: Continuous Probability Models

3.1 Continuous Random Variables

            3.1.1 Empirical Distributions

            3.1.2 Distributions of Continuous Random Variables

3.2 The Normal Distribution

3.3 Other Useful Distributions

            3.3.1 Weibull Distribution

            3.3.2 Gompertz Distribution

            3.3.3 Extreme Value Distribution

            3.3.4 Gamma Distribution

            3.3.5 Chi-Square Distribution

            3.3.6 Lognormal Distribution

3.4 Simulation: Generating Random Variables

            3.4.1 Motivation

            3.4.2 Generating Discrete Random Variables

            3.4.3 Generating Continuous Random Variables

3.5 Distributions of Two or More Continuous Random Variables

            3.5.1 Joint, Marginal, and Conditional Distributions, and Mathematical Expectations

            3.5.2 Propagation of Errors

3.6 Fitting and Checking Models

            3.6.1 Estimation of Parameters

            3.6.2 Checking for Normality

            3.6.3 Checking Other Models through Quantile-Quantile Plots

3.7 Introduction to Reliability


Chapter 4: Statistical Inference: Sampling Distribution, Confidence Intervals, and Tests of Hypotheses

4.1 Sampling Distributions

            4.1.1 Introduction and Motivation

            4.1.2 Distribution of the Sample Mean X

            4.1.3 The Central Limit Theorem

            4.1.4 Normal Approximation of the Binomial Distribution

4.2 Confidence Intervals for Means

            4.2.1 Determination of the Sample Size

            4.2.2 Confidence Intervals for µ1- µ2

4.3 Inferences from Small Samples and with Unknown Variances

            4.3.1 Tolerance Limits

            4.3.2 Confidence Intervals for µ1- µ2

4.4 Other Confidence Intervals

            4.4.1 Confidence Intervals for Variances

            4.4.2 Confidence Intervals for Proportions

4.5 Tests of Characteristics of a Single Distribution

            4.5.1 Introduction

            4.5.2 Possible Errors and Operating Characteristic Curves

            4.5.3 Tests of Hypotheses When the Sample Size Can Be Selected

            4.5.4 Tests of Hypotheses When the Sample Size Is Fixed

4.6 Tests of Characteristics of Two Distributions

            4.6.1 Comparing Two Independent Samples

            4.6.2 Paired-Sample t-Test

            4.6.3 Test of p1= p2

            4.6.4 Test of s2/1 = s2/2

4.7 Certain Chi-Square Tests

            4.7.1 Testing Hypotheses about Parameters in a Multinomial Distribution

            4.7.2 Contingency Tables and Tests of Independence

            4.7.3 Goodness-of-Fit Tests


Chapter 5: Statistical Process Control

5.1 Shewhart Control Charts

            5.1.1 X-Charts and R-charts

            5.1.2 p-Charts and c-Charts

            5.1.3 Other Control Charts

5.2 Process Capability Indices

            5.2.1 Introduction

            5.2.2 Process Capability Indices

            5.2.3 Discussion of Process Capability Indices

5.3 Acceptance Sampling

5.4 Problem Solving

            5.4.1 Introduction

            5.4.2 Pareto Diagram

            5.4.3 Diagnosis of Causes and Defects

            5.4.4 Six Sigma Initiatives


Chapter 6: Experiments with One Factor

6.1 Completely Randomized One-Factor Experiments

            6.1.1 Analysis-of-Variance Table

            6.1.2 F-Test for Treatment Effects

            6.1.3 Graphical Comparison of k Samples

6.2 Other Inferences in One-Factor Experiments

            6.2.1 Reference Distribution for Treatment Averages

            6.2.2 Confidence Intervals for a Particular Difference

            6.2.3 Tukey's Multiple-Comparison Procedure

            6.2.4 Model Checking

            6.2.5 The Random-Effects Model

            6.2.6 Computer Software

6.3 Randomized Complete Block Designs

            6.3.1 Estimation of Parameters and ANOVA

            6.3.2 Expected Mean Squares and Tests of Hypotheses

            6.3.3 Increased Efficiency by Blocking

            6.3.4 Follow-Up Tests

            6.3.5 Diagnostic Checking

            6.3.6 Computer Software

6.4 Designs with Two Blocking Variables: Latin Squares

            6.4.1 Construction and Randomization of Latin Squares

            6.4.2 Analysis of Data from a Latin Square


Chapter 7: Experiments with Two or More Factors

7.1 Two-Factor Factorial Designs

            7.1.1 Graphics in the Analysis of Two-Factor Experiments

            7.1.2 Special Case n = 1

            7.1.3 Random Effects

            7.1.4 Computer Software

7.2 Nested Factors and Hierarchical Designs

7.3 General Factorial and 2K Factorial Experiments

            7.3.1 2 K Factorial Experiments

            7.3.2 Significance of Estimated Effects

7.4 2¿-K Fractional Factorial Experiments

            7.4.1 Half Fractions of 2K Factorial Experiments

            7.4.2 Higher Fractions of 2K Factorial Experiments

            7.4.3 Computer Software


Chapter 8: Regression Analysis

8.1 The Simple Linear Regression Model

            8.1.1 Estimation of Parameters

            8.1.2 Residuals and Fitted Values

            8.1.3 Sampling Distributions of ß0 and ß1

8.2 Inferences in the Regression Model

            8.2.1 Coefficient of Determination

            8.2.2 Analysis-of-Variance Table and F-Test

            8.2.3 Confidence Intervals and Tests of Hypotheses for Regression Coefficients

8.3 The Adequacy of the Fitted Model

            8.3.1 Residual Checks

            8.3.2 Output from Computer Programs

            8.3.3 The Importance of Scatter Plots in Regression

8.4 The Multiple Linear Regression Model

            8.4.1 Estimation of the Regression Coefficients

            8.4.2 Residuals, Fitted Values, and the Sum-of-Squares Decomposition

            8.4.3 Inference in the Multiple Linear Regression Model

            8.4.4 A Further Example: Formaldehyde Concentrations

8.5 More on Multiple Regression

            8.5.1 Multicollinearity among the Explanatory Variables

            8.5.2 Another Example of Multiple Regression

            8.5.3 A Note on Computer Software

            8.5.4 Nonlinear Regression

8.6 Response Surface Methods

            8.6.1 The "Change One Variable at a Time" Approach

            8.6.2 Method of Steepest Ascent

            8.6.3 Designs for Fitting Second-Order Modes: The 3K Factorial and the Central Composite Design

            8.6.4 Interpretation of the Second-Order Model

            8.6.5 An Illustration


Johannes Ledolter is a Professor of Statistics and Actuarial Sciences at the University of Iowa as well as a C. Maxwell Stanley Professor of International Operations Management at the Henry B. Tippie College of Business. Ledolter received his M.S. and Ph.D. degrees in Statistics from the University of Wisconsin-Madison along with an M.S degree in Social and Economic Statistics from the University of Vienna. His research interests are in time series analysis, forecasting, and applied statistical modeling. His publications have appeared in Biometrika, Technometrics, Communications in Statistics, and Management Science. He is the co-author of several books including Experimental Design with Applications in Marketing and Service Operations, Introduction to Regression Modeling, Statistical Quality Control, andStatistical Methods for Forecasting.



Robert V. Hogg, Professor Emeritus of Statistics at the University of Iowa since 2001, received his B.A. in mathematics at the University of Illinois and his M.S. and Ph.D. degrees in mathematics, specializing in actuarial sciences and statistics, from the University of Iowa. Known for his gift of humor and his passion for teaching, Hogg has had far-reaching influence in the field of statistics. Throughout his career, Hogg has played a major role in defining statistics as a unique academic field, and he almost literally "wrote the book" on the subject. He has written more than 70 research articles and co-authored four books including  Introduction of Mathematical Statistics, 6th edition, with J. W. McKean and  A.T. Craig,  as well as  Probability and Statistical Inference, 8th edition and A Brief Course in Mathematical 1st edition, both with E.A. Tanis. His texts have become classroom standards used by hundreds of thousands of students


Among the many awards he has received for distinction in teaching, Hogg has been honored at the national level (the Mathematical Association of America Award for Distinguished Teaching), the state level (the Governor's Science Medal for Teaching), and the university level (Collegiate Teaching Award). His important contributions to statistical research have been acknowledged by his election to fellowship standing in the ASA and the Institute of Mathematical Statistics.

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