Efnisyfirlit

• Contents
• Preface
  • The Purpose and Prerequisites of this Book
  • Our Approach
  • Changes in the Seventh Edition
  • The Exercises
  • Tables and Appendices
  • Acknowledgments
• Note to the Student
• Ch 1: What Is Statistics?
  • 1.1 Introduction
  • 1.2 Characterizing a Set of Measurements: Graphical Methods
  • 1.3 Characterizing a Set of Measurements: Numerical Methods
  • 1.4 How Inferences Are Made
  • 1.5 Theory and Reality
  • 1.6 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 2: Probability
  • 2.1 Introduction
  • 2.2 Probability and Inference
  • 2.3 A Review of Set Notation
  • 2.4 A Probabilistic Model for an Experiment: The Discrete Case
  • 2.5 Calculating the Probability of an Event: The Sample-Point Method
  • 2.6 Tools for Counting Sample Points
  • 2.7 Conditional Probability and the Independence of Events
  • 2.8 Two Laws of Probability
  • 2.9 Calculating the Probability of an Event: The Event-Composition Method
  • 2.10 The Law of Total Probability and Bayes’ Rule
  • 2.11 Numerical Events and Random Variables
  • 2.12 Random Sampling
  • 2.13 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 3: Discrete Random Variables and Their Probability Distributions
  • 3.1 Basic Definition
  • 3.2 The Probability Distribution for a Discrete Random Variable
  • 3.3 The Expected Value of a Random Variable or a Function of a Random Variable
  • 3.4 The Binomial Probability Distribution
  • 3.5 The Geometric Probability Distribution
  • 3.6 The Negative Binomial Probability Distribution (Optional)
  • 3.7 The Hypergeometric Probability Distribution
  • 3.8 The Poisson Probability Distribution
  • 3.9 Moments and Moment-Generating Functions
  • 3.10 Probability-Generating Functions (Optional)
  • 3.11 Tchebysheff’s Theorem
  • 3.12 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 4: Continuous Variables and Their Probability Distributions
  • 4.1 Introduction
  • 4.2 The Probability Distribution for a Continuous Random Variable
  • 4.3 Expected Values for Continuous Random Variables
  • 4.4 The Uniform Probability Distribution
  • 4.5 The Normal Probability Distribution
  • 4.6 The Gamma Probability Distribution
  • 4.7 The Beta Probability Distribution
  • 4.8 Some General Comments
  • 4.9 Other Expected Values
  • 4.10 Tchebysheff’s Theorem
  • 4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)
  • 4.12 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 5: Multivariate Probability Distributions
  • 5.1 Introduction
  • 5.2 Bivariate and Multivariate Probability Distributions
  • 5.3 Marginal and Conditional Probability Distributions
  • 5.4 Independent Random Variables
  • 5.5 The Expected Value of a Function of Random Variables
  • 5.6 Special Theorems
  • 5.7 The Covariance of Two Random Variables
  • 5.8 The Expected Value and Variance of Linear Functions of Random Variables
  • 5.9 The Multinomial Probability Distribution
  • 5.10 The Bivariate Normal Distribution (Optional)
  • 5.11 Conditional Expectations
  • 5.12 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 6: Functions of Random Variables
  • 6.1 Introduction
  • 6.2 Finding the Probability Distribution of a Function of Random Variables
  • 6.3 The Method of Distribution Functions
  • 6.4 The Method of Transformations
  • 6.5 The Method of Moment-Generating Functions
  • 6.6 Multivariable Transformations Using Jacobians (Optional)
  • 6.7 Order Statistics
  • 6.8 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 7: Sampling Distributions and the Central Limit Theorem
  • 7.1 Introduction
  • 7.2 Sampling Distributions Related to the Normal Distribution
  • 7.3 The Central Limit Theorem
  • 7.4 A Proof of the Central Limit Theorem (Optional)
  • 7.5 The Normal Approximation to the Binomial Distribution
  • 7.6 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 8: Estimation
  • 8.1 Introduction
  • 8.2 The Bias and Mean Square Error of Point Estimators
  • 8.3 Some Common Unbiased Point Estimators
  • 8.4 Evaluating the Goodness of a Point Estimator
  • 8.5 Confidence Intervals
  • 8.6 Large-Sample Confidence Intervals
  • 8.7 Selecting the Sample Size
  • 8.8 Small-Sample Confidence Intervals for μ and μ1 − μ2
  • 8.9 Confidence Intervals for σ2
  • 8.10 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 9: Properties of Point Estimators and Methods of Estimation
  • 9.1 Introduction
  • 9.2 Relative Efficiency
  • 9.3 Consistency
  • 9.4 Sufficiency
  • 9.5 The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation
  • 9.6 The Method of Moments
  • 9.7 The Method of Maximum Likelihood
  • 9.8 Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional)
  • 9.9 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 10: Hypothesis Testing
  • 10.1 Introduction
  • 10.2 Elements of a Statistical Test
  • 10.3 Common Large-Sample Tests
  • 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests
  • 10.5 Relationships Between Hypothesis-Testing Procedures and Confidence Intervals
  • 10.6 Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Val
  • 10.7 Some Comments on the Theory of Hypothesis Testing
  • 10.8 Small-Sample Hypothesis Testing for μ and μ1 − μ2
  • 10.9 Testing Hypotheses Concerning Variances
  • 10.10 Power of Tests and the Neyman–Pearson Lemma
  • 10.11 Likelihood Ratio Tests
  • 10.12 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 11: Linear Models and Estimation by Least Squares
  • 11.1 Introduction
  • 11.2 Linear Statistical Models
  • 11.3 The Method of Least Squares
  • 11.4 Properties of the Least-Squares Estimators: Simple Linear Regression
  • 11.5 Inferences Concerning the Parameters βi
  • 11.6 Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
  • 11.7 Predicting a Particular Value of Y by Using Simple Linear Regression
  • 11.8 Correlation
  • 11.9 Some Practical Examples
  • 11.10 Fitting the Linear Model by Using Matrices
  • 11.11 Linear Functions of the Model Parameters: Multiple Linear Regression
  • 11.12 Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression
  • 11.13 Predicting a Particular Value of Y by Using Multiple Regression
  • 11.14 A Test for H0: βg+1 = βg+2 = · · · = βk = 0
  • 11.15 Summary and Concluding Remarks
  • References and Further Readings
  • Supplementary Exercises
• Ch 12: Considerations in Designing Experiments
  • 12.1 The Elements Affecting the Information in a Sample
  • 12.2 Designing Experiments to Increase Accuracy
  • 12.3 The Matched-Pairs Experiment
  • 12.4 Some Elementary Experimental Designs
  • 12.5 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 13: The Analysis of Variance
  • 13.1 Introduction
  • 13.2 The Analysis of Variance Procedure
  • 13.3 Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout
  • 13.4 An Analysis of Variance Table for a One-Way Layout
  • 13.5 A Statistical Model for the One-Way Layout
  • 13.6 Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout (Optional)
  • 13.7 Estimation in the One-Way Layout
  • 13.8 A Statistical Model for the Randomized Block Design
  • 13.9 The Analysis of Variance for a Randomized Block Design
  • 13.10 Estimation in the Randomized Block Design
  • 13.11 Selecting the Sample Size
  • 13.12 Simultaneous Confidence Intervals for More Than One Parameter
  • 13.13 Analysis of Variance Using Linear Models
  • 13.14 Summary
  • References and Further Readings
  • Supplementary Exercises
• Ch 14: Analysis of Categorical Data
  • 14.1 A Description of the Experiment
  • 14.2 The Chi-Square Test
  • 14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test
  • 14.4 Contingency Tables
  • 14.5 r x c Tables with Fixed Row or Column Totals
  • 14.6 Other Applications
  • 14.7 Summary and Concluding Remarks
  • References and Further Readings
  • Supplementary Exercises
• Ch 15: Nonparametric Statistics
  • 15.1 Introduction
  • 15.2 A General Two-Sample Shift Model
  • 15.3 The Sign Test for a Matched-Pairs Experiment
  • 15.4 The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment
  • 15.5 Using Ranks for Comparing Two Population Distributions: Independent Random Samples
  • 15.6 The Mann–Whitney U Test: Independent Random Samples
  • 15.7 The Kruskal–Wallis Test for the One-Way Layout
  • 15.8 The Friedman Test for Randomized Block Designs
  • 15.9 The Runs Test: A Test for Randomness
  • 15.10 Rank Correlation Coefficient
  • 15.11 Some General Comments on Nonparametric Statistical Tests
  • References and Further Readings
  • Supplementary Exercises
• Ch 16: Introduction to Bayesian Methods for Inference
  • 16.1 Introduction
  • 16.2 Bayesian Priors, Posteriors, and Estimators
  • 16.3 Bayesian Credible Intervals
  • 16.4 Bayesian Tests of Hypotheses
  • 16.5 Summary and Additional Comments
  • References and Further Readings
• Appendix 1: Matrices and Other Useful Mathematical Results
  • A1.1 Matrices and Matrix Algebra
  • A1.2 Addition of Matrices
  • A1.3 Multiplication of a Matrix by a Real Number
  • A1.4 Matrix Multiplication
  • A1.5 Identity Elements
  • A1.6 The Inverse of a Matrix
  • A1.7 The Transpose of a Matrix
  • A1.8 A Matrix Expression for a System of Simultaneous Linear Equations
  • A1.9 Inverting a Matrix
  • A1.10 Solving a System of Simultaneous Linear Equations
  • A1.11 Other Useful Mathematical Results
• Appendix 2: Common Probability Distributions, Means, Variances, and Moment-Generating Functions
• Appendix 3: Tables
• Answers
• Index

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