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Full Description
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.
Contents
Preface1. Introduction to Statistics and Data Analysis1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability1.2 Sampling Procedures; Collection of Data1.3 Measures of Location: The Sample Mean and MedianExercises1.4 Measures of VariabilityExercises1.5 Discrete and Continuous Data1.6 Statistical Modeling, Scientific Inspection, and Graphical Methods 191.7 General Types of Statistical Studies: Designed Experiment,Observational Study, and Retrospective StudyExercises2. Probability2.1 Sample Space2.2 EventsExercises2.3 Counting Sample PointsExercises2.4 Probability of an Event2.5 Additive RulesExercises2.6 Conditional Probability, Independence and Product RulesExercises2.7 Bayes' RuleExercisesReview Exercises2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters3. Random Variables and Probability Distributions3.1 Concept of a Random Variable3.2 Discrete Probability Distributions3.3 Continuous Probability DistributionsExercises3.4 Joint Probability DistributionsExercisesReview Exercises3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters4. Mathematical Expectation4.1 Mean of a Random VariableExercises4.2 Variance and Covariance of Random VariablesExercises4.3 Means and Variances of Linear Combinations of Random Variables 1274.4 Chebyshev's TheoremExercisesReview Exercises4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters5. Some Discrete Probability Distributions5.1 Introduction and Motivation5.2 Binomial and Multinomial DistributionsExercises5.3 Hypergeometric DistributionExercises5.4 Negative Binomial and Geometric Distributions5.5 Poisson Distribution and the Poisson ProcessExercisesReview Exercises5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters6. Some Continuous Probability Distributions6.1 Continuous Uniform Distribution6.2 Normal Distribution6.3 Areas under the Normal Curve6.4 Applications of the Normal DistributionExercises6.5 Normal Approximation to the BinomialExercises6.6 Gamma and Exponential Distributions6.7 Chi-Squared Distribution6.8 Beta Distribution6.9 Lognormal Distribution (Optional)6.10 Weibull Distribution (Optional)ExercisesReview Exercises6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters7. Functions of Random Variables (Optional)7.1 Introduction7.2 Transformations of Variables7.3 Moments and Moment-Generating FunctionsExercises8. Sampling Distributions and More Graphical Tools8.1 Random Sampling and Sampling Distributions8.2 Some Important StatisticsExercises8.3 Sampling Distributions8.4 Sampling Distribution of Means and the Central Limit TheoremExercises8.5 Sampling Distribution of S28.6 t-Distribution8.7 F-Distribution8.8 Quantile and Probability PlotsExercisesReview Exercises8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters9. One- and Two-Sample Estimation Problems9.1 Introduction9.2 Statistical Inference9.3 Classical Methods of Estimation9.4 Single Sample: Estimating the Mean9.5 Standard Error of a Point Estimate9.6 Prediction Intervals9.7 Tolerance LimitsExercises9.8 Two Samples: Estimating the Difference Between Two Means9.9 Paired ObservationsExercises9.10 Single Sample: Estimating a Proportion9.11 Two Samples: Estimating the Difference between Two ProportionsExercises9.12 Single Sample: Estimating the Variance9.13 Two Samples: Estimating the Ratio of Two VariancesExercises9.14 Maximum Likelihood Estimation (Optional)ExercisesReview Exercises9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters10. One- and Two-Sample Tests of Hypotheses10.1 Statistical Hypotheses: General Concepts10.2 Testing a Statistical Hypothesis10.3 The Use of P-Values for Decision Making in Testing HypothesesExercises10.4 Single Sample: Tests Concerning a Single Mean10.5 Two Samples: Tests on Two Means10.6 Choice of Sample Size for Testing Means10.7 Graphical Methods for Comparing MeansExercises10.8 One Sample: Test on a Single Proportion10.9 Two Samples: Tests on Two ProportionsExercises10.10 One- and Two-Sample Tests Concerning VariancesExercises10.11 Goodness-of-Fit Test10.12 Test for Independence (Categorical Data)10.13 Test for Homogeneity10.14 Two-Sample Case StudyExercisesReview Exercises10.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters11. Simple Linear Regression and Correlation11.1 Introduction to Linear Regression11.2 The Simple Linear Regression Model11.3 Least Squares and the Fitted ModelExercises11.4 Properties of the Least Squares Estimators11.5 Inferences Concerning the Regression Coefficients11.6 PredictionExercises11.7 Choice of a Regression Model11.8 Analysis-of-Variance Approach11.9 Test for Linearity of Regression: Data with Repeated Observations 416Exercises11.10 Data Plots and Transformations11.11 Simple Linear Regression Case Study11.12 CorrelationExercisesReview Exercises11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters12. Multiple Linear Regression and Certain Nonlinear Regression Models12.1 Introduction12.2 Estimating the Coefficients12.3 Linear Regression Model Using MatricesExercises12.4 Properties of the Least Squares Estimators12.5 Inferences in Multiple Linear RegressionExercises12.6 Choice of a Fitted Model through Hypothesis Testing12.7 Special Case of Orthogonality (Optional)Exercises12.8 Categorical or Indicator VariablesExercises12.9 Sequential Methods for Model Selection12.10 Study of Residuals and Violation of Assumptions12.11 Cross Validation, Cp, and Other Criteria for Model SelectionExercises12.12 Special Nonlinear Models for Nonideal ConditionsExercisesReview Exercises12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters13. One-Factor Experiments: General13.1 Analysis-of-Variance Technique13.2 The Strategy of Experimental Design13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA)13.4 Tests for the Equality of Several VariancesExercises13.5 Multiple ComparisonsExercises13.6 Comparing a Set of Treatments in Blocks13.7 Randomized Complete Block Designs13.8 Graphical Methods and Model Checking13.9 Data Transformations In Analysis of Variance)Exercises13.10 Random Effects Models13.11 Case StudyExercisesReview Exercises13.12 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters14. Factorial Experiments (Two or More Factors)14.1 Introduction14.2 Interaction in the Two-Factor Experiment14.3 Two-Factor Analysis of VarianceExercises14.4 Three-Factor ExperimentsExercises14.5 Factorial Experiments for Random Effects and Mixed ModelsExercisesReview Exercises14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters15. 2k Factorial Experiments and Fractions15.1 Introduction15.2 The 2k Factorial: Calculation of Effects and Analysis of Variance 59815.3 Nonreplicated 2k Factorial ExperimentExercises15.4 Factorial Experiments in a Regression Setting15.5 The Orthogonal DesignExercises15.6 Fractional Factorial Experiments15.7 Analysis of Fractional Factorial ExperimentsExercises15.8 Higher Fractions and Screening Designs15.9 Construction of Resolution III and IV Designs15.10 Other Two-Level Resolution III Designs; The Plackett-Burman Designs15.11 Introduction to Response Surface Methodology15.12 Robust Parameter DesignExercisesReview Exercises15.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters16. Nonparametric Statistics16.1 Nonparametric Tests16.2 Signed-Rank TestExercises16.3 Wilcoxon Rank-Sum Test16.4 Kruskal-Wallis TestExercises16.5 Runs Test16.6 Tolerance Limits16.7 Rank Correlation CoefficientExercisesReview Exercises17. Statistical Quality Control17.1 Introduction17.2 Nature of the Control Limits17.3 Purposes of the Control Chart17.4 Control Charts for Variables17.5 Control Charts for Attributes17.6 Cusum Control ChartsReview Exercises18 Bayesian Statistics18.1 Bayesian Concepts18.2 Bayesian Inferences18.3 Bayes Estimates Using Decision Theory FrameworkExercisesBibliographyA. Statistical Tables and ProofsB. Answers to Odd-Numbered Non-Review ExercisesIndex
