Statistical Methods

Description

This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection. Statistical Methods Copyright Page Contents Preface Chapter 1. Data and Statistics 1.1 Introduction 1.2 Observations and Variables 1.3 Types of Measurements for Variables 1.4 Distributions 1.5 Numerical Descriptive Statistics 1.6 Exploratory Data Analysis 1.7 Bivariate Data 1.8 Populations, Samples, and Statistical Inference — A Preview 1.9 Chapter Summary 1.10 Chapter Exercises Chapter 2. Probability and Sampling Distributions 2.1 Introduction 2.2 Probability 2.3 Discrete Probability Distributions 2.4 Continuous Probability Distributions 2.5 Sampling Distributions 2.6 Other Sampling Distributions 2.7 Chapter Summary 2.8 Chapter Exercises Chapter 3. Principles of Inference 3.1 Introduction 3.2 Hypothesis Testing 3.3 Estimation 3.4 Sample Size 3.5 Assumptions 3.6 Chapter Summary 3.7 Chapter Exercises Chapter 4. Inferences on a Single Population 4.1 Introduction 4.2 Inferences on the Population Mean 4.3 Inferences on a Proportion 4.4 Inferences on the Variance of One Population 4.5 Assumptions 4.6 Chapter Summary 4.7 Chapter Exercises Chapter 5. Inferences for Two Populations 5.1 Introduction 5.2 Inferences on the Difference between Means Using Independent Samples 5.3 Inferences on Variances 5.4 Inferences on Means for Dependent Samples 5.5 Inferences on Proportions 5.6 Assumptions and Remedial Methods 5.7 Chapter Summary 5.8 Chapter Exercises Chapter 6. Inferences for Two or More Means 6.1 Introduction 6.2 The Analysis of Variance 6.3 The Linear Model 6.4 Assumptions 6.5 Specific Comparisons 6.6 Random Models 6.7 Unequal Sample Sizes 6.8 Analysis of Means 6.9 Chapter Summary 6.10 Chapter Exercises Chapter 7. Linear Regression 7.1 Introduction 7.2 The Regression Model 7.3 Estimation of Parameters β0 and β1 7.4 Estimation of σ2 and the Partitioning of Sums of Squares 7.5 Inferences for Regression 7.6 Using the Computer 7.7 Correlation 7.8 Regression Diagnostics 7.9 Chapter Summary 7.10 Chapter Exercises Chapter 8. Multiple Regression 8.1 The Multiple Regression Model 8.2 Estimation of Coefficients 8.3 Inferential Procedures 8.4 Correlations 8.5 Using the Computer 8.6 Special Models 8.7 Multicollinearity 8.8 Variable Selection 8.9 Detection of Outliers, Row Diagnostics 8.10 Chapter Summary 8.11 Chapter Exercises Chapter 9. Factorial Experiments 9.1 Introduction 9.2 Concepts and Definitions 9.3 The Two-Factor Factorial Experiment 9.4 Specific Comparisons 9.5 No Replications 9.6 Three or More Factors 9.7 Chapter Summary 9.8 Chapter Exercises Chapter 10. Design of Experiments 10.1 Introduction 10.2 The Randomized Block Design 10.3 Randomized Blocks with Sampling 10.4 Latin Square Design 10.5 Other Designs 10.6 Chapter Summary 10.7 Chapter Exercises Chapter 11. Other Linear Models 11.1 Introduction 11.2 The Dummy Variable Model 11.3 Unbalanced Data 11.4 Computer Implementation of the Dummy Variable Model 11.5 Models with Dummy and Interval Variables 11.6 Extensions to Other Models 11.7 Binary Response Variables 11.8 Chapter Summary 11.9 Chapter Exercises Chapter 12. Categorical Data 12.1 Introduction 12.2 Hypothesis Tests for a Multinomial Population 12.3 Goodness of Fit Using the X2 Test 12.4 Contingency Tables 12.5 Log linear Model 12.6 Chapter Summary 12.7 Chapter Exercises Chapter 13. Nonparametric Methods 13.1 Introduction 13.2 One Sample 13.3 Two Independent Samples 13.4 More Than Two Samples 13.5 Randomized Block Design 13.6 Rank Correlation 13.7 Chapter Summary 13.8 Chapter Exercises Chapter 14. Sampling and Sample Surveys 14.1 Introduction 14.2 Some Practical Considerations 14.3 Simple Random Sampling 14.4 Stratified Sampling 14.5 Other Topics 14.6 Chapter Summary Appendix A. A.1 The Normal Distribution—Probabilities Exceeding Z A.1A Selected Probability Values for the Normal Distribution— Values of Z Exceeded with Given Probability A.2 The t Distribution—Values of t Exceeded with Given Probability A.3 X2 Distribution—X2 Values Exceeded with Given Probability A.4 The F Distribution, p= 0.1 A.4A The F Distribution, p = 0.05 A.4B The F Distribution, p = 0.025 A.4C The F Distribution, p = 0.01 A.4D The F Distribution, p = 0.005 A.5 The Fmax Distribution—Percentage Points of Fmax = s2 max/s2 min A.6 Orthogonal Polynomials (Tables of Coefficients for Polynomial Trends) A.7 Percentage Points of the Studentized Range A.8 Percentage Points of the Duncan Multiple Range Test A.9 Critical Values for the Wilcoxon Signed Rank Test N= 5(1)50 A.10 The Mann–Whitney Two-Sample Test A.11 Exact Critical Values for Use with the Analysis of Means Appendix B. A Brief Introduction to Matrices Matrix Algebra Solving Linear Equations References Solutions to Selected Exercises Index