Statistical methods / Rudolf J. Freund, William J. Wilson, Donna L. Mohr.

CONTENTS

Chapter 1. Data and statistics
1.1. Introduction
1.1.1. Data Sources
1.1.2. Using the Computer
1.2. Observations and Variables
1.3. Types of Measurements for Variables
1.4. Distributions
1.4.1. Graphical Representation of Distributions
1.5. Numerical Descriptive Statistics
1.5.1. Location
1.5.2. Dispersion
Usefulness of the Mean and Standard Deviation
1.5.3. Other Measures
1.5.4. Computing the Mean and Standard Deviation from a Frequency Distribution
1.5.5. Change of Scale
1.6. Exploratory Data Analysis
1.6.1. The Stem and Leaf Plot
1.6.2. The Box Plot
1.6.3. Comments
1.7. Bivariate Data
1.7.1. Categorical Variables
1.7.2. Categorical and Interval Variables
1.7.3. Interval Variables
1.8. Populations, Samples, and Statistical Inference — A Preview
1.9. Data Collection
1.10. Chapter Summary
Solution to Example 1.1
Summary
1.11. Chapter Exercises



Chapter 2. Probability and sampling distributions
2.1. Introduction
2.1.1. Chapter Preview
2.2. Probability
2.2.1. Definitions and Concepts
Rules for Probabilities Involving More Than One Event
2.2.2. System Reliability
2.2.3. Random Variables
2.3. Discrete Probability Distributions
2.3.1. Properties of Discrete Probability Distributions
2.3.2. Descriptive Measures for Probability Distributions
Solution to Example 2.1
2.3.3. The Discrete Uniform Distribution
2.3.4. The Binomial Distribution
Derivation of the Binomial Probability Distribution Function
2.3.5. The Poisson Distribution
2.4. Continuous Probability Distributions
2.4.1. Characteristics of a Continuous Probability Distribution
2.4.2. The Continuous Uniform Distribution
2.4.3. The Normal Distribution
2.4.4. Calculating Probabilities Using the Table of the Normal Distribution
2.5. Sampling Distributions
2.5.1. Sampling Distribution of the Mean
2.5.2. Usefulness of the Sampling Distribution
2.5.3. Sampling Distribution of a Proportion
2.6. Other Sampling Distributions
2.6.1. The χ2 Distribution
2.6.2. Distribution of the Sample Variance
2.6.3. The t Distribution
2.6.4. Using the t Distribution
2.6.5. The F Distribution
2.6.6. Using the F Distribution
2.6.7. Relationships among the Distributions
2.7. Chapter Summary
2.8. Chapter Exercises
Concept Questions
Practice Exercises
Exercises



Chapter 3. Principles of inference
3.1. Introduction
3.2. Hypothesis Testing
3.2.1. General Considerations
3.2.2. The Hypotheses
3.2.3. Rules for Making Decisions
3.2.4. Possible Errors in Hypothesis Testing
3.2.5. Probabilities of Making Errors
Calculating for Example 3.2
Calculating for Example 3.3
Calculating for Example 3.2
Calculating for Example 3.3
3.2.6. Choosing between and
3.2.7. Five-Step Procedure for Hypothesis Testing
3.2.8. Why Do We Focus on the Type I Error?
3.2.9. Choosing
3.2.10. The Five Steps for Example 3.3
3.2.11. Values
3.2.12. The Probability of a Type II Error
3.2.13. Power
3.2.14. Uniformly Most Powerful Tests
3.2.15. One-Tailed Hypothesis Tests
Solution to Example 3.1
3.3. Estimation
3.3.1. Interpreting the Confidence Coefficient
3.3.2. Relationship between Hypothesis Testing and Confidence Intervals
3.4. Sample Size
3.5. Assumptions
3.5.1. Statistical Significance versus Practical Significance
3.6. Chapter Summary
3.7. Chapter Exercises
Concept Questions
Practice Exercises
Multiple Choice Questions
Exercises



Chapter 4. Inferences on a single population
4.1. Introduction
4.2. Inferences on the Population Mean
4.2.1. Hypothesis Test on
4.2.2. Estimation of
4.2.3. Sample Size
4.2.4. Degrees of Freedom
4.3. Inferences on a Proportion
4.3.1. Hypothesis Test on
4.3.2. Estimation of
An Alternate Approximation for the Confidence Interval
4.3.3. Sample Size
4.4. Inferences on the Variance of One Population
4.4.1. Hypothesis Test on
4.4.2. Estimation of
4.5. Assumptions
4.5.1. Required Assumptions and Sources of Violations
4.5.2. Detection of Violations
4.5.3. Tests for Normality
4.5.4. If Assumptions Fail
4.5.5. Alternate Methodology
4.6. Chapter Summary
4.7. Chapter Exercises
Concept Questions
Practice Exercises
Exercises
Project



Chapter 5. Inferences for two populations
5.1. Introduction
Independent Samples
Dependent or Paired Samples
5.2. Inferences on the Difference between Means Using Independent Samples
5.2.1. Sampling Distribution of a Linear Function of Random Variables
5.2.2. The Sampling Distribution of the Difference between Two Means
5.2.3. Variances Known
Hypothesis Testing
5.2.4. Variances Unknown but Assumed Equal
5.2.5. The Pooled Variance Estimate
5.2.6. The “Pooled” t  Test
5.2.7. Variances Unknown but Not Equal
5.3. Inferences on Variances
5.4. Inferences on Means for Dependent Samples
5.5. Inferences on Proportions
5.5.1. Comparing Proportions Using Independent Samples
An Alternate Approximation for the Confidence Interval
5.5.2. Comparing Proportions Using Paired Samples
5.6. Assumptions and Remedial Methods
5.7. Chapter Summary
Solution to Example 5.1
5.8. Chapter Exercises
Concept Questions
Practice Exercises
Exercises
Projects


Chapter 6. Inferences for two or more means
6.1. Introduction
6.1.1. Using the Computer
6.2. The Analysis of Variance
6.2.1. Notation and Definitions
6.2.2. Heuristic Justification for the Analysis of Variance
6.2.3. Computational Formulas and the Partitioning of Sums of Squares
6.2.4. The Sum of Squares among Means
6.2.5. The Sum of Squares within Groups
6.2.6. The Ratio of Variances
6.2.7. Partitioning of the Sums of Squares
6.3. The Linear Model
6.3.1. The Linear Model for a Single Population
6.3.2. The Linear Model for Several Populations
6.3.3. The Analysis of Variance Model
6.3.4. Fixed and Random Effects Model
6.3.5. The Hypotheses
6.3.6. Expected Mean Squares
6.3.7. Notes on Exercises
6.4. Assumptions
6.4.1. Assumptions Required
6.4.2. Detection of Violated Assumptions
6.4.3. Tests for Equal Variance
The Hartley F-Max Test
Levene Test
6.4.4. Violated Assumptions
6.4.5. Variance Stabilizing Transformations
6.4.6. Notes on Exercises
6.5. Specific Comparisons
6.5.1. Contrasts
6.5.2. Orthogonal Contrasts
6.5.3. Fitting Trends
6.5.4. Lack of Fit Test
6.5.5. Notes on Exercises
6.5.6. Post Hoc Comparisons
The Fisher LSD Procedure
Tukey's Procedure
Duncan's Multiple-Range Test
The Scheffé Procedure
Bonferroni's Method
6.5.7. Comments
6.5.8. Confidence Intervals
6.6. Random Models
6.7. Unequal Sample Sizes
6.8. Analysis of Means
6.8.1. ANOM for Proportions
6.8.2. ANOM for Count Data
6.9. Chapter Summary
6.10. Chapter Exercises
Concept Questions
Exercises
Projects


Chapter 7. Linear regression
7.1. Introduction
7.1.1. Notes on Exercises
7.2. The Regression Model
7.3. Estimation of Parameters and
7.3.1. A Note on Least Squares
7.4. Estimation of and the Partitioning of Sums of Squares
7.5. Inferences for Regression
7.5.1. The Analysis of Variance Test for
7.5.2. The (Equivalent) Test for
7.5.3. Confidence Interval for
7.5.4. Inferences on the Response Variable
7.6. Using the Computer
7.7. Correlation
7.8. Regression Diagnostics
7.9. Chapter Summary
Solution to Example 7.1
7.10. Chapter Exercises
Concept Questions
Exercises
Projects


Chapter 8. Multiple regression
8.1. The Multiple Regression Model
8.1.1. The Partial Regression Coefficient
8.2. Estimation of Coefficients
8.2.1. Simple Linear Regression with Matrices
8.2.2. Estimating the Parameters of a Multiple Regression Model
8.2.3. Correcting for the Mean, an Alternative Calculating Method
8.3. Inferential Procedures
8.3.1. Estimation of and the Partitioning of the Sums of Squares
8.3.2. The Coefficient of Variation
8.3.3. Inferences for Coefficients
General Principle for Hypothesis Testing
8.3.4. Tests Normally Provided by Computer Outputs
The Test for the Model
Tests for Individual Coefficients
8.3.5. The Equivalent Statistic for Individual Coefficients
8.3.6. Inferences on the Response Variable
8.4. Correlations
8.4.1. Multiple Correlation
8.4.2. How Useful is the Statistic?
8.4.3. Partial Correlation
8.5. Using the Computer
8.6. Special Models
8.6.1. The Polynomial Model
8.6.3. Nonlinear Models
8.7. Multicollinearity
8.7.1. Redefining Variables
8.7.2. Other Methods
8.8. Variable Selection
8.8.1. Other Selection Procedures
8.9. Detection of Outliers, Row Diagnostics
A Physical Analogue to Least Squares
8.10. Chapter Summary
Solution to Example 8.1
8.11. Chapter Exercises
Concept Questions
Exercises
Projects


Chapter 9. Linear models
9.1. Introduction
9.2. Concepts and Definitions
9.3. The Two-Factor Factorial Experiment
9.3.1. The Linear Model
9.3.2. Notation
9.3.3. Computations for the Analysis of Variance
9.3.4. Between Cells Analysis
9.3.5. The Factorial Analysis
9.3.6. Expected Mean Squares
9.3.7. Unbalanced Data
9.3.8. Notes on Exercises
9.4. Specific Comparisons
9.4.1. Preplanned Contrasts
9.4.2. Basic Test Statistic for Contrasts
Special Computing Technique for Orthogonal Contrasts
9.4.3. Multiple Comparisons
When only Main Effects Are Important
When Interactions Are Important
9.5. Quantitative Factors
9.5.1. Lack of Fit
9.6. No Replications
9.7. Three or More Factors
9.7.1. Additional Considerations
9.8. Chapter Summary
9.9. Chapter Exercises
Concept Questions
Exercises
Project


Chapter 10. Factorial experiments
10.1. Introduction
10.1.1. Notes on Exercises
10.2. The Randomized Block Design
10.2.1. The Linear Model
Solution Example 10.2: Revisited
10.2.2. Relative Efficiency
10.2.3. Random Treatment Effects in the Randomized Block Design
10.3. Randomized Blocks with Sampling
10.4. Other Designs
10.4.1. Factorial Experiments in a Randomized Block Design
Stage One
Stage Two
Final Stage
10.4.2. Nested Designs
10.5. Repeated Measures Designs
10.5.1. One Between-Subject and One Within-Subject Factor
10.5.2. Two Within-Subject Factors
10.5.3. Assumptions of the Repeated Measures Model
10.5.4. Split Plot Designs
10.5.5. Additional Topics
10.6. Chapter Summary
Solution to Example 10.1
10.7. Chapter Exercises
Concept Questions
Exercises
Projects


Chapter 11. Design of experiments
11.1. Introduction
11.2. The Dummy Variable Model
11.2.1. Factor Effects Coding
11.2.2. Reference Cell Coding
11.2.3. Comparing Coding Schemes
11.3. Unbalanced Data
11.4. Computer Implementation of the Dummy Variable Model
11.5. Models with Dummy and Interval Variables
11.5.1. Analysis of Covariance
11.5.2. Multiple Covariates
11.5.3. Unequal Slopes
11.5.4. Independence of Covariates and Factors
11.6. Extensions to Other Models
11.7. Estimating Linear Combinations of Regression Parameters
11.7.1. Covariance Matrices
11.7.2. Linear Combination of Regression Parameters
11.8. Weighted Least Squares
11.9. Correlated Errors
11.10. Chapter Summary
Solution to Example 11.1
11.10.1. An Example of Extremely Unbalanced Data
11.11. Chapter Exercises
Concept Questions
Exercises
Projects
Figures (10)


Chapter 12. Categorical data
12.1. Introduction
12.2. Hypothesis Tests for a Multinomial Population
12.3. Goodness of Fit Using the Test
12.3.1. Test for a Discrete Distribution
12.3.2. Test for a Continuous Distribution
12.4. Contingency Tables
12.4.1. Computing the Test Statistic
12.4.2. Test for Homogeneity
12.4.3. Test for Independence
12.4.4. Measures of Dependence
12.4.5. Likelihood Ratio Test
12.4.6. Fisher's Exact Test
12.5. Loglinear Model
12.6. Chapter Summary
12.7. Chapter Exercises
Concept Questions
Exercises
Projects


Chapter 13. Generalized linear models
13.1. Introduction
13.1.1. Maximum Likelihood and Least Squares
13.2. Logistic Regression
13.3. Poisson Regression
13.3.1. Choosing Between Logistic and Poisson Regression
13.4. Nonlinear Least-Squares Regression
13.4.1. Sigmoidal Shapes (S Curves)
13.4.2. Symmetric Unimodal Shapes
13.5. Chapter Summary
13.6. Chapter Exercises
Concept Questions
Exercises
Project


Chapter 14. Nonparametric methods
14.1. Introduction
14.1.1. Ranks
14.1.2. Randomization Tests
14.1.3. Comparing Parametric and Nonparametric Procedures
14.2. One Sample
The Randomization Approach for Example 14.3
14.3. Two Independent Samples
Randomization Approach to Example 14.4
14.4. More Than Two Samples
Randomization Approach to Example 14.5
14.5. Randomized Block Design
14.6. Rank Correlation
14.7. The Bootstrap
14.8. Chapter Summary
14.9. Chapter Exercises
Concept Questions
Exercises
Projects

Includes bibliographical references and index.