Statistical methods

Statistical Methods
Copyright
Contents
Preface
	Guiding Principles
	New to this Edition
	Using this Book
		Organization
		Coverage
		Sequencing
		Data Sets
		Computing
Acknowledgments
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 Examples of Exploratory Data Analysis
	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
	Summary
	1.11 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
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
		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
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 α for Example 3.2
			Calculating α for Example 3.3
			Calculating β for Example 3.2
			Calculating β for Example 3.3
		3.2.6 Choosing between α and β
		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 α
		3.2.10 The Five Steps for Example 3.3
		3.2.11 p 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 NAEP Reading Scores
	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
4 Inferences on a Single Population
	4.1 Introduction
	4.2 Inferences on the Population Mean
		4.2.1 Hypothesis Test on μ
		4.2.2 Estimation of μ
			WARNING!!! DUMMY ENTRY
				Solution to Example 4.1 Perceptions of Area
		4.2.3 Sample Size
		4.2.4 Degrees of Freedom
	4.3 Inferences on a Proportion for Large Samples
		4.3.1 Hypothesis Test on p
		4.3.2 Estimation of p
			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 σ2
		4.4.2 Estimation of σ2
	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
		Projects
5 Inferences for Two Populations
	5.1 Introduction
		WARNING!!! DUMMY ENTRY
			Independent Samples
			Dependent Samples
			Comparing the Two Sampling Procedures
	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
		5.2.8 Choosing between the Pooled and Unequal Variance t Tests
	5.3 Inferences on Variances
		WARNING!!! DUMMY ENTRY
			WARNING!!! DUMMY ENTRY
				WARNING!!! DUMMY ENTRY
					Count Five Rule
	5.4 Inferences on Means for Dependent Samples
	5.5 Inferences on Proportions for Large Samples
		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: PE Ratios Revisited
			Independent Samples
			Dependent samples
	5.8 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
6 Inferences for Two or More Means
	6.1 Introduction
		6.1.1 Using Statistical Software
	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 between 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
	6.4 Assumptions
		6.4.1 Assumptions and Detection of Violations
		6.4.2 Formal Tests for the Assumption of Equal Variance
			Bartlett’s Test
			Levene Test and the Brown-Forsythe Test
		6.4.3 Remedial Measures
	6.5 Specific Comparisons
		6.5.1 Contrasts
		6.5.2 Constructing a t Statistic for a Contrast
		6.5.3 Planned Contrasts with No Pattern—Bonferroni’s Method
		6.5.4 Planned Comparisons versus Control—Dunnett’s Method
		6.5.5 Planned All Possible Pairwise Comparisons—Fisher’s LSD and Tukey’s HSD
			Fisher’s LSD
			Tukey’s HSD
		6.5.6 Planned Orthogonal Contrasts
		6.5.7 Unplanned Contrasts—Scheffé’s Method
		6.5.8 Comments
	6.6 Random Models
	6.7 Analysis of Means
		6.7.1 ANOM for Proportions
		6.7.2 ANOM for Count Data
	6.8 Chapter Summary
	6.9 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
	Projects
7 Linear Regression
	7.1 Introduction
	7.2 The Regression Model
	7.3 Estimation of Parameters β0 and β1
		7.3.1 A Note on Least Squares
	7.4 Estimation of σ2 and the Partitioning of Sums of Squares
	7.5 Inferences for Regression
		7.5.1 The Analysis of Variance Test for β1
		7.5.2 The (Equivalent) t Test for β1
		7.5.3 Confidence Interval for β1
		7.5.4 Inferences on the Response Variable
	7.6 Using Statistical Software
	7.7 Correlation
	7.8 Regression Diagnostics
	7.9 Chapter Summary
	7.10 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
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 σ2 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 Statistical Software
			The Test for the Model
			Tests for Individual Coefficients
		8.3.5 The Equivalent t 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 R2 Statistic?
		8.4.3 Partial Correlation
	8.5 Using Statistical Software
	8.6 Special Models
		8.6.1 The Polynomial Model
		8.6.2 The Multiplicative 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
		WARNING!!! DUMMY ENTRY
			A Physical Analogue to Least Squares
	8.10 Chapter Summary
	8.11 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
9 Factorial Experiments
	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
	9.4 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
		Practice Exercises
		Exercises
		Project
10 Design of Experiments
	10.1 Introduction
	10.2 The Randomized Block Design
		10.2.1 The Linear Model
		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
	10.7 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
11 Other Linear Models
	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 Statistical Software’s 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
	11.11 Chapter Exercises
		Concept Questions
	Practice Exercises
	Exercises
	Projects
12 Categorical Data
	12.1 Introduction
	12.2 Hypothesis Tests for a Multinomial Population
	12.3 Goodness of Fit Using the χ2 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 Specific Comparisons in Contingency Tables
	12.6 Chapter Summary
	12.7 Chapter Exercises
		Concept Questions
		Practice Exercises
		Exercises
		Projects
13 Special Types of Regression
	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
		Practice Exercises
		Exercises
		Projects
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
		WARNING!!! DUMMY ENTRY
			The Randomization Approach for Example 14.3
	14.3 Two Independent Samples
		WARNING!!! DUMMY ENTRY
			Randomization Approach to Example 14.4
	14.4 More Than Two Samples
		WARNING!!! DUMMY ENTRY
			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
		Practice Exercises
		Exercises
		Projects
Appendix A Tables of Distributions
Appendix B
Appendix B A Brief Introduction to Matrices
	B.1 Matrix Algebra
	B.2 Solving Linear Equations
Appendix C Descriptions of Data Sets
	C.1 Florida Lake Data
	C.2 State Education Data
	C.3 National Atmospheric Deposition Program (NADP) Data
	C.4 Florida County Data
	C.5 Cowpea Data
	C.6 Jax House Prices Data
	C.7 Gainesville, FL, Weather Data
	C.8 General Social Survey (GSS) 2016 Data
Hints for Selected Exercises
	Chapter 1
		Practice Exercises
		Exercises
	Chapter 2
		Practice Exercises
		Exercises
	Chapter 3
		Practice Exercises
		Exercises
	Chapter 4
		Practice Exercises
		Exercises
	Chapter 5
		Practice Exercises
		Exercises
	Chapter 6
		Practice Exercises
		Exercises
	Chapter 7
		Practice Exercises
		Exercises
	Chapter 8
		Practice Exercises
		Exercises
	Chapter 9
		Practice Exercises
		Exercises
	Chapter 10
		Practice Exercises
		Exercises
	Chapter 11
		Practice Exercises
		Exercises
	Chapter 12
		Practice Exercises
		Exercises
	Chapter 13
		Practice Exercises
		Exercises
	Chapter 14
		Practice Exercises
		Exercises
References
Index