 # Statistical Methods

2nd Edition - January 7, 2003

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• Authors: Rudolf Freund, William Wilson
• eBook ISBN: 9780080498225

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## 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.

## Key Features

* Provides a complete discussion of analysis of data including estimation, diagnostics, and remedial actions
* Examples contain graphical illustration for ease of interpretation
* Intended for use with almost any statistical software
* Examples are worked to a logical conclusion, including interpretation of results
* A complete Instructor's Manual is available to adopters

Reference for researchers and practitioners in engineering, business, social sciences or agriculture.

• Contents
Preface
1 DATA AND STATISTICS
1.1 Introduction
Data Sources
Using the Computer
1.2 Observations and Variables
1.3 Types of Measurements for Variables
1.4 Distributions
Graphical Representation of Distributions
1.5 Numerical Descriptive Statistics
Location
Dispersion
Other Measures
Computing the Mean and Standard Deviation
from a Frequency Distribution
Change of Scale
1.6 Exploratory Data Analysis
The Stem and Leaf Plot
The Box Plot
1.7 Bivariate Data
Categorical Variables
Categorical and Interval Variables
Interval Variables
1.8 Populations, Samples, and Statistical Inference — A Preview
1.9 Chapter Summary
Summary
1.10 Chapter Exercises
Concept Questions
Practice Exercises
Exercises
2 PROBABILITY AND SAMPLING DISTRIBUTIONS
2.1 Introduction
Chapter Preview
2.2 Probability
Definitions and Concepts
System Reliability
Random Variables
2.3 Discrete Probability Distributions
Properties of Discrete Probability Distributions
Descriptive Measures for Probability Distributions
The Discrete Uniform Distribution
The Binomial Distribution
The Poisson Distribution
2.4 Continuous Probability Distributions
Characteristics of a Continuous Probability Distribution
The Continuous Uniform Distribution
The Normal Distribution
Calculating Probabilities Using the Table
of the Normal Distribution
2.5 Sampling Distributions
Sampling Distribution of the Mean
Usefulness of the Sampling Distribution
Sampling Distribution of a Proportion
2.6 Other Sampling Distributions
The ÷2 Distribution
Distribution of the Sample Variance
The t Distribution
Using the t Distribution
The F Distribution
Using of the F Distribution
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
General Considerations
The Hypotheses
Rules for Making Decisions
Possible Errors in Hypothesis Testing
Probabilities of Making Errors
The Trade-off between á and â
Five-Step Procedure for Hypothesis Testing
Why Do We Focus on the Type I Error?
The Trade-off between á and â
The Five Steps for Example 3.3
P Values
Type II Error and Power
Power
Uniformly Most Powerful Tests
One-Tailed Hypothesis Tests
3.3 Estimation
Interpreting the Confidence Coefficient
Relationship between Hypothesis Testing
and Confidence Intervals
3.4 Sample Size
3.5 Assumptions
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
Hypothesis Test on µ
Estimation of µ
Sample Size
Degrees of Freedom
4.3 Inferences on a Proportion
Hypothesis Test on p
Estimation of p
Sample Size
4.4 Inferences on the Variance of One Population
Hypothesis Test on ó2
Estimation of ó2
4.5 Assumptions
Required Assumptions and Sources of Violations
Prevention of Violations
Detection of Violations
Tests for Normality
If Assumptions Fail
Alternate Methodology
4.6 Chapter Summary
4.7 Chapter Exercises
Concept Questions
Practice Exercises
Exercises
5 INFERENCES FOR TWO POPULATIONS
5.1 Introduction
5.2 Inferences on the Difference between Means
Using Independent Samples
Sampling Distribution of a Linear Function
of Random Variables
The Sampling Distribution of the Difference
between Two Means
Variances Known
Variances UnKnown but Assumed Equal
The Pooled Variance Estimate
The "Pooled" t Test
Variances Unknown but Not Equal
5.3 Inferences on Variances
5.4 Inferences on Means for Dependent Samples
5.5 Inferences on Proportions
Comparing Proportions Using Independent Samples
Comparing Proportions Using Paired Samples
5.6 Assumptions and Remedial Methods
5.7 Chapter Summary
5.8 Chapter Exercises
Concept Questions
Practice Exercises
Exercises
6 INFERENCES FOR TWO OR MORE MEANS
6.1 Introduction
Using the Computer
6.2 The Analysis of Variance
Notation and Definitions
Heuristic Justification for the Analysis of Variance
Computational Formulas and the Partitioning
of Sums of Squares
The Sum of Squares among Means
The Sum of Squares within Groups
The Ratio of Variances
Partitioning of the Sums of Squares
6.3 The Linear Model
The Linear Model for a Single Population
The Linear Model for Several Populations
The Analysis of Variance Model
Fixed and Random Effects Model
The Hypotheses
Expected Mean Squares
Notes on Exercises
6.4 Assumptions
Assumptions Required
Detection of Violated Assumptions
The Hartley F-Max Test
Violated Assumptions
Variance Stabilizing Transformations
Notes on Exercises
6.5 Specific Comparisons
Contrasts
Orthogonal Contrasts
Fitting Trends
Lack of Fit Test
Notes on Exercises
Computer Hint
Post Hoc Comparisons
Confidence Intervals
6.6 Random Models
6.7 Unequal Sample Sizes
6.8 Analysis of Means
ANOM for Proportions
Analysis of Means for Count Data
6.9 Chapter Summary
6.10 Chapter Exercises
Concept Questions
Exercises
7 LINEAR REGRESSION
7.1 Introduction
Notes on Exercises
7.2 The Regression Model
7.3 Estimation of Parameters â0 and â1
A Note on Least Squares
7.4 Estimation of ó2 and the Partitioning of Sums of Squares
7.5 Inferences for Regression
The Analysis of Variance Test for â1
The (Equivalent) t Test for â1
Confidence Interval for â1
Inferences on the Response Variable
7.6 Using the Computer
7.7 Correlation
7.8 Regression Diagnostics
7.9 Chapter Summary
7.10 Chapter Exercises
Concept Questions
Exercises
8 MULTIPLE REGRESSION
Notes on Exercises
8.1 The Multiple Regression Model
The Partial Regression Coefficient
8.2 Estimation of Coefficients
Simple Linear Regression with Matrices
Estimating the Parameters of a Multiple Regression Model
Correcting for the Mean, an Alternative Calculating Method
8.3 Inferential Procedures
Estimation of ó2 and the Partitioning of the Sums of Squares
The Coefficient of Variation
Inferences for Coefficients
Tests Normally Provided by Computer Outputs
The Equivalent t Statistic for Individual Coefficients
Inferences on the Response Variable
8.4 Correlations
Multiple Correlation
How Useful is the R2 Statistic?
Partial Correlation
8.5 Using the Computer
8.6 Special Models
The Polynomial Model
The Multiplicative Model
Nonlinear Models
8.7 Multicollinearity
Redefining Variables
Other Methods
8.8 Variable Selection
Other Selection Procedures
8.9 Detection of Outliers, Row Diagnostics
8.10 Chapter Summary
8.11 Chapter Exercises
Concept Questions
Exercises
9 FACTORIAL EXPERIMENTS
9.1 Introduction
9.2 Concepts and Definitions
9.3 The Two-Factor Factorial Experiment
The Linear Model
Notation
Computations for the Analysis of Variance
Between Cells Analysis
The Factorial Analysis
Expected Mean Squares
Notes on Exercises
9.4 Specific Comparisons
Preplanned Contrasts
Computing Contrast Sums of Squares
Polynomial Responses
Lack of Fit Test
Multiple Comparisons
9.5 No Replications
9.6 Three or More Factors
9.7 Chapter Summary
9.8 Chapter Exercises
Exercises
10 DESIGN OF EXPERIMENTS
10.1 Introduction
Notes on Exercises
10.2 The Randomized Block Design
The Linear Model
Relative Efficiency
Random Treatment Effects in the Randomized Block Design
10.3 Randomized Blocks with Sampling
10.4 Latin Square Design
10.5 Other Designs
Factorial Experiments in a Randomized Block Design
Nested Designs
Split Plot Designs
10.6 Chapter Summary
10.7 Chapter Exercises
Exercises
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
Analysis of Covariance
Multiple Covariates
Unequal Slopes
11.6 Extensions to Other Models
11.7 Binary Response Variables
Linear Model with a Dichotomous Dependent Variable
Weighted Least Squares
Logistic Regression
Other Methods
11.8 Chapter Summary
An Example of Extremely Unbalanced Data
Chapter Summary
11.9 Chapter Exercises
Exercises
12 CATEGORICAL DATA
12.1 Introduction
12.2 Hypothesis Tests for a Multinomial Population
12.3 Goodness of Fit Using the ÷2 Test
Test for a Discrete Distribution
Test for a Continuous Distribution
12.4 Contingency Tables
Computing the Test Statistic
Test for Homogeneity
Test for Independence
Measures of Dependence
Other Methods
12.5 Log linear Model
12.6 Chapter Summary
12.7 Chapter Exercises
Exercises
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
Exercises
14 SAMPLING AND SAMPLE SURVEYS
14.1 Introduction
14.2 Some Practical Considerations
14.3 Simple Random Sampling
Notation
Sampling Procedure
Estimation
Systematic Sampling
Sample Size
14.4 Stratified Sampling
Estimation
Sample Sizes
Efficiency
An Example
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 ÷2 Distribution—÷2 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 Exercises
REFERENCES
SOLUTIONS TO SELECTED EXERCISES
INDEX

## Product details

• No. of pages: 673
• Language: English
• Published: January 7, 2003
• eBook ISBN: 9780080498225

### Rudolf Freund

Rudolf J. Freund works at Texas A&M University in the USA.

#### Affiliations and Expertise

Texas A&M University, USA

### William Wilson

William J. Wilson works at University of North Florida in Jacksonville, FL, USA.

#### Affiliations and Expertise

University of North Florida, Jacksonville, FL, USA

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