Statistical Methods

Statistical Methods

2nd Edition - January 7, 2003

Write a review

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

Purchase options

Purchase options
DRM-free (PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order

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

Readership

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

Table of Contents

  • 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
    Comments
    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
    Comments
    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
    Additional Considerations
    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
    Additional Topics
    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
    Additional Topics in 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 ÷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
  • Copyright: © Academic Press 2003
  • Published: January 7, 2003
  • Imprint: Academic Press
  • eBook ISBN: 9780080498225

About the Authors

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

Ratings and Reviews

Write a review

There are currently no reviews for "Statistical Methods"