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Concepts and Examples of Research
Concepts
Examples
Concluding Remarks
Classification of Variables and the Choice of Analysis
Classification of Variables
Overlapping of Classification Schemes
Choice of Analysis
Basic Statistics A Review
Preview
Descriptive Statistics
Random Variables and Distributions
Sampling Distributions of t, x, and F
Statistical Inference Estimation
Statistical Inference Hypothesis Testing
Error Rates, Power, and Sample Size
Problems
Introduction to Regression Analysis
Preview
Association versus Causality
Statistical versus Deterministic Models
Concluding Remarks
Straight-Line Regression Analysis
Preview
Regression with a Single Independent Variable
Mathematical Properties of a Straight Line
Statistical Assumptions for a Straight-Line Model
Determining the Best-Fitting Straight Line
Measure of the Quality of the Straight-Line Fit and Estimate of o
Inferences about the Slope and Intercept
Interpretations of Tests for Slope and Intercept
The Mean Value of Y at a Specified Value of X
Prediction of a New Value of Y at X
Assessing the Appropriateness of the Straight-Line Model
Example BRFSS Analysis
Problems
The Correlation Coefficient and Straight-Line Regression Analysis
Definition of r
r as a Measure of Association
The Bivariate Normal Distribution
r and the Strength of the Straight-Line Relationship
What r Does Not Measure
Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient
Testing for the Equality of Two Correlations
Example BRFSS Analysis
How Large Should r Be in Practice?
Problems
The Analysis-of-Variance Table
Preview
The ANOVA Table for Straight-Line Regression
Problems
Multiple Regression Analysis General Considerations
Preview
Multiple Regression Models
Graphical Look at the Problem
Assumptions of Multiple Regression
Determining the Best Estimate of the Multiple Regression Equation
The ANOVA Table for Multiple Regression
Example BRFSS Analysis
Numerical Examples
Problems
Statistical Inference in Multiple Regression
Preview
Test for Significant Overall Regression
Partial F Test
Multiple Partial F Test
Strategies for Using Partial F Tests
Additional Inference Methods for Multiple Regression
Example BRFSS Analysis
Problems
Correlations Multiple, Partial, and Multiple Partial
Preview
Correlation Matrix
Multiple Correlation Coefficient
Relationship of RY|X, X,, XK to the Multivariate Normal Distribution
Partial Correlation Coefficient
Alternative Representation of the Regression Model
Multiple Partial Correlation
Concluding Remarks
Problems
Confounding and Interaction in Regression
Preview
Overview
Interaction in Regression
Confounding in Regression
Summary and Conclusions
Problems
Dummy Variables in Regression
Preview
Definitions
Rule for Defining Dummy Variables
Comparing Two Straight-Line Regression Equations An Example
Questions for Comparing Two Straight Lines
Methods of Comparing Two Straight Lines
Method I Using Separate Regression Fits to Compare Two Straight Lines
Method II Using a Single Regression Equation to Compare Two Straight Lines
Comparison of Methods I and II
Testing Strategies and Interpretation Comparing Two Straight Lines
Other Dummy Variable Models
Comparing Four Regression Equations
Comparing Several Regression Equations Involving Two Nominal Variables
Problems
Analysis of Covariance and Other Methods for Adjusting Continuous Data
Preview
Adjustment Problem
Analysis of Covariance
Assumption of Parallelism A Potential Drawback
Analysis of Covariance Several Groups and Several Covariates
Analysis of Covariance Several Nominal Independent Variables
Comments and Cautions
Problems
Regression Diagnostics
Preview
Simple Approaches to Diagnosing Problems in Data
Residual Analysis Detecting Outliers and Violations of Model Assumptions
Strategies for Addressing Violations of Regression Assumptions
Collinearity
Diagnostics Example
Problems
Polynomial Regression
Preview
Polynomial Models
Least-Squares Procedure for Fitting a Parabola
ANOVA Table for Second-Order Polynomial Regression
Inferences Associated with Second-Order Polynomial Regression
Example Requiring a Second-Order Model
Fitting and Testing Higher-Order Models
Lack-of-Fit Tests
Orthogonal Polynomials
Strategies for Choosing a Polynomial Model
Problems
Selecting the Best Regression Equation
Preview
Steps in Selecting the Best Regression Equation Prediction Goal
Step Specifying the Maximum Model Prediction Goal
Step Specifying a Criterion for Selecting a Model Prediction Goal
Step Specifying a Strategy for Selecting Variables Prediction Goal
Step Conducting the Analysis Prediction Goal
Step Evaluating Reliability with Split Samples Prediction Goal
Example Analysis of Actual Data
Selecting the Most Valid Model
Problems
One-Way Analysis of Variance
Preview
One-Way ANOVA The Problem, Assumptions, and Data Configuration
Methodology for One-Way Fixed-Effects ANOVA
Regression Model for Fixed-Effects One-Way ANOVA
Fixed-Effects Model for One-Way ANOVA
Random-Effects Model for One-Way ANOVA
Multiple-Comparison Procedures for Fixed-Effects One-Way ANOVA
Choosing a Multiple-Comparison Technique
Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares
Problems
Randomized Blocks Special Case of Two-Way ANOVA
Preview
Equivalent Analysis of a Matched-Pairs Experiment
Principle of Blocking
Analysis of a Randomized-Blocks Study
ANOVA Table for a Randomized-Blocks Study
Regression Models for a Randomized-Blocks Study
Fixed-Effects ANOVA Model for a Randomized-Blocks Study
Problems
Two-Way ANOVA with Equal Cell Numbers
Preview
Using a Table of Cell Means
General Methodology
F Tests for Two-Way ANOVA
Regression Model for Fixed-Effects Two-Way ANOVA
Interactions in Two-Way ANOVA
Random- and Mixed-Effects Two-Way ANOVA Models
Problems
Two-Way ANOVA with Unequal Cell Numbers
Preview
Presentation of Data for Two-Way ANOVA Unequal Cell Numbers
Problem with Unequal Cell Numbers Nonorthogonality
Regression Approafor Unequal Cell Sample Sizes
Higher-Way ANOVA
Problems
The Method of Maximum Likelihood
Preview
The Principle of Maximum Likelihood
Statistical Inference Using Maximum Likelihood
Problems
Logistic Regression Analysis
Preview
The Logistic Model
Estimating the Odds Ratio Using Logistic Regression
A Numerical Example of Logistic Regression
Theoretical Considerations
An Example of Conditional ML Estimation Involving Pair-Matched Data with Unmatched Covariates
Problems
Polytomous and Ordinal Logistic Regression
Preview
Why Not Use Binary Regression?
An Example of Polytomous Logistic Regression One Predictor, Three Outcome Categories
An Example Extending the Polytomous Logistic Model to Several Predictors
Ordinal Logistic Regression Overview
A "Simple" Example Three Ordinal Categories and One Dichotomous Exposure Variable
Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables
Problems
Poisson Regression Analysis
Preview
The Poisson Distribution
An Example of Poisson Regression
Poisson Regression
Measures of Goodness of Fit
Continuation of Skin Cancer Data Example
A Second Illustration of Poisson Regression Analysis
Problems
Analysis of Correlated Data Part The General Linear Mixed Model
Preview
Examples
General Linear Mixed Model Approach
Example Study of Effects of an Air Pollution Episode on FEV Levels
Summary-Analysis of Correlated Data Part
Problems
Analysis of Correlated Data Part Random Effects and Other Issues
Preview
Random Effects Revisited
Results for Models with Random Effects Applied to Air Pollution Study Data
Second Example-Analysis of Posture Measurement Data
Recommendations about Choice of Correlation Structure
Analysis of Data for Discrete Outcomes
Problems
Sample Size Planning for Linear and Logistic Regression and Analysis of Variance
Preview
Review Sample Size Calculations for Comparisons of Means and Proportions
Sample Size Planning for Linear Regression
Sample Size Planning for Logistic Regression
Power and Sample Size Determination for Linear Models A General Approach
Sample Size Determination for Matched Case-Control Studies with a Dichotomous Outcome
Practical Considerations and Cautions
Problems
Appendix A Tables
Appendix B Matrices and Their Relationship to Regression Analysis
Appendix C SAS Computer Appendix
Appendix D Answers to Selected Problems