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Applied Statistics II
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Applied Statistics II
Multivariable and Multivariate Techniques

Third Edition
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January 2020 | 712 pages | SAGE Publications, Inc

Rebecca M. Warner’s bestselling Applied Statistics: From Bivariate Through Multivariate Techniques has been split into two volumes for ease of use over a two-course sequence. Applied Statistics II: Multivariable and Multivariate Techniques, Third Edition is a core multivariate statistics text based on chapters from the second half of the original book. 

The text begins with two new chapters: an introduction to the new statistics, and a chapter on handling outliers and missing values. All chapters on statistical control and multivariable or multivariate analyses from the previous edition are retained (with the moderation chapter heavily revised) and new chapters have been added on structural equation modeling, repeated measures, and on additional statistical techniques. Each chapter includes a complete example, and begins by considering the types of research questions that chapter’s technique can answer, progresses to data screening, and provides screen shots of SPSS menu selections and output, and concludes with sample results sections. By-hand computation is used, where possible, to show how elements of the output are related to each other, and to obtain confidence interval and effect size information when SPSS does not provide this. Datasets are available on the accompanying website.
  

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Applied Statistics II + Applied Statistics I: Basic Bivariate Techniques, Third Edition 
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Preface
 
Acknowledgments
 
About the Author
 
1. The New Statistics
Required Background

 
What Is the “New Statistics”?

 
Common Misinterpretations of p Values

 
Problems With NHST Logic

 
Common Misuses of NHST

 
The Replication Crisis

 
Some Proposed Remedies for Problems With NHST

 
Review of Confidence Intervals

 
Effect Size

 
Brief Introduction to Meta-Analysis

 
Recommendations for Better Research and Analysis

 
Summary

 
 
2. Advanced Data Screening: Outliers and Missing Values
Introduction

 
Variable Names and File Management

 
Sources of Bias

 
Screening Sample Data

 
Possible Remedy for Skewness: Nonlinear Data Transformations

 
Identification of Outliers

 
Handling Outliers

 
Testing Linearity Assumptions

 
Evaluation of Other Assumptions Specific to Analyses

 
Describing Amount of Missing Data

 
How Missing Data Arise

 
Patterns in Missing Data

 
Empirical Example: Detecting Type a Missingness

 
Possible Remedies for Missing Data

 
Empirical Example: Multiple Imputation to Replace Missing Values

 
Data Screening Checklist

 
Reporting Guidelines

 
Summary

 
Appendix 2A: Brief Note About Zero-Inflated Binomial or Poisson Regression

 
 
3. Statistical Control: What Can Happen When You Add a Third Variable?
What Is Statistical Control?

 
First Research Example: Controlling for a Categorical X2 Variable

 
Assumptions for Partial Correlation Between X1 and Y, Controlling for X2

 
Notation for Partial Correlation

 
Understanding Partial Correlation: Use of Bivariate Regressions to Remove Variance Predictable by X2 From Both X1 and Y

 
Partial Correlation Makes No Sense if There Is an X1 × X2 Interaction

 
Computation of Partial r From Bivariate Pearson Correlations

 
Significance Tests, Confidence Intervals, and Statistical Power for Partial Correlations

 
Comparing Outcomes for ry1.2 and ry1

 
Introduction to Path Models

 
Possible Paths Among X1, Y, and X2

 
One Possible Model: X1 and Y are Not Related Whether You Control for X2 or Not

 
Possible Model: Correlation Between X1 and Y is the Same Whether X2 Is Statistically Controlled or Not (X2 is Irrelevant to the X1, Y Relationship)

 
When You Control for X2, Correlation Between X1 and Y Drops to Zero

 
When You Control for X2, the Correlation Between X1 and Y Becomes Smaller (But Does not Drop to 0 or Change Sign)

 
Some Forms of Suppression: When You Control for X2, r1y.2 Becomes Larger Than r1y or Opposite in Sign to r1y

 
“None of the Above”

 
Results Section

 
Summary

 
 
4. Regression Analysis and Statistical Control
Introduction

 
Hypothetical Research Example

 
Graphic Representation of Regression Plane

 
Semipartial (or “Part”) Correlation

 
Partition of Variance In Y in Regression With Two Predictors

 
Assumptions for Regression With Two Predictors

 
Formulas for Regression With Two Predictors

 
SPSS Regression

 
Conceptual Basis: Factors That Affect the Magnitude and Sign of ß and b Coefficients in Multiple Regression With Two Predictors

 
Tracing Rules for Path Models

 
Comparison of Equations for ß, b, pr, and sr

 
Nature of Predictive Relationships

 
Effect Size Information in Regression with Two Predictors

 
Statistical Power

 
Issues in Planning a Study

 
Results

 
Summary

 
 
5. Multiple Regression With Multiple Predictors
Research Questions

 
Empirical Example

 
Screening for Violations of Assumptions

 
Issues in Planning a Study

 
Computation of Regression Coefficients with k Predictor Variables

 
Methods of Entry for Predictor Variables

 
Variance Partitioning in Standard Regression Versus Hierarchical and Statistical Regression

 
Significance Test for an Overall Regression Model

 
Significance Tests for Individual Predictors in Multiple Regression

 
Effect Size

 
Changes in F and R as Additional Predictors Are Added to a Model in Sequential or Statistical Regression

 
Statistical Power

 
Nature of the Relationship Between Each X Predictor and Y (Controlling for Other Predictors)

 
Assessment of Multivariate Outliers in Regression

 
SPSS Examples

 
Summary

 
Appendix 5A: Use of Matrix Algebra to Estimate Regression Coefficients for Multiple Predictors

 
Appendix 5B: Tables for Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Forward Statistical Regression

 
Appendix 5C: Confidence Interval for R2

 
 
6. Dummy Predictor Variables in Multiple Regression
What Dummy Variables Are and When They Are Used

 
Empirical Example

 
Screening for Violations of Assumptions

 
Issues in Planning a Study

 
Parameter Estimates and Significance Tests for Regressions With Dummy Predictor Variables

 
Group Mean Comparisons Using One-Way Between-S ANOVA

 
Three Methods of Coding for Dummy Variables

 
Regression Models That Include Both Dummy and Quantitative Predictor Variables

 
Effect Size and Statistical Power

 
Nature of the Relationship and/or Follow-Up Tests

 
Results

 
Summary

 
 
7. Moderation: Interaction in Multiple Regression
Terminology

 
Interaction Between Two Categorical Predictors: Factorial ANOVA

 
Interaction Between One Categorical and One Quantitative Predictor

 
Preliminary Data Screening: One Categorical and One Quantitative Predictor

 
Scatterplot for Preliminary Assessment of Possible Interaction Between Categorical and Quantitative Predictor

 
Regression to Assess Statistical Significance of Interaction Between One Categorical and One Quantitative Predictor

 
Interaction Analysis With More Than Three Categories

 
Example With Different Data: Significant Sex-by-Years Interaction

 
Follow-Up: Analysis of Simple Main Effects

 
Interaction Between Two Quantitative Predictors

 
SPSS Example of Interaction Between Two Quantitative Predictors

 
Results for Interaction of Age and Habits as Predictors of Symptoms

 
Graphing Interaction for Two Quantitative Predictors

 
Results Section for Interaction of Two Quantitative Predictors

 
Additional Issues and Summary

 
Appendix 7A: Graphing Interactions Between Quantitative Variables “by Hand”

 
 
8. Analysis of Covariance
Research Situations for Analysis of Covariance

 
Empirical Example

 
Screening for Violations of Assumptions

 
Variance Partitioning in ANCOVA

 
Issues in Planning a Study

 
Formulas for ANCOVA

 
Computation of Adjusted Effects and Adjusted Y * Means

 
Conceptual Basis: Factors That Affect the Magnitude of SSAadj and SSresidual and the Pattern of Adjusted Group Means

 
Effect Size

 
Statistical Power

 
Nature of the Relationship and Follow-Up Tests: Information to Include in the “Results” Section

 
SPSS Analysis and Model Results

 
Additional Discussion of ANCOVA Results

 
Summary

 
Appendix 8A: Alternative Methods for the Analysis of Pretest–Posttest Data

 
 
9. Mediation
Definition of Mediation

 
Hypothetical Research Example

 
Limitations of “Causal” Models

 
Questions in a Mediation Analysis

 
Issues in Designing a Mediation Analysis Study

 
Assumptions in Mediation Analysis and Preliminary Data Screening

 
Path Coefficient Estimation

 
Conceptual Issues: Assessment of Direct Versus Indirect Paths

 
Evaluating Statistical Significance

 
Effect Size Information

 
Sample Size and Statistical Power

 
Additional Examples of Mediation Models

 
Note About Use of Structural Equation Modeling Programs to Test Mediation Models

 
Results Section

 
Summary

 
 
10. Discriminant Analysis
Research Situations and Research Questions

 
Introduction to Empirical Example

 
Screening for Violations of Assumptions

 
Issues in Planning a Study

 
Equations for Discriminant Analysis

 
Conceptual Basis: Factors That Affect the Magnitude of Wilks’ Lambda

 
Effect Size

 
Statistical Power and Sample Size Recommendations

 
Follow-Up Tests to Assess What Pattern of Scores Best Differentiates Groups

 
Results

 
One-Way ANOVA on Scores on Discriminant Functions

 
Summary

 
Appendix 10A: The Eigenvalue/Eigenvector Problem

 
Appendix 10B: Additional Equations for Discriminant Analysis

 
 
11. Multivariate Analysis of Variance
Research Situations and Research Questions

 
First Research Example: One-Way MANOVA

 
Why Include Multiple Outcome Measures?

 
Equivalence of MANOVA and DA

 
The General Linear Model

 
Assumptions and Data Screening

 
Issues in Planning a Study

 
Conceptual Basis of MANOVA

 
Multivariate Test Statistics

 
Factors That Influence the Magnitude of Wilks’ Lambda

 
Effect Size for MANOVA

 
Statistical Power and Sample Size Decisions

 
One-Way MANOVA: Career Group Data

 
2 × 3 Factorial MANOVA: Career Group Data

 
Significant Interaction in a 3 × 6 MANOVA

 
Comparison of Univariate and Multivariate Follow-Up Analyses

 
Summary

 
 
12. Exploratory Factor Analysis
Research Situations

 
Path Model for Factor Analysis

 
Factor Analysis as a Method of Data Reduction

 
Introduction of Empirical Example

 
Screening for Violations of Assumptions

 
Issues in Planning a Factor-Analytic Study

 
Computation of Factor Loadings

 
Steps in the Computation of PC and Factor Analysis

 
Analysis 1: PC Analysis of Three Items Retaining All Three Components

 
Analysis 2: PC Analysis of Three Items Retaining Only the First Component

 
PC Versus PAF

 
Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation

 
Geometric Representation of Factor Rotation

 
Factor Analysis as Two Sets of Multiple Regressions

 
Analysis 4: PAF With Varimax Rotation

 
Questions to Address in the Interpretation of Factor Analysis

 
Results Section for Analysis 4: PAF With Varimax Rotation

 
Factor Scores Versus Unit-Weighted Composites

 
Summary of Issues in Factor Analysis

 
Appendix 12A: The Matrix Algebra of Factor Analysis

 
Appendix 12B: A Brief Introduction to Latent Variables in SEM

 
 
13. Reliability, Validity, and Multiple-Item Scales
Assessment of Measurement Quality

 
Cost and Invasiveness of Measurements

 
Empirical Examples of Reliability Assessment

 
Concepts from Classical Measurement Theory

 
Use of Multiple-Item Measures to Improve Measurement Reliability

 
Computation of Summated Scales

 
Assessment of Internal Homogeneity for Multiple-Item Measures: Cronbach’s Alpha Reliability Coefficient

 
Validity Assessment

 
Typical Scale Development Process

 
A Brief Note About Modern Measurement Theories

 
Reporting Reliability

 
Summary

 
Appendix 13A: The CES-D

 
Appendix 13B: Web Resources on Psychological Measurement

 
 
14. More About Repeated Measures
Introduction

 
Review of Assumptions for Repeated-Measures ANOVA

 
First Example: Heart Rate and Social Stress

 
Test for Participant-by-Time or Participant-by-Treatment Interaction

 
One-Way Repeated-Measures Results for Heart Rate and Social Stress Data

 
Testing the Sphericity Assumption

 
MANOVA for Repeated Measures

 
Results for Heart Rate and Social Stress Analysis Using MANOVA

 
Doubly Multivariate Repeated Measures

 
Mixed-Model ANOVA: Between-S and Within-S Factors

 
Order and Sequence Effects

 
First Example: Order Effect as a Nuisance

 
Second Example: Order Effect Is of Interest

 
Summary and Other Complex Designs

 
 
15. Structural Equation Modeling With AMOS: A Brief Introduction
What Is Structural Equation Modeling?

 
Review of Path Models

 
More Complex Path Models

 
First Example: Mediation Structural Model

 
Introduction to AMOS®

 
Screening and Preparing Data for SEM

 
Specifying the SEM Model (Variable Names and Paths)

 
Specify the Analysis Properties

 
Running the Analysis and Examining Results

 
Locating Bootstrapped CI Information

 
Sample Results for the Mediation Analysis

 
Selected SEM Model Terminology

 
SEM Goodness-of-Fit Indexes

 
Second Example: Confirmatory Factor Analysis

 
Third Example: Model With Both Measurement and Structural Components

 
Comparing Structural Equation Models

 
Reporting SEM

 
Summary

 
 
16. Binary Logistic Regression
Research Situations

 
First Example: Dog Ownership and Odds of Death

 
Conceptual Basis for Binary Logistic Regression Analysis

 
Definition and Interpretation of Odds

 
A New Type of Dependent Variable: The Logit

 
Terms Involved in Binary Logistic Regression Analysis

 
Logistic Regression for First Example: Prediction of Death From Dog Ownership

 
Issues in Planning and Conducting a Study

 
More Complex Models

 
Binary Logistic Regression for Second Example: Drug Dose and Sex as Predictors of Odds of Death

 
Comparison of Discriminant Analysis With Binary Logistic Regression

 
Summary

 
 
17. Additional Statistical Techniques
Introduction

 
A Brief History of Developments in Statistics

 
Survival Analysis

 
Cluster Analyses

 
Time-Series Analyses

 
Poisson and Binomial Regression for Zero-Inflated Count Data

 
Bayes’ Theorem

 
Multilevel Modeling

 
Some Final Words

 
 
Glossary
 
References
 
Index

Supplements

Instructor Teaching Site
study.sagepub.com/warner3e

Password-protected Instructor Resources include the following:
  • Editable, chapter-specific Microsoft® PowerPoint® slides offer you complete flexibility in easily creating a multimedia presentation for your course. 
  • Test banks in Word and LMS-ready formats provide a diverse range of pre-written options as well as the opportunity to edit any question and/or insert your own personalized questions to effectively assess students’ progress and understanding.
  • Tables and figures from the printed book are available in an easily-downloadable format for use in papers, hand-outs, and presentations.

Open-access Student Resources include flashcards and data sets provided by the author for student download to complete the in-chapter exercises. 

 

“Combined, these texts provide both simplistic explanations of analyses, and also in-depth exploration of them with examples. Thus, it proves to be a useful resource to beginning statistics students all the way through the dissertation level, and even for faculty conducting research.”

Karla Hamlen Mansour
Cleveland State University

“This book presents statistical complexity in a friendly and uncomplicated way with friendly text and plenty of helpful diagrams and tables.”

Beverley Hale
University of Chichester, U.K.

“Well-written, comprehensive statistics book. A very valuable resource for advanced undergraduate and graduate students.”

Dan Ispas
Illinois State University

“Warner's textbook is ideal for graduate or advanced undergraduate students providing extensive, yet highly accessible, coverage of important issues in fundamental research design and statistical analysis and newer recommendations in how to conduct statistical analysis and report results ethically. She writes extremely well and my students find her book very readable and useful.”

Paul F. Tremblay
University of Western Ontario

“Rebecca Warner has made a great book even better with the addition of new chapters covering advanced topics (data screening) and procedures (Structural Equation Modeling). Using the same clear, organized format of earlier editions, Warner provides the reader with the newest and most pertinent topics in the field, along, of course, with the tried and true forms of analysis. The new edition is truly comprehensive, and will well serve the vast majority of undergraduate and graduate students who require a solid introduction to statistical thinking and analysis.”

Barry Trunk
Capella University

“The book is well-written and focuses on practical applications of the concepts rather than typical ‘textbook’ applications. The focus on meaning rather than the mechanics of computation is also a strength.”

Linda M. Bajdo
Wayne State University
Key features
NEW TO THIS EDITION:
  • Extensive coverage of outliers and missing values are included due to increasing concerns about transparency in data reporting. Authors are now required to document and justify decisions about identification and handling of outliers, and about the amount and pattern of missing data. Multiple imputation of missing score values is now expected by many reviewers.
  • Added material about repeated measures such as factorial designs, evaluation of violations of assumptions, MANOVA approach, and order effects fills a gap left by many comparable textbooks.
  • Introduction to Structural Equation Modeling (SEM) using AMOS combines latent variables, measurement models and structural models for a valuable bridge to more complex latent variable analyses.
  • Brief Introductions to Survival Analysis, Cluster Analyses, Time Series Analyses, Poisson and Zero-Inflated Regression for Count Data, Bayes’ Theorem, and Multilevel Modeling help students ‘see outside the box’ and think about different research questions.

KEY FEATURES:

 

  • A beginning chapter on the New Statistics helps students understand the limitations of significance tests, the need to report effect sizes and confidence intervals, and the use of meta-analysis to summarize effect size information across studies
  • Chapter 3 introduces ‘adding a third variable’ to provide a strong foundation in statistical control and bridges the gap between introductory and multivariable statistics and multivariate techniques.
  • The text helps students deal with the “messiness” of real-world data by providing methods to screen for multivariate outliers, evaluate amount and pattern of missing data, and replace missing scores by multiple imputation.
  • Each chapter utilizes a complete example. Chapters begin with questions a technique can answer, progress to data screening, screen shots of SPSS menu selections and output; and conclude with sample results sections. By-hand computation is used, where possible, to show how elements of the output are related to each other and to obtain confidence interval and effect size information when SPSS does not provide this.

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