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Applied Statistics II

Applied Statistics II
Multivariable and Multivariate Techniques

Third Edition

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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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


2. Advanced Data Screening: Outliers and Missing Values

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


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


4. Regression Analysis and Statistical Control

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



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


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



7. Moderation: Interaction in Multiple Regression

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


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


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


One-Way ANOVA on Scores on Discriminant Functions


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


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


Appendix 13A: The CES-D

Appendix 13B: Web Resources on Psychological Measurement

14. More About Repeated Measures

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


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


17. Additional Statistical Techniques

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



Instructor Teaching Site

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

E-library is too hard to assess book. Not a good sign for eLearning. Likely too challenging for my undergrads.

Dr Andrew Joseph Evelo
Dept Psychology, University of Waikato - Hamilton Campus
August 30, 2023
Key features
  • 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.



  • 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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