# Applied Statistics From Bivariate Through Multivariate Techniques

## Edition: 2007

### Authors: Rebecca M. Warner

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### Description:

This textbook provides a clear introduction to widely used topics in bivariate and??multivariate statistics, including multiple regression, discriminant analysis, MANOVA, factor analysis, and binary logistic regression. The approach is applied and does not require formal mathematics; equations are accompanied by verbal explanations. Students are asked to think about the meaning of equations. For example, "How do researchers' decisions about treatment dosage levels and sample size tend to influence the magnitude of??t and F ratios?" Each chapter presents a complete empirical research example to illustrate the application of a specific method, such as multiple regression. Although SPSS examples are used throughout the book, the conceptual material will be helpful for users of different programs. Each chapter has a glossary and comprehension questions. The robust ancillaries include??datasets in SPSS and??Excel; answers to all comprehension questions; Microsoft(R) PowerPoint?? slides for each chapter; a listing of useful Web sites; and more.?? Visit www.sagepub.com/warnerstudy??for more information.Key Features: The text begins with a clear review and a fresh perspective on concepts including effect size, variance partitioning, and statistical control. Depending on student background and the level of the course, instructors can begin with chapters that review basic material, or they can begin with more advanced topics and use earlier chapters as supplemental review material.Chapters 10 through 13 examine three variable research situations in detail and teach students how to think about statistical control: How does the nature and strength of the association between an??X1 predictorvariable and a Y outcome variable change when we statistically control for another (X2) variable? This understanding of statistical control is essential for comprehension of multivariate analyses.The book includes a chapter on reliability, validity, and multiple item scales, and draws extensively on path models to illustrate theories about possible causal and non-causal associations among variables, beginning with simple three variable research situations.Graphics are used to explain concepts such as variance partitioning, statistical control, and factor rotation.A glossary and extensive practice exercises help readers to digest the material presented. ??
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### Book details

List price: \$111.00
Publisher: SAGE Publications, Incorporated
Publication date: 9/6/2007
Binding: Hardcover
Pages: 1128
Size: 7.00" wide x 10.00" long x 1.75" tall
Weight: 3.828

Rebecca M. Warner received a B.A. from Carnegie-Mellon University in Social Relations in 1973 and a Ph.D. in Social Psychology from Harvard in 1978. She has taught statistics for more than 25 years: from Introductory and Intermediate Statistics to advanced topics seminars in Multivariate Statistics, Structural Equation Modeling, and Time Series Analysis. She is currently a Full Professor in the Department of Psychology at the University of New Hampshire. She is a Fellow in the Association for Psychological Science and a member of the American Psychological Association, the International Association for Relationships Research, the Society of Experimental Social Psychology, and the Society for Personality and Social Psychology. She has consulted on statistics and data management for the World Health Organization in Geneva and served as a visiting faculty member at Shandong Medical University in China.

 Preface Acknowledgments Review of Basic Concepts Introduction A Simple Example of a Research Problem Discrepancies Between Real and Ideal Research Situations Samples and Populations Descriptive Versus Inferential Uses of Statistics Levels of Measurement and Types of Variables The Normal Distribution Research Design Parametric Versus Nonparametric Statistics Additional Implicit Assumptions Selection of an Appropriate Bivariate Analysis Summary Comprehension Questions Introduction to SPSS: Basic Statistics, Sampling Error, and Confidence Intervals Introduction Research Example: Description of a Sample of HR Scores Sample Mean (M) Sum of Squared Deviations and Sample Variance (s2) Degrees of Freedom (df) for a Sample Variance Why Is There Variance? Sample Standard Deviation (s) Assessment of Location of a Single X Score Relative to a Distribution of Scores A Shift in Level of Analysis: The Distribution of Values of M Across Many Samples From the Same Population An Index of Amount of Sampling Error: The Standard Error of the Mean (oM) Effect of Sample Size (N) on the Magnitude of the Standard Error (oM ) Sample Estimate of the Standard Error of the Mean (SEM) The Family of t Distributions Confidence Intervals Summary Appendix on SPSS Comprehension Questions Statistical Significance Testing The Logic of Null Hypothesis Significance Testing (NHST) Type I Versus Type II Error Formal NHST Procedures: The z Test for a Null Hypothesis About One Population Mean Common Research Practices Inconsistent With Assumptions and Rules for NHST Strategies to Limit Risk of Type I Error Interpretation of Results When Is a t Test Used Instead of a z Test? Effect Size Statistical Power Analysis Numerical Results for a One-Sample t Test Obtained From SPSS Guidelines for Reporting Results Summary Comprehension Questions Preliminary Data Screening Introduction: Problems in Real Data Quality Control During Data Collection Example of an SPSS Data Worksheet Identification of Errors and Inconsistencies Missing Values Empirical Example of Data Screening for Individual Variables Identification and Handling of Outliers Screening Data for Bivariate Analyses Nonlinear Relations Data Transformations Verifying That Remedies Had the Desired Effects Multivariate Data Screening Reporting Preliminary Data Screening Summary and Checklist for Data Screening Comprehension Questions Comparing Group Means Using the Independent Samples t Test Research Situations Where the Independent Samples t Test Is Used A Hypothetical Research Example Assumptions About the Distribution of Scores on the Quantitative Dependent Variable Preliminary Data Screening Issues in Designing a Study Formulas for the Independent Samples t Test Conceptual Basis: Factors That Affect the Size of the t Ratio Effect Size Indexes for t Statistical Power and Decisions About Sample Size for the Independent Samples t Test Describing the Nature of the Outcome SPSS Output and Model Results Section Summary Comprehension Questions One-Way Between-Subjects Analysis of Variance Research Situations Where One-Way Between-Subjects Analysis of Variance (ANOVA) Is Used Hypothetical Research Example Assumptions About Scores on the Dependent Variable for One-Way Between-S ANOVA Issues in Planning a Study Data Screening Partition of Scores Into Components Computations for the One-Way Between-S ANOVA Effect Size Index for One-Way Between-S ANOVA Statistical Power Analysis for One-Way Between-S ANOVA Nature of Differences Among Group Means SPSS Output and Model Results Summary Comprehension Questions Bivariate Pearson Correlation Research Situations Where Pearson r Is Used Hypothetical Research Example Assumptions for Pearson r Preliminary Data Screening Design Issues in Planning Correlation Research Computation of Pearson r Statistical Significance Tests for Pearson r Setting Up CIs for Correlations Factors That Influence the Magnitude and Sign of Pearson r Pearson r and r2 as Effect Size Indexes Statistical Power and Sample Size for Correlation Studies Interpretation of Outcomes for Pearson r SPSS Output and Model Results Write-Up Summary Comprehension Questions Alternative Correlation Coefficients Correlations for Different Types of Variables Two Research Examples Correlations for Rank or Ordinal Scores Correlations for True Dichotomies Correlations for Artificially Dichotomized Variables Assumptions and Data Screening for Dichotomous Variables Analysis of Data: Dog Ownership and Survival After a Heart Attack Chi-Square Test of Association (Computational Methods for Tables of Any Size) Other Measures of Association for Contingency Tables SPSS Output and Model Results Write-Up Summary Comprehension Questions Bivariate Regression Research Situations Where Bivariate Regression Is Used A Research Example: Prediction of Salary From Years of Job Experience Assumptions and Data Screening Issues in Planning a Bivariate Regression Study Formulas for Bivariate Regression Statistical Significance Tests for Bivariate Regression Setting Up Confidence Intervals Around Regression Coefficients Factors That Influence the Magnitude and Sign of b Effect Size/Partition of Variance in Bivariate Regression Statistical Power Raw Score Versus Standard Score Versions of the Regression Equation Removing the Influence of X From the Y Variable by Looking at Residuals From Bivariate Regression Empirical Example Using SPSS Summary Comprehension Questions Adding a Third Variable: Preliminary Exploratory Analyses Three-Variable Research Situations First Research Example Exploratory Statistical Analyses for Three-Variable Research Situations Separate Analysis of X1, Y Relationship for Each Level of the Control Variable X2 Partial Correlation Between X1 and Y Controlling for X2 Understanding Partial Correlation as the Use of Bivariate Regression to Remove Variance Predictable by X2 From Both X1 and Y Computation of Partial r From Bivariate Pearson Correlations Intuitive Approach to Understanding Partial r Significance Tests, Confidence Intervals, and Statistical Power for Partial Correlations Interpretation of Various Outcomes for rY1.2 and rY1 Two-Variable Causal Models Three-Variable Models: Some Possible Patterns of Association Among X1, Y, and X2 Mediation Versus Moderation Model Results Summary Comprehension Questions Multiple Regression With Two Predictor Variables Research Situations Involving Regression With Two Predictor Variables Hypothetical Research Example Graphic Representation of Regression Plane Semipartial (or "Part") Correlation Graphic Representation of Partition of Variance in Regression With Two Predictors Assumptions for Regression With Two Predictors Formulas for Regression Coefficients, Significance Tests, and Confidence Intervals SPSS Regression Results Conceptual Basis: Factors That Affect the Magnitude and Sign of B and b Coefficients in Multiple Regression With Two Predictors Tracing Rules for Causal Model Path Diagrams Comparison of Equations for B, b, pr, and sr Nature of Predictive Relationships Effect Size Information in Regression With Two Predictors Statistical Power Issues in Planning a Study Use of Regression With Two Predictors to Test Mediated Causal Models Results Summary Comprehension Questions Dummy Predictor Variables and Interaction Terms in Multiple Regression Research Situations Where Dummy Predictor Variables Can Be Used Empirical Example Screening for Violations of Assumptions Issues in Planning a Study Parameter Estimates and Significance Tests for Regressions With Dummy 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 Tests for Interaction (or Moderation) Interaction Terms That Involve Two Quantitative Predictors Effect Size and Statistical Power Nature of the Relationship and/or Follow-Up Tests Results Summary Comprehension Questions Factorial Analysis of Variance Research Situations and Research Questions Screening for Violations of Assumptions Issues in Planning a Study Empirical Example: Description of Hypothetical Data Computations for Between-S Factorial ANOVA Conceptual Basis: Factors That Affect the Size of Sums of Squares and F Ratios in Factorial ANOVA Effect Size Estimates for Factorial ANOVA Statistical Power Nature of the Relationships, Follow-Up Tests, and Information to Include in the Results Factorial ANOVA Using the SPSS GLM Procedure Summary Appendix: Nonorthogonal Factorial ANOVA (ANOVA With Unbalanced Numbers of Cases in the Cells or Groups) Comprehension Questions Multiple Regression With More Than Two 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 Regression for Standard or Simultaneous Regression Versus Regressions That Involve a Series of Steps 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 Example and Results Summary A Review of Matrix Algebra Notation and Operations and Application of Matrix Algebra to Estimation of Slope Coefficients for Regression With More Than k Predictor Variables Tables for Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Method = Forward Statistical Regression Comprehension Questions Analysis of Covariance Research Situations and Research Questions 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: Alternative Methods for the Analysis of Pretest/Posttest Data Comprehension Questions Discriminant Analysis Research Situations and Research Questions Introduction of an 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's 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: Eigenvalue/Eigenvector Problem Comprehension Questions Multivariate Analysis of Variance Research Situations and Research Questions Introduction of the Initial Research Example: A 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 and Some Formulas for MANOVA Multivariate Test Statistics Factors That Influence the Magnitude of Wilks's Lambda Effect Size for MANOVA Statistical Power and Sample Size Decisions SPSS Output for a One-Way MANOVA: Career Group Data From Chapter 16 A 2 x 3 Factorial MANOVA of the Career Group Data A Significant Interaction in a 3 x 6 MANOVA Comparison of Univariate and Multivariate Follow-Up Analyses for MANOVA Summary Comprehension Questions Principal Components and Factor Analysis Research Situations Path Model for Factor Analysis Factor Analysis as a Method of Data Reduction Introduction of an Empirical Example Screening for Violations of Assumptions Issues in Planning a Factor Analytic Study Computation of Loadings Steps in the Computation of Principal Components or Factor Analysis Analysis 1: Principal Components Analysis of Three Items Retaining All Three Components Analysis 2: Principal Component Analysis of Three Items Retaining Only the First Component Principal Components Versus Principal Axis Factoring Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation Geometric Representation of Correlations Between Variables and Correlations Between Components or Factors The Two 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 Optional: Brief Introduction to Concepts in Structural Equation Modeling Appendix: The Matrix Algebra of Factor Analysis Comprehension Questions 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 Three Methods for the Computation of Summated Scales Assessment of Internal Homogeneity for Multiple-Item Measures Correlations Among Scores Obtained Using Different Methods of Summing Items Validity Assessment Typical Scale Development Study Summary Appendix: The CESD Scale Comprehension Questions Analysis of Repeated Measures Introduction Empirical Example: Experiment to Assess Effect of Stress on Heart Rate Discussion of Sources of Within-Group Error in Between-S Versus Within-S Data The Conceptual Basis for the Paired Samples t Test and One-Way Repeated Measures ANOVA Computation of a Paired Samples t Test to Compare Mean HR Between Baseline and Pain Conditions SPSS Example: Analysis of Stress/HR Data Using a Paired Samples t Test Comparison Between Independent Samples t Test and Paired Samples t Test SPSS Example: Analysis of Stress/HR Data Using a Univariate One-Way Repeated Measures ANOVA Using the SPSS GLM Procedure for Repeated Measures ANOVA Screening for Violations of Assumptions in Univariate Repeated Measures The Greenhouse-Geisser e and Huynh Feldt e Correction Factors MANOVA Approach to Analysis of Repeated Measures Data Effect Size Statistical Power Planned Contrasts Results Design Problems in Repeated Measures Studies More Complex Designs Alternative Analyses for Pretest and Posttest Scores Summary Comprehension Questions Binary Logistic Regression Research Situations Simple Empirical 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 Analysis of Data for First Empirical Example: Dog Ownership/Death Study Issues in Planning and Conducting a Study More Complex Models Binary Logistic Regression for Second Empirical Analysis: Drug Dose and Gender as Predictors of Odds of Death Comparison of Discriminant Analysis to Binary Logistic Regression Summary Comprehension Questions Proportions of Area Under Standard Normal Curve Critical Values for t Distribution Critical Values of F Critical Values of Chi-Square Critical Values of the Correlation Coefficient Critical Values of the Studentized Range Statistic Transformation of r (Pearson Correlation) to Fisher Z Glossary References Index About the Author
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