Applied Statistics : From Bivariate Through Multivariate Techniques

by Rebecca M. Warner

• ISBN13: 9780761927723
• ISBN10: 0761927727
• Format: Hardcover
• Copyright: 2007-09-06
• Publisher: SAGE Publications, Inc

Summary

a??This is an excellent treatment of a complex subject. [Warner] has done a great job of making the ideas as clear and accessible as possible.a??A a?? W. James Potter, University of California at Santa Barbara a??I very much like the authora??s style of writinga??she explains complex concepts in simple and accessible language.a?? a??Ruth Childs, University of Toronto, Canada a??The book is easy to read. The author provides excellent practical advice, including the benefits and consequences of different statistical methods, as well as useful APA guidelines for research reports.a?? a??Patrick Leung, University of Houston Applied Statistics: From Bivariate Through Multivariate TechniquesA provides a clear introduction to widely used topics in bivariate andA 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 ofA 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 includeA datasets in SPSS andA Excel; answers to all comprehension questions; Microsoft PowerPointA? slides for each chapter; a listing of useful Web sites; and more.A Visit www.sagepub.com/warnerstudy A for more information. Key Features: 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. Examines three-variable research situations in detail and teaches students how to think about statistical control, which is essential for comprehension of multivariate analyses. Includes a chapter on reliability, validity, and multiple item scales, and draws extensively on path models to illustrate theories about possible causal and noncausal associations among variables, beginning with simple three-variable research situations. Utilizes graphics to explain concepts such as variance partitioning, statistical control, and factor rotation. Contains a glossary and extensive practice exercises to help readers digest the material presented. A

Table of Contents

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

Table of Contents provided by Ingram. All Rights Reserved.