Dedication
Title
Copyright
Brief Contents
Detailed Contents
Preface
Acknowledgments
About the Author
Chapter 1. Review of Basic Concepts
1.1 Introduction
1.2 A Simple Example of a Research Problem
1.3 Discrepancies Between Real and Ideal Research Situations
1.4 Samples and Populations
1.5 Descriptive Versus Inferential Uses of Statistics
1.6 Levels of Measurement and Types of Variables
1.7 The Normal Distribution
1.8 Research Design
1.8.1 Experimental Design
1.8.2 Quasi-Experimental Design
1.8.3 Nonexperimental Research Design
1.8.4 Between-Subjects Versus Within-Subjects or Repeated Measures
1.9 Combinations of These Design Elements
1.10 Parametric Versus Nonparametric Statistics
1.11 Additional Implicit Assumptions
1.12 Selection of an Appropriate Bivariate Analysis
1.13 Summary
Comprehension Questions
Chapter 2. Basic Statistics, Sampling Error, and Confidence Intervals
2.1 Introduction
2.2 Research Example: Description of a Sample of HR Scores
2.3 Sample Mean (M)
2.4 Sum of Squared Deviations (SS) and Sample Variance (s2)
2.5 Degrees of Freedom (df) for a Sample Variance
2.6 Why Is There Variance?
2.7 Sample Standard Deviation (s)
2.8 Assessment of Location of a Single X Score Relative to a Distribution of Scores
2.9 A Shift in Level of Analysis: The Distribution of Values of M Across Many Samples From the Same Population
2.10 An Index of Amount of Sampling Error: The Standard Error of the Mean (σM)
2.11 Effect of Sample Size (N) on the Magnitude of the Standard Error (σM)
2.12 Sample Estimate of the Standard Error of the Mean (SEM)
2.13 The Family of t Distributions
2.14 Confidence Intervals
2.14.1 The General Form of a CI
2.14.2 Setting Up a CI for M When σ Is Known
2.14.3 Setting Up a CI for M When the Value of σ Is Not Known
2.14.4 Reporting CIs
2.15 Summary
Appendix on SPSS
Comprehension Questions
Chapter 3. Statistical Significance Testing
3.1 The Logic of Null Hypothesis Significance Testing (NHST)
3.2 Type I Versus Type II Error
3.3 Formal NHST Procedures: The z Test for a Null Hypothesis About One Population Mean
3.3.1 Obtaining a Random Sample From the Population of Interest
3.3.2 Formulating a Null Hypothesis (H0) for the One-Sample z Test
3.3.3 Formulating an Alternative Hypothesis (H1)
3.3.4 Choosing a Nominal Alpha Level
3.3.5 Determining the Range of z Scores Used to Reject H0
3.3.6 Determining the Range of Values of M Used to Reject H0
3.3.7 Reporting an “Exact” p Value
3.4 Common Research Practices Inconsistent With Assumptions and Rules for NHST
3.4.1 Use of Convenience Samples
3.4.2 Modification of Decision Rules After the Initial Decision
3.4.3 Conducting Large Numbers of Significance Tests
3.4.4 Impact of Violations of Assumptions on Risk of Type I Error
3.5 Strategies to Limit Risk of Type I Error
3.5.1 Use of Random and Representative Samples
3.5.2 Adherence to the Rules for NHST
3.5.3 Limit the Number of Significance Tests
3.5.4 Bonferroni-Corrected Per-Comparison Alpha Levels
3.5.5 Replication of Outcome in New Samples
3.5.6 Cross-Validation
3.6 Interpretation of Results
3.6.1 Interpretation of Null Results
3.6.2 Interpretation of Statistically Significant Results
3.7 When Is a t Test Used Instead of a z Test?
3.8 Effect Size
3.8.1 Evaluation of “Practical” (vs. Statistical) Significance
3.8.2 Formal Effect-Size Index: Cohen’s d
3.9 Statistical Power Analysis
3.10 Numerical Results for a One-Sample t Test Obtained From SPSS
3.11 Guidelines for Reporting Results
3.12 Summary
3.12.1 Logical Problems With NHST
3.12.2 Other Applications of the t Ratio
3.12.3 What Does It Mean to Say “p < .05”?
Comprehension Questions
Chapter 4. Preliminary Data Screening
4.1 Introduction: Problems in Real Data
4.2 Quality Control During Data Collection
4.3 Example of an SPSS Data Worksheet
4.4 Identification of Errors and Inconsistencies
4.5 Missing Values
4.6 Empirical Example of Data Screening for Individual Variables
4.6.1 Frequency Distribution Tables
4.6.2 Removal of Impossible or Extreme Scores
4.6.3 Bar Chart for a Categorical Variable
4.6.4 Histogram for a Quantitative Variable
4.7 Identification and Handling of Outliers
4.8 Screening Data for Bivariate Analyses
4.8.1 Bivariate Data Screening for Two Categorical Variables
4.8.2 Bivariate Data Screening for One Categorical and One Quantitative Variable
4.8.3 Bivariate Data Screening for Two Quantitative Variables
4.9 Nonlinear Relations
4.10 Data Transformations
4.11 Verifying That Remedies Had the Desired Effects
4.12 Multivariate Data Screening
4.13 Reporting Preliminary Data Screening
4.14 Summary and Checklist for Data Screening
4.15 Final Notes
Comprehension Questions
Chapter 5. Comparing Group Means Using the Independent Samples t Test
5.1 Research Situations Where the Independent Samples t Test Is Used
5.2 A Hypothetical Research Example
5.3 Assumptions About the Distribution of Scores on the Quantitative Dependent Variable
5.3.1 Quantitative, Approximately Normally Distributed
5.3.2 Equal Variances of Scores Across Groups (the Homogeneity of Variance Assumption)
5.3.3 Independent Observations Both Between and Within Groups
5.3.4 Robustness to Violations of Assumptions
5.4 Preliminary Data Screening
5.5 Issues in Designing a Study
5.6 Formulas for the Independent Samples t Test
5.6.1 The Pooled Variances t Test
5.6.2 Computation of the Separate Variances t Test and Its Adjusted df
5.6.3 Evaluation of Statistical Significance of a t Ratio
5.6.4 Confidence Interval Around M1 – M2
5.7 Conceptual Basis: Factors That Affect the Size of the t Ratio
5.7.1 Design Decisions That Affect the Difference Between Group Means, M1 – M2
5.7.2 Design Decisions That Affect Pooled Within-Group Variance, s2p
5.7.3 Design Decisions About Sample Sizes, n1 and n2
5.7.4 Summary: Factors That Influence the Size of t
5.8 Effect-Size Indexes for t
5.8.1 Eta Squared (η2)
5.8.2 Cohen’s d
5.8.3 Point Biserial r (rpb)
5.9 Statistical Power and Decisions About Sample Size for the Independent Samples t Test
5.10 Describing the Nature of the Outcome
5.11 SPSS Output and Model Results Section
5.12 Summary
Comprehension Questions
Chapter 6. One-Way Between-Subjects Analysis of Variance
6.1 Research Situations Where One-Way Between-Subjects Analysis of Variance (ANOVA) Is Used
6.2 Hypothetical Research Example
6.3 Assumptions About Scores on the Dependent Variable for One-Way Between-S ANOVA
6.4 Issues in Planning a Study
6.5 Data Screening
6.6 Partition of Scores Into Components
6.7 Computations for the One-Way Between-S ANOVA
6.7.1 Comparison Between the Independent Samples t Test and One-Way Between-S ANOVA
6.7.2 Summarizing Information About Distances Between Group Means: Computing MSbetween
6.7.3 Summarizing Information About Variability of Scores Within Groups: Computing MSwithin
6.7.4 The F Ratio: Comparing MSbetween With MSwithin
6.7.5 Patterns of Scores Related to the Magnitudes of MSbetween and MSwithin
6.7.6 Expected Value of F When H0 Is True
6.7.7 Confidence Intervals (CIs) for Group Means
6.8 Effect-Size Index for One-Way Between-S ANOVA
6.9 Statistical Power Analysis for One-Way Between-S ANOVA
6.10 Nature of Differences Among Group Means
6.10.1 Planned Contrasts
6.10.2 Post Hoc or “Protected” Tests
6.11 SPSS Output and Model Results
6.12 Summary
Comprehension Questions
Chapter 7. Bivariate Pearson Correlation
7.1 Research Situations Where Pearson’s r Is Used
7.2 Hypothetical Research Example
7.3 Assumptions for Pearson’s r
7.4 Preliminary Data Screening
7.5 Design Issues in Planning Correlation Research
7.6 Computation of Pearson’s r
7.7 Statistical Significance Tests for Pearson’s r
7.7.1 Testing the Hypothesis That ρXY = 0
7.7.2 Testing Other Hypotheses About ρXY
7.7.3 Assessing Differences Between Correlations
7.7.4 Reporting Many Correlations: Need to Control Inflated Risk of Type I Error
7.7.4.1 Limiting the Number of Correlations
7.7.4.2 Cross-Validation of Correlations
7.7.4.3 Bonferroni Procedure: A More Conservative Alpha Level for Tests of Individual Correlations
7.8 Setting Up CIs for Correlations
7.9 Factors That Influence the Magnitude and Sign of Pearson’s r
7.9.1 Pattern of Data Points in the X, Y Scatter Plot
7.9.2 Biased Sample Selection: Restricted Range or Extreme Groups
7.9.3 Correlations for Samples That Combine Groups
7.9.4 Control of Extraneous Variables
7.9.5 Disproportionate Influence by Bivariate Outliers
7.9.6 Shapes of Distributions of X and Y
7.9.7 Curvilinear Relations
7.9.8 Transformations of Data
7.9.9 Attenuation of Correlation Due to Unreliability of Measurement
7.9.10 Part-Whole Correlations
7.9.11 Aggregated Data
7.10 Pearson’s r and r2 as Effect-Size Indexes
7.11 Statistical Power and Sample Size for Correlation Studies
7.12 Interpretation of Outcomes for Pearson’s r
7.12.1 “Correlation Does Not Necessarily Imply Causation” (So What Does It Imply?)
7.12.2 Interpretation of Significant Pearson’s r Values
7.12.3 Interpretation of a Nonsignificant Pearson’s r Value
7.13 SPSS Output and Model Results Write-Up
7.14 Summary
Comprehension Questions
Chapter 8. Alternative Correlation Coefficients
8.1 Correlations for Different Types of Variables
8.2 Two Research Examples
8.3 Correlations for Rank or Ordinal Scores
8.4 Correlations for True Dichotomies
8.4.1 Point Biserial r (rpb)
8.4.2 Phi Coefficient (Φ)
8.5 Correlations for Artificially Dichotomized Variables
8.5.1 Biserial r (rb)
8.5.2 Tetrachoric r (rtet)
8.6 Assumptions and Data Screening for Dichotomous Variables
8.7 Analysis of Data: Dog Ownership and Survival After a Heart Attack
8.8 Chi-Square Test of Association (Computational Methods for Tables of Any Size)
8.9 Other Measures of Association for Contingency Tables
8.10 SPSS Output and Model Results Write-Up
8.11 Summary
Comprehension Questions
Chapter 9. Bivariate Regression
9.1 Research Situations Where Bivariate Regression Is Used
9.2 A Research Example: Prediction of Salary From Years of Job Experience
9.3 Assumptions and Data Screening
9.4 Issues in Planning a Bivariate Regression Study
9.5 Formulas for Bivariate Regression
9.6 Statistical Significance Tests for Bivariate Regression
9.7 Setting Up Confidence Intervals Around Regression Coefficients
9.8 Factors That Influence the Magnitude and Sign of b
9.8.1 Factors That Affect the Size of the b Coefficient
9.8.2 Comparison of Coefficients for Different Predictors or for Different Groups
9.9 Effect Size/Partition of Variance in Bivariate Regression
9.10 Statistical Power
9.11 Raw Score Versus Standard Score Versions of the Regression Equation
9.12 Removing the Influence of X From the Y Variable by Looking at Residuals From Bivariate Regression
9.13 Empirical Example Using SPSS
9.13.1 Information to Report From a Bivariate Regression
9.14 Summary
Comprehension Questions
Chapter 10. Adding a Third Variable: Preliminary Exploratory Analyses
10.1 Three-Variable Research Situations
10.2 First Research Example
10.3 Exploratory Statistical Analyses for Three-Variable Research Situations
10.4 Separate Analysis of the X1, Y Relationship for Each Level of the Control Variable X2
10.5 Partial Correlation Between X1 and Y, Controlling for X2
10.6 Understanding Partial Correlation as the Use of Bivariate Regression to Remove Variance Predictable by X2 From Both X1 and Y
10.7 Computation of Partial r From Bivariate Pearson Correlations
10.8 Intuitive Approach to Understanding Partial r
10.9 Significance Tests, Confidence Intervals, and Statistical Power for Partial Correlations
10.9.1 Statistical Significance of Partial r
10.9.2 Confidence Intervals for Partial r
10.9.3 Effect Size, Statistical Power, and Sample Size Guidelines for Partial r
10.10 Interpretation of Various Outcomes for rY1.2 and rY1
10.11 Two-Variable Causal Models
10.12 Three-Variable Models: Some Possible Patterns of Association Among X1, Y, and X2
10.12.1 X1 and Y Are Not Related Whether You Control for X2 or Not
10.12.2 X2 Is Irrelevant to the X1, Y Relationship
10.12.3 When You Control for X2, the X1, Y Correlation Drops to 0 or Close to 0
10.12.3.1 Completely Spurious Correlation
10.12.3.2 Completely Mediated Association Between X1 and Y
10.12.4 When You Control for X, the Correlation Between X2 and Y1 Becomes Smaller (but Does Not Drop to 0 and Does Not Change Sign)
10.12.4.1 X2 Partly Accounts for the X1, Y Association, or X1 and X2 Are Correlated Predictors of Y
10.12.4.2 X2 Partly Mediates the X1, Y Relationship
10.12.5 Suppression: When You Control for X2, the X1, Y Correlation Becomes Larger Than r1Y or Becomes Opposite in Sign Relative to r1Y
10.12.5.1 Suppression of Error Variance in a Predictor Variable
10.12.5.2 Sign of X1 as a Predictor of Y Reverses When Controlling for X2
10.12.5.3 Predictor Variables With Opposite Signs
10.12.6 “None of the Above”
10.13 Mediation Versus Moderation
10.13.1 Preliminary Analysis to Identify Possible Moderation
10.13.2 Preliminary Analysis to Detect Possible Mediation
10.13.3 Experimental Tests for Mediation Models
10.14 Model Results
10.15 Summary
Comprehension Questions
Chapter 11. Multiple Regression With Two Predictor Variables
11.1 Research Situations Involving Regression With Two Predictor Variables
11.2 Hypothetical Research Example
11.3 Graphic Representation of Regression Plane
11.4 Semipartial (or “Part”) Correlation
11.5 Graphic Representation of Partition of Variance in Regression With Two Predictors
11.6 Assumptions for Regression With Two Predictors
11.7 Formulas for Regression Coefficients, Significance Tests, and Confidence Intervals
11.7.1 Formulas for Standard Score Beta Coefficients
11.7.2 Formulas for Raw Score (b) Coefficients
11.7.3 Formula for Multiple R and Multiple R2
11.7.4 Test of Significance for Overall Regression: Overall F Test for H0: R = 0
11.7.5 Test of Significance for Each Individual Predictor: t Test for H0: bi = 0
11.7.6 Confidence Interval for Each b Slope Coefficient
11.8 SPSS Regression Results
11.9 Conceptual Basis: Factors That Affect the Magnitude and Sign of β and b Coefficients in Multiple Regression With Two Predictors
11.10 Tracing Rules for Causal Model Path Diagrams
11.11 Comparison of Equations for β, b, pr, and sr
11.12 Nature of Predictive Relationships
11.13 Effect-Size Information in Regression With Two Predictors
11.13.1 Effect Size for Overall Model
11.13.2 Effect Size for Individual Predictor Variables
11.14 Statistical Power
11.15 Issues in Planning a Study
11.15.1 Sample Size
11.15.2 Selection of Predictor Variables
11.15.3 Multicollinearity Among Predictors
11.15.4 Range of Scores
11.16 Results
11.17 Summary
Comprehension Questions
Chapter 12. Dummy Predictor Variables in Multiple Regression
12.1 Research Situations Where Dummy Predictor Variables Can Be Used
12.2 Empirical Example
12.3 Screening for Violations of Assumptions
12.4 Issues in Planning a Study
12.5 Parameter Estimates and Significance Tests for Regressions With Dummy Variables
12.6 Group Mean Comparisons Using One-Way Between-S ANOVA
12.6.1 Gender Differences in Mean Salary
12.6.2 College Differences in Mean Salary
12.7 Three Methods of Coding for Dummy Variables
12.7.1 Regression With Dummy-Coded Dummy Predictor Variables
12.7.1.1 Two-Group Example With a Dummy-Coded Dummy Variable
12.7.1.2 Multiple-Group Example With Dummy-Coded Dummy Variables
12.7.2 Regression With Effect-Coded Dummy Predictor Variables
12.7.2.1 Two-Group Example With an Effect-Coded Dummy Variable
12.7.2.2 Multiple-Group Example With Effect-Coded Dummy Variables
12.7.3 Orthogonal Coding of Dummy Predictor Variables
12.8 Regression Models That Include Both Dummy and Quantitative Predictor Variables
12.9 Effect Size and Statistical Power
12.10 Nature of the Relationship and/or Follow-Up Tests
12.11 Results
12.12 Summary
Comprehension Questions
Chapter 13. Factorial Analysis of Variance
13.1 Research Situations and Research Questions
13.1.1 First Null Hypothesis: Test of Main Effect for Factor A
13.1.2 Second Null Hypothesis: Test of Main Effect for Factor B
13.1.3 Third Null Hypothesis: Test of the A × B Interaction
13.2 Screening for Violations of Assumptions
13.3 Issues in Planning a Study
13.4 Empirical Example: Description of Hypothetical Data
13.5 Computations for Between-S Factorial ANOVA
13.5.1 Notation for Sample Statistics That Estimate Score Components in Factorial ANOVA
13.5.2 Notation for Theoretical Effect Terms (or Unknown Population Parameters) in Factorial ANOVA
13.5.3 Formulas for Sums of Squares and Degrees of Freedom
13.6 Conceptual Basis: Factors That Affect the Size of Sums of Squares and F Ratios in Factorial ANOVA
13.6.1 Distances Between Group Means (Magnitude of the α and β Effects)
13.6.2 Number of Scores (n) Within Each Group or Cell
13.6.3 Variability of Scores Within Groups or Cells (Magnitude of MSwithin)
13.7 Effect-Size Estimates for Factorial ANOVA
13.8 Statistical Power
13.9 Nature of the Relationships, Follow-Up Tests, and Information to Include in the Results
13.9.1 Nature of a Two-Way Interaction
13.9.2 Nature of Main Effect Differences
13.10 Factorial ANOVA Using the SPSS GLM Procedure
13.10.1 Further Discussion of Results: Comparison of the Factorial ANOVA (in Figures 13.7 and 13.8) With the One-Way ANOVA (in Figure 13.1)
13.11 Summary
Appendix: Nonorthogonal Factorial ANOVA (ANOVA With Unbalanced Numbers of Cases in the Cells or Groups)
Comprehension Questions
Chapter 14. Multiple Regression With More Than Two Predictors
14.1 Research Questions
14.2 Empirical Example
14.3 Screening for Violations of Assumptions
14.4 Issues in Planning a Study
14.5 Computation of Regression Coefficients With k Predictor Variables
14.6 Methods of Entry for Predictor Variables
14.6.1 Standard or Simultaneous Method of Entry
14.6.2 Sequential or Hierarchical (User-Determined) Method of Entry
14.6.3 Statistical (Data-Driven) Order of Entry
14.7 Variance Partitioning in Regression for Standard or Simultaneous Regression Versus Regressions That Involve a Series of Steps
14.8 Significance Test for an Overall Regression Model
14.9 Significance Tests for Individual Predictors in Multiple Regression
14.10 Effect Size
14.10.1 Effect Size for Overall Regression (Multiple R)
14.10.2 Effect Sizes for Individual Predictor Variables (sr2)
14.11 Changes in F and R as Additional Predictors Are Added to a Model in Sequential or Statistical Regression
14.12 Statistical Power
14.13 Nature of the Relationship Between Each X Predictor and Y (Controlling for Other Predictors)
14.14 Assessment of Multivariate Outliers in Regression
14.15 SPSS Example and Results
14.15.1 SPSS Screen Shots, Output, and Results for Standard Regression
14.15.2 SPSS Screen Shots, Output, and Results for Sequential Regression
14.15.3 SPSS Screen Shots, Output, and Results for Statistical Regression
14.16 Summary
Appendix 14.A: 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
Appendix 14.B: Tables for the Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Method = Forward Statistical Regression
Comprehension Questions
Chapter 15. Moderation: Tests for Interaction in Multiple Regression
15.1 Moderation Versus Mediation
15.2 Situations in Which Researchers Test Interactions
15.2.1 Factorial ANOVA Designs
15.2.2 Regression Analyses That Include Interaction Terms
15.3 When Should Interaction Terms Be Included in Regression Analysis?
15.4 Types of Predictor Variables Included in Interactions
15.4.1 Interaction Between Two Categorical Predictor Variables
15.4.2 Interaction Between a Quantitative and a Categorical Predictor Variable
15.4.3 Interaction Between Two Quantitative Predictor Variables
15.5 Assumptions and Preliminary Data Screening
15.6 Issues in Designing a Study
15.7 Sample Size and Statistical Power in Tests of Moderation or Interaction
15.8 Effect Size for Interaction
15.9 Additional Issues in Analysis
15.10 Preliminary Example: One Categorical and One Quantitative Predictor Variable With No Significant Interaction
15.11 Example 1: Significant Interaction Between One Categorical and One Quantitative Predictor Variable
15.12 Graphing Regression Lines for Subgroups
15.13 Interaction With a Categorical Predictor With More Than Two Categories
15.14 Results Section for Interaction Involving One Categorical and One Quantitative Predictor Variable
15.15 Example 2: Interaction Between Two Quantitative Predictors
15.16 Results for Example 2: Interaction Between Two Quantitative Predictors
15.17 Graphing the Interaction for Selected Values of Two Quantitative Predictors
15.18 Results Section for Example 2: Interaction of Two Quantitative Predictors
15.19 Additional Issues and Summary
Comprehension Questions
Chapter 16. Mediation
16.1 Definition of Mediation
16.1.1 Path Model Notation
16.1.2 Circumstances When Mediation May Be a Reasonable Hypothesis
16.2 A Hypothetical Research Example Involving One Mediating Variable
16.3 Limitations of Causal Models
16.3.1 Reasons Why Some Path Coefficients May Be Not Statistically Significant
16.3.2 Possible Interpretations for a Statistically Significant Path
16.4 Questions in a Mediation Analysis
16.5 Issues in Designing a Mediation Analysis Study
16.5.1 Type and Measurement of Variables in Mediation Analysis
16.5.2 Temporal Precedence or Sequence of Variables in Mediation Studies
16.5.3 Time Lags Between Variables
16.6 Assumptions in Mediation Analysis and Preliminary Data Screening
16.7 Path Coefficient Estimation
16.8 Conceptual Issues: Assessment of Direct Versus Indirect Paths
16.8.1 The Mediated or Indirect Path: ab
16.8.2 Mediated and Direct Path as Partition of Total Effect
16.8.3 Magnitude of Mediated Effect
16.9 Evaluating Statistical Significance
16.9.1 Causal-Steps Approach
16.9.2 Joint Significance Test
16.9.3 Sobel Test of H0: ab = 0
16.9.4 Bootstrapped Confidence Interval for ab
16.10 Effect-Size Information
16.11 Sample Size and Statistical Power
16.12 Additional Examples of Mediation Models
16.12.1 Tests of Multiple Mediating Variables
16.12.2 Multiple-Step Mediated Paths
16.12.3 Mediated Moderation and Moderated Mediation
16.13 Use of Structural Equation Modeling Programs to Test Mediation Models
16.13.1 Comparison of Regression and SEM Tests of Mediation
16.13.2 Steps in Running Amos
16.13.3 Opening the Amos Graphics Program
16.13.4 Amos Tools
16.13.5 First Steps Toward Drawing and Labeling an Amos Path Model
16.13.6 Adding Additional Variables and Paths to the Amos Path Diagram
16.13.7 Adding Error Terms for Dependent Variables
16.13.8 Correcting Mistakes and Printing the Path Model
16.13.9 Opening a Data File From Amos
16.13.10 Specification of Analysis Method and Request for Output
16.13.11 Running the Amos Analysis and Examining Preliminary Results
16.13.12 Unstandardized Path Coefficients on Path Diagram
16.13.13 Examining Text Output From Amos
16.13.14 Locating and Interpreting Output for Bootstrapped CI for the ab Indirect Effect
16.13.15 Why Use Amos/SEM Rather Than OLS Regression?
16.14 Results Section
16.15 Summary
Comprehension Questions
Chapter 17. Analysis of Covariance
17.1 Research Situations and Research Questions
17.2 Empirical Example
17.3 Screening for Violations of Assumptions
17.4 Variance Partitioning in ANCOVA
17.5 Issues in Planning a Study
17.6 Formulas for ANCOVA
17.7 Computation of Adjusted Effects and Adjusted Y* Means
17.8 Conceptual Basis: Factors That Affect the Magnitude of SSAadj and SSresidual and the Pattern of Adjusted Group Means
17.9 Effect Size
17.10 Statistical Power
17.11 Nature of the Relationship and Follow-Up Tests: Information to Include in the Results Section
17.12 SPSS Analysis and Model Results
17.13 Additional Discussion of ANCOVA Results
17.14 Summary
Appendix: Alternative Methods for the Analysis of Pretest/Posttest Data
Comprehension Questions
Chapter 18. Discriminant Analysis
18.1 Research Situations and Research Questions
18.2 Introduction of an Empirical Example
18.3 Screening for Violations of Assumptions
18.4 Issues in Planning a Study
18.5 Equations for Discriminant Analysis
18.6 Conceptual Basis: Factors That Affect the Magnitude of Wilks’s Λ
18.7 Effect Size
18.8 Statistical Power and Sample Size Recommendations
18.9 Follow-Up Tests to Assess What Pattern of Scores Best Differentiates Groups
18.10 Results
18.11 One-Way ANOVA on Scores on Discriminant Functions
18.12 Summary
Appendix: Eigenvalue/Eigenvector Problem
Comprehension Questions
Chapter 19. Multivariate Analysis of Variance
19.1 Research Situations and Research Questions
19.2 Introduction of the Initial Research Example: A One-Way MANOVA
19.3 Why Include Multiple Outcome Measures?
19.4 Equivalence of MANOVA and DA
19.5 The General Linear Model
19.6 Assumptions and Data Screening
19.7 Issues in Planning a Study
19.8 Conceptual Basis of MANOVA and Some Formulas for MANOVA
19.9 Multivariate Test Statistics
19.10 Factors That Influence the Magnitude of Wilks’s Λ
19.11 Effect Size for MANOVA
19.12 Statistical Power and Sample Size Decisions
19.13 SPSS Output for a One-Way MANOVA: Career Group Data From Chapter 18
19.14 A 2 × 3 Factorial MANOVA of the Career Group Data
19.14.1 Potential Follow-Up Tests to Assess the Nature of Significant Main Effects
19.14.2 Possible Follow-Up Tests to Assess the Nature of the Interaction
19.14.3 Further Discussion of Problems With This 2 × 3 Factorial MANOVA
19.15 A Significant Interaction in a 3 × 6 MANOVA
19.16 Comparison of Univariate and Multivariate Follow-Up Analyses for MANOVA
19.17 Summary
Comprehension Questions
Chapter 20. Principal Components and Factor Analysis
20.1 Research Situations
20.2 Path Model for Factor Analysis
20.3 Factor Analysis as a Method of Data Reduction
20.4 Introduction of an Empirical Example
20.5 Screening for Violations of Assumptions
20.6 Issues in Planning a Factor-Analytic Study
20.7 Computation of Loadings
20.8 Steps in the Computation of Principal Components or Factor Analysis
20.8.1 Computation of the Correlation Matrix R
20.8.2 Computation of the Initial Loading Matrix A
20.8.3 Limiting the Number of Components or Factors
20.8.4 Rotation of Factors
20.8.5 Naming or Labeling Components or Factors
20.9 Analysis 1: Principal Components Analysis of Three Items Retaining All Three Components
20.9.1 Communality for Each Item Based on All Three Components
20.9.2 Variance Reproduced by Each of the Three Components
20.9.3 Reproduction of Correlations From Loadings on All Three Components
20.10 Analysis 2: Principal Component Analysis of Three Items Retaining Only the First Component
20.10.1 Communality for Each Item Based on One Component
20.10.2 Variance Reproduced by the First Component
20.10.3 Partial Reproduction of Correlations From Loadings on Only One Component
20.11 Principal Components Versus Principal Axis Factoring
20.12 Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation
20.12.1 Communality for Each Item Based on Two Retained Factors
20.12.2 Variance Reproduced by Two Retained Factors
20.12.3 Partial Reproduction of Correlations From Loadings on Only Two Factors
20.13 Geometric Representation of Correlations Between Variables and Correlations Between Components or Factors
20.13.1 Factor Rotation
20.14 The Two Sets of Multiple Regressions
20.14.1 Construction of Factor Scores (Such as Score on F1) From z Scores
20.14.2 Prediction of Standard Scores on Variables (zxi) From Factors (F1, F2, …, F9)
20.15 Analysis 4: PAF With Varimax Rotation
20.15.1 Variance Reproduced by Each Factor at Three Stages in the Analysis
20.15.2 Rotated Factor Loadings
20.15.3 Example of a Reverse-Scored Item
20.16 Questions to Address in the Interpretation of Factor Analysis
20.16.1 How Many Factors or Components or Latent Variables Are Needed to Account for (or Reconstruct) the Pattern of Correlations Among the Measured Variables?
20.16.2 How “Important” Are the Factors or Components? How Much Variance Does Each Factor or Component Explain?
20.16.3 What, if Anything, Do the Retained Factors or Components Mean? Can We Label or Name Our Factors?
20.16.4 How Adequately Do the Retained Components or Factors Reproduce the Structure in the Original Data—That Is, the Correlation Matrix?
20.17 Results Section for Analysis 4: PAF With Varimax Rotation
20.18 Factor Scores Versus Unit-Weighted Composites
20.19 Summary of Issues in Factor Analysis
20.20 Optional: Brief Introduction to Concepts in Structural Equation Modeling
Appendix: The Matrix Algebra of Factor Analysis
Comprehension Questions
Chapter 21. Reliability, Validity, and Multiple-Item Scales
21.1 Assessment of Measurement Quality
21.1.1 Reliability
21.1.2 Validity
21.1.3 Sensitivity
21.1.4 Bias
21.2 Cost and Invasiveness of Measurements
21.2.1 Cost
21.2.2 Invasiveness
21.2.3 Reactivity of Measurement
21.3 Empirical Examples of Reliability Assessment
21.3.1 Definition of Reliability
21.3.2 Test-Retest Reliability Assessment for a Quantitative Variable
21.3.3 Interobserver Reliability Assessment for Scores on a Categorical Variable
21.4 Concepts From Classical Measurement Theory
21.4.1 Reliability as Partition of Variance
21.4.2 Attenuation of Correlations Due to Unreliability of Measurement
21.5 Use of Multiple-Item Measures to Improve Measurement Reliability
21.6 Computation of Summated Scales
21.6.1 Assumption: All Items Measure Same Construct and Are Scored in Same Direction
21.6.2 Initial (Raw) Scores Assigned to Individual Responses
21.6.3 Variable Naming, Particularly for Reverse-Worded Questions
21.6.4 Factor Analysis to Assess Dimensionality of a Set of Items
21.6.5 Recoding Scores for Reverse-Worded Items
21.6.6 Summing Scores Across Items to Compute Total Score: Handling Missing Data
21.6.7 Sums of (Unit-Weighted) Item Scores Versus Saved Factor Scores
21.6.7.1 Simple Unit-Weighted Sum of Raw Scores
21.6.7.2 Simple Unit-Weighted Sum of z Scores
21.6.7.3 Saved Factor Scores or Other Optimally Weighted Linear Composites
21.6.7.4 Correlation Between Sums of Items Versus Factor Scores
21.6.7.5 Choice Among Methods of Scoring
21.7 Assessment of Internal Homogeneity for Multiple-Item Measures: Cronbach’s Alpha Reliability Coefficient
21.7.1 Cronbach’s Alpha: Conceptual Basis
21.7.2 Empirical Example: Cronbach’s Alpha for Five Selected CES-D Scale Items
21.7.3 Improving Cronbach’s Alpha by Dropping a “Poor” Item
21.7.4 Improving Cronbach’s Alpha by Increasing the Number of Items
21.7.5 Other Methods of Reliability Assessment for Multiple-Item Measures
21.7.5.1 Split-Half Reliability
21.7.5.2 Parallel Forms Reliability
21.8 Validity Assessment
21.8.1 Content and Face Validity
21.8.2 Criterion-Oriented Validity
21.8.2.1 Convergent Validity
21.8.2.2 Discriminant Validity
21.8.2.3 Concurrent Validity
21.8.2.4 Predictive Validity
21.8.3 Construct Validity: Summary
21.9 Typical Scale Development Process
21.9.1 Generating and Modifying the Pool of Items or Measures
21.9.2 Administer Survey to Participants
21.9.3 Factor Analyze Items to Assess the Number and Nature of Latent Variables or Constructs
21.9.4 Development of Summated Scales
21.9.5 Assess Scale Reliability
21.9.6 Assess Scale Validity
21.9.7 Iterative Process
21.9.8 Create the Final Scale
21.10 Modern Measurement Theory
21.11 Reporting Reliability Assessment
21.12 Summary
Appendix: The CES-D Scale
Comprehension Questions
Chapter 22. Analysis of Repeated Measures
22.1 Introduction
22.2 Empirical Example: Experiment to Assess Effect of Stress on Heart Rate
22.2.1 Analysis of Data From the Stress/HR Study as a Between-S or Independent Samples Design
22.2.2 Independent Samples t Test for the Stress/HR Data
22.2.3 One-Way Between-S ANOVA for the Stress/HR Data
22.3 Discussion of Sources of Within-Group Error in Between-S Versus Within-S Data
22.4 The Conceptual Basis for the Paired Samples t Test and One-Way Repeated Measures ANOVA
22.5 Computation of a Paired Samples t Test to Compare Mean HR Between Baseline and Pain Conditions
22.6 SPSS Example: Analysis of Stress/HR Data Using a Paired Samples t Test
22.7 Comparison Between Independent Samples t Test and Paired Samples t Test
22.8 SPSS Example: Analysis of Stress/HR Data Using a Univariate One-Way Repeated Measures ANOVA
22.9 Using the SPSS GLM Procedure for Repeated Measures ANOVA
22.10 Screening for Violations of Assumptions in Univariate Repeated Measures
22.11 The Greenhouse-Geisser ε and Huynh-Feldt ε Correction Factors
22.12 MANOVA Approach to Analysis of Repeated Measures Data
22.13 Effect Size
22.14 Statistical Power
22.15 Planned Contrasts
22.16 Results
22.17 Design Problems in Repeated Measures Studies
22.18 More Complex Designs
22.19 Alternative Analyses for Pretest and Posttest Scores
22.20 Summary
Comprehension Questions
Chapter 23. Binary Logistic Regression
23.1 Research Situations
23.1.1 Types of Variables
23.1.2 Research Questions
23.1.3 Assumptions Required for Linear Regression Versus Binary Logistic Regression
23.2 Simple Empirical Example: Dog Ownership and Odds of Death
23.3 Conceptual Basis for Binary Logistic Regression Analysis
23.3.1 Why Ordinary Linear Regression Is Inadequate
23.3.2 Modifying the Method of Analysis to Handle These Problems
23.4 Definition and Interpretation of Odds
23.5 A New Type of Dependent Variable: The Logit
23.6 Terms Involved in Binary Logistic Regression Analysis
23.6.1 Estimation of Coefficients for a Binary Logistic Regression Model
23.6.2 Assessment of Overall Goodness of Fit for a Binary Logistic Regression Model
23.6.3 Alternative Assessments of Overall Goodness of Fit
23.6.4 Information About Predictive Usefulness of Individual Predictor Variables
23.6.5 Evaluating Accuracy of Group Classification
23.7 Analysis of Data for First Empirical Example: Dog Ownership/Death Study
23.7.1 SPSS Menu Selections and Dialog Windows
23.7.2 SPSS Output
23.7.2.1 Null Model
23.7.2.2 Full Model
23.7.3 Results for the Dog Ownership/Death Study
23.8 Issues in Planning and Conducting a Study
23.8.1 Preliminary Data Screening
23.8.2 Design Decisions
23.8.3 Coding Scores on Binary Variables
23.9 More Complex Models
23.10 Binary Logistic Regression for Second Empirical Analysis: Drug Dose and Gender as Predictors of Odds of Death
23.11 Comparison of Discriminant Analysis to Binary Logistic Regression
23.12 Summary
Comprehension Questions
Appendix A: Proportions of Area Under a Standard Normal Curve
Appendix B: Critical Values for t Distribution
Appendix C: Critical Values of F
Appendix D: Critical Values of Chi-Square
Appendix E: Critical Values of the Pearson Correlation Coefficient
Appendix F: Critical Values of the Studentized Range Statistic
Appendix G: Transformation of r (Pearson Correlation) to Fisher Z
Glossary
References
Index