1 Introduction 3
What is Multivariate Thinking? 3
Benefits 4
Drawbacks 6
Context for Multivariate Thinking 7
2 Multivariate Themes 10
Overriding Theme of Multiplicity 10
Theory 11
Hypotheses 11
Empirical Studies 12
Measurement 12
Multiple Time Points 13
Multiple Controls 13
Multiple Samples 14
Practical Implications 15
Multiple Statistical Methods 15
Summary of Multiplicity Theme 17
Central Themes 17
Variance 18
Covariance 18
Ratio of (Co-)Variances 18
Linear Combinations 19
Components 19
Factors 20
Summary of Central Themes 20
Interpretation Themes 21
Macro-Assessment 21
vii
viii CONTENTS
Significance Test 21
Effect Sizes 22
Micro-Assessment 23
Means 23
Weights 24
Summary of Interpretation Themes 25
Summary of Multivariate Themes 25
3 Background Themes 28
Preliminary Considerations before Multivariate Analyses 28
Data 28
Measurement Scales 29
Roles of Variables 30
Incomplete Information 31
Missing Data . 32
Descriptive Statistics 33
Inferential Statistics 34
Roles of Variables and Choice of Methods 35
Summary of Background Themes 36
Questions to Help Apply Themes to Multivariate Methods 37
II: INTERMEDIATE MULTIVARIATE METHODS WITH
1 CONTINUOUS OUTCOME
4 Multiple Regression 43
Themes Applied to Multiple Regression (MR)
What Is MR and How Is It Similar to and Different from
Other Methods? 43
When Is MR Used and What Research Questions Can It Address? 44
What Are the Main Multiplicity Themes for MR? 45
What Are the Main Background Themes Applied to MR? 45
What Is the Statistical Model That Is Tested with MR? 46
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to MR? 47
What Are the Main Themes Needed to Interpret Results
at a Macro-Level? 47
What Are the Main Themes Needed to Interpret Results
at a Micro-Level? 49
Significance t-Tests for Variables 49
Weights 49
Squared Semipartial Correlations 50
What Are Some Other Considerations or Next Steps After
Applying MR? 50
What Is an Example of Applying MR to a Research Question? 51
Descriptive Statistics 51
Reliability Coefficients and Correlations 52
Standard Multiple Regression (DV: STAGEB) 52
Hierarchical Multiple Regression (DV: STAGEB) 54
Stepwise Multiple Regression (DV: STAGEB) 56
Summary 61
5 Analysis of Covariance 63
Themes Applied to Analysis of Covariance (ANCOVA)
What Is ANCOVA and How Is It Similar to and Different
from Other Methods? 63
When is ANCOVA Used and What Research Questions
Can it Address? 65
What Are the Main Multiplicity Themes for ANCOVA? 66
What Are the Main Background Themes Applied to ANCOVA? 67
What Is the Statistical Model That Is Tested with ANCOVA? 68
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to ANCOVA? 69
What Are the Main Themes Needed to Interpret ANCOVA Results
at a Macro-Level? 69
Significance Test 70
Effect Size 70
What Are the Main Themes Needed to Interpret ANCOVA results
at a Micro-Level? 70
What Are Some Other Considerations or Next Steps After
Applying ANCOVA? 71
What Is an Example of Applying ANCOVA to a Research Question? 71
Descriptive Statistics 72
Correlations 73
Test of Homogeneity of Regressions 74
ANOVA and Follow-up Tukey Tests 74
ANCOVA and Follow-up Tukey Tests 77
Summary 80
III: MATRICES
6 Matrices and Multivariate Methods 85
Themes Applied to Matrices
What Are Matrices and How Are They Similar to and Different
from Other Tools? 85
What Kinds of Matrices Are Commonly Used with
Multivariate Methods? 86
What Are the Main Multiplicity Themes for Matrices? 89
What Are the Main Background Themes Applied to Matrices? 89
What Kinds of Calculations Can Be Conducted with Matrices? 89
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to Matrices? 93
What Are the Main Themes Needed to Interpret Matrix Results
at a Macro-Level? 95
What Are the Main Themes Needed to Interpret Matrix Results
at a Micro-Level? 95
What Are Some Questions to Clarify the Use of Matrices? 96
What Is an Example of Applying Matrices to a Research Question? 97
Summary 100
IV: MULTIVARIATE GROUP METHODS
7 Multivariate Analysis of Variance 105
Themes Applied to Multivariate Analysis of Variance (MANOVA)
What Is MANOVA and How Is It Similar to and Different from
Other Methods? 105
When Is MANOVA used and What Research Questions
Can it Address? 106
What Are the Main Multiplicity Themes for MANOVA? 107
What Are the Main Background Themes Applied to MANOVA? 108
What Is the Statistical Model That Is Tested with MANOVA? 110
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to MANOVA? 1ll
What Are the Main Themes Needed to Interpret MANOVA
Results at a Macro-Level? 1ll
Significance Test 112
Effect Size 113
What Are the Main Themes Needed to Interpret MANOVA
Results at a Micro- (and Mid-) Level? 113
What Are Some Other Considerations or Next Steps After
Applying These Methods? 115
What Is an Example of Applying MANOVA to a Research
Question? 115
Descriptive Statistics 116
Correlations 117
MANOVA 118
ANOVAs 118
Tukey's Tests of Honestly Significant Differences Between Groups 124
Summary 127
8 Discriminant Function Analysis 129
Themes Applied to Discriminant Function Analysis (DFA)
What Is DFA and How Is It Similar to and Different
from Other Methods? 129
When Is DFA Used and What Research Questions Can It Address? 130
What Are the Main Multiplicity Themes for DFA? 131
What Are the Main Background Themes Applied to DFA? 131
What Is the Statistical Model That Is Tested with DFA? 132
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to DFA? 133
What Are the Main Themes Needed to Interpret DFA Results at a
Macro-Level? 133
Significance Test 134
Effect Size 134
Significance F-Tests (Mid-Level) 134
Effect Size (Mid-Level) 135
What Are the Main Themes Needed to Interpret DFA Results at a
Micro-Level? 135
Weights 135
Effect Size 136
What Are Some Other Considerations or Next Steps
After Applying DFA? 136
What Is an Example of Applying DFA to a Research Question? 137
DFA Follow-up Results 137
Descriptive Statistics for Stand-Alone DFA 142
Correlations for Stand-Alone DFA 143
Stand-Alone DFA Results 143
Summary 150
9 Logistic Regression 152
Themes Applied to Logistic Regression (LR)
What Is LR and How Is It Similar to and Different from
Other Methods? 152
When is LR Used and What Research Questions Can it Address? 153
What Are the Main Multiplicity Themes for LR? 154
What Are the Main Background Themes Applied to LR? 154
What Is the Statistical Model That Is Tested with LR? 155
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to LR? 156
What Are the Main Themes Needed to Interpret LR Results at a
Macro-Level? 156
Significance Test 157
Effect Size 157
What Are the Main Themes Needed to Interpret LR Results at a
Micro-Level? 158
What Are Some Other Considerations or Next Steps After
Applying LR? 158
What Is an Example of Applying LR to a Research Question? 159
LR Results for 5-Stage DV 160
LR Results for Dichotomous STAGE2B DV (Stage 2 Versus 1) 164
LR Results for Dichotomous STAGE3B DV (Stage 3 Versus 1) 167
LR Results for Dichotomous STAGE4B DV (Stage 4 Versus 1) 169
LR Results for Dichotomous STAGE5B DV (Stage 5 Versus 1) 171
Summary 172
V: MULTIVARIATE CORRELATION METHODS WITH
CONTINUOUS VARIABLES
10 Canonical Correlation 177
Themes Applied to Canonical Correlation (CC)
What Is CC and How Is It Similar to and Different from
Other Methods? 177
When Is CC used and What Research Questions Can It Address? 180
What Are the Main Multiplicity Themes for CC? 181
What Are the Main Background Themes Applied to CC? 181
What Is the Statistical Model That Is Tested with CC? 181
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to CC? 182
What Are the Main Themes Needed to Interpret CC Results at a
Macro-Level? 183
What Are the Main Themes Needed to Interpret CC Results at a
Micro-Level? 184
What Are Some Other Considerations or Next Steps
After Applying CC? 185
What Is an Example of Applying CC to a Research Question? 185
Correlations Among the p IVs and q DVs 186
A Macro-Level Assessment of CC 188
Mid-Level Assessment of the CCs Among the Pairs
of Canonical Variates 189
Micro-level Assessment: Canonical Loadings for Both the IVs
and DVs 190
Micro-Level Assessment of Redundancy: Variables on One Side
and Canonical Variates on the Other Side 191
Follow-Up MRs, One for Each DV, to Attempt to Examine the
Directional Ordering of the Variables 191
Summary 196
11 Principal Components and Factor Analysis 199
Themes Applied to Principal Components and Factor Analysis
(PCA, FA)
What Are PCA and FA and How Are They Similar to and
Different From Other Methods? 199
When Are PCA and FA Used and What Research Questions Can
They Address? 201
What Are the Main Multiplicity Themes for PCA and FA? 202
What Are the Main Background Themes Applied to PCA and FA? 202
What Is the Statistical Model That Is Tested with PCA and FA? 203
How Do Central Themes of Variance, Covariance, and Linear
Combinations Apply to PCA and FA? 204
What Are the Main Themes Needed to Interpret PCA and FA
Results at a Macro-Level? 205
What Are the Main Themes Needed to Interpret PCA and FA
Results at a Micro-Level? 206
What Are Some Other Considerations or Next Steps After
Applying PCA or FA? 207
What Is an Example of Applying PCA and FA to a
Research Question? 208
Descriptive Statistics for the Variables 208
Correlations Among the p Variables 209
Macro- and Micro-level Assessment of PCA 209
Macro- and Micro-Level Assessment of FA 214


Themes A