Advanced and Multivariate Statistical Methods: Practical Application and Interpretation

391 Pages·2016·19.028 MB·English

by  Craig A. Mertler, Rachel Vannatta Reinhart

Advanced and Multivariate
Statistical Methods
Practical Application
and Interpretation
Sixth Edition
Craig A. Mertler
Arizona State University
Rachel Vannatta Reinhart
Bowling Green State University
Sixtheditionpublished2017
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Contents

Detailed Chapter Contents v
Preface xi
Acknowledgments xiv
Dedications xv
Chapter 1 Introduction to Multivariate Statistics 1
Chapter 2 A Guide to Multivariate Techniques 13
Chapter 3 Pre-Analysis Data Screening 27
Chapter 4 Factorial Analysis of Variance 71
Chapter 5 Analysis of Covariance 99
Chapter 6 Multivariate Analysis of Variance and Covariance 125
Chapter 7 Multiple Regression 169
Chapter 8 Path Analysis 203
Chapter 9 Factor Analysis 247
Chapter 10 Discriminant Analysis 279
Chapter 11 Logistic Regression 307
Appendix A SPSS Data Sets 327
Appendix B The Chi-Square Distribution 357
Glossary 359
References 369
Subject Index 371

iii
Notes

iv
Detailed Chapter Contents

Chapter 1 Introduction to Multivariate Statistics .........................................1

Section 1.1 Multivariate Statistics: Some Background ................................................................. 2
Research Designs .................................................................................................................... 2
The Nature of Variables .......................................................................................................... 3
Data Appropriate for Multivariate Analyses ........................................................................... 4
Standard and Sequential Analyses .......................................................................................... 5
Difficulties in Interpreting Results .......................................................................................... 7
Section 1.2 Review of Descriptive and Inferential Statistics ........................................................ 7
Descriptive Statistics ............................................................................................................... 7
Inferential Statistics ................................................................................................................. 9
Section 1.3 Organization of the Book ......................................................................................... 12

Chapter 2 A Guide to Multivariate Techniques ......................................... 13

Section 2.1 Degree of Relationship Among Variables................................................................ 14
Bivariate Correlation and Regression .................................................................................... 14
Multiple Regression .............................................................................................................. 14
Path Analysis ......................................................................................................................... 14
Section 2.2 Significance of Group Differences ........................................................................... 15
t Test ...................................................................................................................................... 15
One-Way Analysis of Variance ............................................................................................. 15
One-Way Analysis of Covariance ......................................................................................... 15
Factorial Analysis of Variance .............................................................................................. 16
Factorial Analysis of Covariance .......................................................................................... 16
One-Way Multivariate Analysis of Variance ........................................................................ 16
One-Way Multivariate Analysis of Covariance .................................................................... 17
Factorial Multivariate Analysis of Variance ......................................................................... 17
Factorial Multivariate Analysis of Covariance...................................................................... 17
Section 2.3 Prediction of Group Membership ............................................................................. 17
Discriminant Analysis ........................................................................................................... 17
Logistic Regression ............................................................................................................... 18
Section 2.4 Structure ................................................................................................................... 18
Factor Analysis and Principal Components Analysis ........................................................... 18
Section 2.5 The Table of Statistical Tests ................................................................................... 19
Section 2.6 The Decision-Making Tree for Statistical Tests....................................................... 20
Summary ....................................................................................................................................... 21
Exercises for Chapter 2 ................................................................................................................. 25

Chapter 3 Pre-Analysis Data Screening ...................................................... 27

Section 3.1 Why Screen Data? .................................................................................................... 27
Section 3.2 Missing Data ............................................................................................................ 28
Section 3.3 Outliers ..................................................................................................................... 29
Section 3.4 Normality ................................................................................................................. 32
Section 3.5 Linearity ................................................................................................................... 34
Section 3.6 Homoscedasticity ..................................................................................................... 35
Section 3.7 Using SPSS to Examine Data for Univariate Analysis ............................................ 36
v
Detailed Chapter Contents
Univariate Example With Grouped Data .............................................................................. 36
Univariate Example With Ungrouped Data .......................................................................... 52
Section 3.8 Using SPSS to Examine Grouped Data for Multivariate Analysis .......................... 58
Summary ....................................................................................................................................... 62
Steps for Screening Grouped Data ............................................................................................... 64
Steps for Screening Ungrouped Data ........................................................................................... 66
Exercises for Chapter 3 ................................................................................................................. 68

Chapter 4 Factorial Analysis of Variance ................................................... 71

I. Univariate Analysis of Variance .............................................................................................. 71

II. Factorial Analysis of Variance ................................................................................................. 74

Section 4.1 Practical View .......................................................................................................... 75
Purpose .................................................................................................................................. 75
Sample Research Questions .................................................................................................. 78
Section 4.2 Assumptions and Limitations ................................................................................... 79
Methods of Testing Assumptions .......................................................................................... 79
Section 4.3 Process and Logic .................................................................................................... 80
The Logic Behind Factorial ANOVA ................................................................................... 80
Interpretation of Results ........................................................................................................ 81
Writing Up Results ................................................................................................................ 84
Section 4.4 Sample Study and Analysis ...................................................................................... 84
Problem ................................................................................................................................. 84
Methods and SPSS “How To” .............................................................................................. 85
Output and Interpretation of Results ..................................................................................... 90
Presentation of Results .......................................................................................................... 92
Section 4.5 Variations of the Two-Factor Design ....................................................................... 93
Summary ....................................................................................................................................... 94
Checklist for Conducting a Factorial ANOVA .............................................................................. 95
Exercises for Chapter 4 ................................................................................................................. 96

Chapter 5 Analysis of Covariance ................................................................ 99

I. Analysis of Variance Versus Analysis of Covariance .............................................................. 99

II. Analysis of Covariance ........................................................................................................... 100

Section 5.1 Practical View ........................................................................................................ 100
Purpose ................................................................................................................................ 100
Sample Research Questions ................................................................................................ 103
Section 5.2 Assumptions and Limitations ................................................................................. 103
Methods of Testing Assumptions ........................................................................................ 104
Section 5.3 Process and Logic .................................................................................................. 105
The Logic Behind ANCOVA .............................................................................................. 105
Interpretation of Results ...................................................................................................... 107
Writing Up Results .............................................................................................................. 111
Section 5.4 Sample Study and Analysis .................................................................................... 112
Problem ............................................................................................................................... 112
Methods and SPSS “How To” ............................................................................................ 113
Output and Interpretation of Results ................................................................................... 119
Presentation of Results ........................................................................................................ 121
Summary ..................................................................................................................................... 122
vi
Detailed Chapter Contents
Checklist for Conducting ANCOVA ............................................................................................ 123
Exercises for Chapter 5 ............................................................................................................... 124

Chapter 6 Multivariate Analysis of Variance and Covariance ............... 125

I. MANOVA .............................................................................................................................. 125

Section 6.1 Practical View ........................................................................................................ 126
Purpose ................................................................................................................................ 126
Sample Research Questions ................................................................................................ 129
Section 6.2 Assumptions and Limitations ................................................................................. 129
Methods of Testing Assumptions ........................................................................................ 130
Section 6.3 Process and Logic .................................................................................................. 131
The Logic Behind MANOVA ............................................................................................. 131
Interpretation of Results ...................................................................................................... 132
Writing Up Results .............................................................................................................. 135
Section 6.4 MANOVA Sample Study and Analysis ................................................................. 136
Problem ............................................................................................................................... 136
Methods and SPSS “How To” ............................................................................................ 137
Output and Interpretation of Results ................................................................................... 140
Presentation of Results ........................................................................................................ 144

II. MANCOVA ........................................................................................................................... 145

Section 6.5 Practical View ........................................................................................................ 145
Purpose ................................................................................................................................ 145
Sample Research Questions ................................................................................................ 146
Section 6.6 Assumptions and Limitations ................................................................................. 147
Methods of Testing Assumptions ........................................................................................ 148
Section 6.7 Process and Logic .................................................................................................. 148
The Logic Behind MANCOVA .......................................................................................... 148
Interpretation of Results ...................................................................................................... 149
Writing Up Results .............................................................................................................. 153
Section 6.8 MANCOVA Sample Study and Analysis .............................................................. 154
Problem ............................................................................................................................... 154
Methods and SPSS “How To” ............................................................................................ 154
Output and Interpretation of Results ................................................................................... 159
Presentation of Results ........................................................................................................ 161
Summary ..................................................................................................................................... 162
Checklist for Conducting MANOVA ........................................................................................... 163
Checklist for Conducting MANCOVA ......................................................................................... 165
Exercises for Chapter 6 ............................................................................................................... 166

Chapter 7 Multiple Regression ................................................................... 169

Section 7.1 Practical View ........................................................................................................ 169
Purpose ................................................................................................................................ 169
Sample Research Questions ................................................................................................ 177
Section 7.2 Assumptions and Limitations ................................................................................. 177
Methods of Testing Assumptions ........................................................................................ 178
Section 7.3 Process and Logic .................................................................................................. 181
The Logic Behind Multiple Regression .............................................................................. 181
Interpretation of Results ...................................................................................................... 182
Writing Up Results .............................................................................................................. 188
vii
Detailed Chapter Contents
Section 7.4 Sample Study and Analysis .................................................................................... 189
Problem ............................................................................................................................... 189
Methods and SPSS “How To” ............................................................................................ 189
Output and Interpretation of Results ................................................................................... 196
Presentation of Results ........................................................................................................ 197
Summary ..................................................................................................................................... 197
Checklist for Conducting Multiple Regression ........................................................................... 199
Exercises for Chapter 7 ............................................................................................................... 200

Chapter 8 Path Analysis .............................................................................. 203

Section 8.1 Practical View ........................................................................................................ 203
Purpose ................................................................................................................................ 203
Sample Research Questions ................................................................................................ 208
Section 8.2 Assumptions and Limitations ................................................................................. 208
Methods of Testing Assumptions ........................................................................................ 210
Section 8.3 Process and Logic .................................................................................................. 210
The Logic Behind Path Analysis ......................................................................................... 210
Interpretation of Results ...................................................................................................... 219
Writing Up Results .............................................................................................................. 224
Section 8.4 Sample Study and Analysis .................................................................................... 226
Problem ............................................................................................................................... 226
Methods, SPSS “How To,” Output, and Interpretation ....................................................... 227
Presentation of Results ........................................................................................................ 241
Summary ..................................................................................................................................... 241
Checklist for Conducting Path Analysis ..................................................................................... 243
Exercises for Chapter 8 ............................................................................................................... 244

Chapter 9 Factor Analysis ........................................................................... 247

Section 9.1 Practical View ........................................................................................................ 247
Purpose ................................................................................................................................ 247
Sample Research Questions ................................................................................................ 255
Section 9.2 Assumptions and Limitations ................................................................................. 255
Methods of Testing Assumptions ........................................................................................ 257
Section 9.3 Process and Logic .................................................................................................. 257
The Logic Behind Factor Analysis ...................................................................................... 257
Interpretation of Results ...................................................................................................... 258
Writing Up Results .............................................................................................................. 263
Section 9.4 Sample Study and Analysis .................................................................................... 264
Problem ............................................................................................................................... 264
Methods, SPSS “How To,” Output, and Interpretation ....................................................... 264
Presentation of Results ........................................................................................................ 272
Summary ..................................................................................................................................... 273
Checklist for Conducting Factor Analysis .................................................................................. 274
Exercises for Chapter 9 ............................................................................................................... 275

Chapter 10 Discriminant Analysis ............................................................. 279
Section 10.1 Practical View ...................................................................................................... 279
Purpose ................................................................................................................................ 279
Sample Research Questions ................................................................................................ 284
Section 10.2 Assumptions and Limitations ............................................................................... 284
viii
Detailed Chapter Contents
Methods of Testing Assumptions ........................................................................................ 285
Section 10.3 Process and Logic ................................................................................................ 286
The Logic Behind Discriminant Analysis ........................................................................... 286
Interpretation of Results ...................................................................................................... 287
Writing Up Results .............................................................................................................. 293
Section 10.4 Sample Study and Analysis .................................................................................. 294
Problem ............................................................................................................................... 294
Methods and SPSS “How To” ............................................................................................ 294
Output and Interpretation of Results ................................................................................... 299
Presentation of Results ........................................................................................................ 303
Summary ..................................................................................................................................... 303
Checklist for Conducting Discriminant Analysis ........................................................................ 305
Exercises for Chapter 10 ............................................................................................................. 306

Chapter 11 Logistic Regression .................................................................. 307

Section 11.1 Practical View ...................................................................................................... 307
Purpose ................................................................................................................................ 307
Sample Research Questions ................................................................................................ 311
Section 11.2 Assumptions and Limitations ............................................................................... 311
Section 11.3 Process and Logic ................................................................................................ 312
The Logic Behind Logistic Regression ............................................................................... 312
Interpretation of Results ...................................................................................................... 313
Writing Up Results .............................................................................................................. 315
Section 11.4 Sample Study and Analysis .................................................................................. 316
Problem ............................................................................................................................... 316
Methods and SPSS “How To” ............................................................................................ 316
Output and Interpretation of Results ................................................................................... 320
Presentation of Results ........................................................................................................ 322
Summary ..................................................................................................................................... 322
Checklist for Conducting Binary Logistic Regression ................................................................ 323
Exercises for Chapter 11 ............................................................................................................. 324

ix