Using Multivariate Statistics

1018 Pages·2012·5.89 MB·English

by  Barbara G. Tabachnick

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Using Multivariate Statistics
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S I X T H E D I T I O N
Using Multivariate Statistics
Barbara G. Tabachnick
California State University, Northridge
Linda S. Fidell
California State University, Northridge
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10 9 8 7 6 5 4 3 2
ISBN-10: 0-205-89081-4
ISBN-13: 978-0-205-89081-1
C O N T E N T S
Preface xxxi
1
Introduction 1
1.1 Multivariate Statistics: Why? 1
1.1.1 The Domain of Multivariate Statistics: Numbers of IVs
and DVs 1
1.1.2 Experimental and Nonexperimental Research 2
1.1.3 Computers and Multivariate Statistics 3
1.1.4 Garbage In, Roses Out? 5
1.2 Some Useful Definitions 5
1.2.1 Continuous, Discrete, and Dichotomous Data 5
1.2.2 Samples and Populations 7
1.2.3 Descriptive and Inferential Statistics 7
1.2.4 Orthogonality: Standard and Sequential Analyses 8
1.3 Linear Combinations of Variables 10
1.4 Number and Nature of Variables to Include 11
1.5 Statistical Power 11
1.6 Data Appropriate for Multivariate Statistics 12
1.6.1 The Data Matrix 12
1.6.2 The Correlation Matrix 13
1.6.3 The Variance–Covariance Matrix 14
1.6.4 The Sum-of-Squares and Cross-Products Matrix 14
1.6.5 Residuals 16
1.7 Organization of the Book 16
2
A Guide to Statistical Techniques: Using the Book 17
2.1 Research Questions and Associated Techniques 17
2.1.1 Degree of Relationship Among Variables 17
2.1.1.1 Bivariate r 17
2.1.1.2 MultipleR 18
2.1.1.3 SequentialR 18
2.1.1.4 CanonicalR 18
2.1.1.5 Multiway Frequency Analysis 19
2.1.1.6 Multilevel Modeling 19
vii
viii CONTENTS
2.1.2 Significance of Group Differences 19
2.1.2.1 One-Way ANOVA and t Test 19
2.1.2.2 One-Way ANCOVA 19
2.1.2.3 Factorial ANOVA 20
2.1.2.4 Factorial ANCOVA 20
2.1.2.5 Hotelling’s T2 20
2.1.2.6 One-Way MANOVA 21
2.1.2.7 One-Way MANCOVA 21
2.1.2.8 Factorial MANOVA 22
2.1.2.9 Factorial MANCOVA 22
2.1.2.10 Profile Analysis of Repeated Measures 22
2.1.3 Prediction of Group Membership 23
2.1.3.1 One-Way Discriminant Analysis 23
2.1.3.2 Sequential One-Way Discriminant Analysis 24
2.1.3.3 Multiway Frequency Analysis (Logit) 24
2.1.3.4 Logistic Regression 24
2.1.3.5 Sequential Logistic Regression 24
2.1.3.6 Factorial Discriminant Analysis 25
2.1.3.7 Sequential Factorial Discriminant Analysis 25
2.1.4 Structure 25
2.1.4.1 Principal Components 25
2.1.4.2 Factor Analysis 25
2.1.4.3 Structural Equation Modeling 26
2.1.5 Time Course of Events 26
2.1.5.1 Survival/Failure Analysis 26
2.1.5.2 Time-Series Analysis 26
2.2 Some Further Comparisons 27
2.3 ADecisionTree 28
2.4 Technique Chapters 31
2.5 Preliminary Check of the Data 32
3
Review of Univariate and Bivariate Statistics 33
3.1 HypothesisTesting 33
3.1.1 One-Samplez Test as Prototype 33
3.1.2 Power 36
3.1.3 Extensions of the Model 37
3.1.4 Controversy Surrounding Significance Testing 37
3.2 Analysis of Variance 37
3.2.1 One-Way Between-Subjects ANOVA 39
3.2.2 Factorial Between-Subjects ANOVA 42
3.2.3 Within-Subjects ANOVA 43
3.2.4 Mixed Between-Within-Subjects ANOVA 46
CONTENTS ix
3.2.5 Design Complexity 47
3.2.5.1 Nesting 47
3.2.5.2 Latin-Square Designs 47
3.2.5.3 Unequaln and Nonorthogonality 48
3.2.5.4 Fixed and Random Effects 49
3.2.6 Specific Comparisons 49
3.2.6.1 Weighting Coefficients for Comparisons 50
3.2.6.2 Orthogonality of Weighting Coefficients 50
3.2.6.3 ObtainedF for Comparisons 51
3.2.6.4 CriticalF for Planned Comparisons 52
3.2.6.5 CriticalF for Post Hoc Comparisons 52
3.3 Parameter Estimation 53
3.4 Effect Size 54
3.5 Bivariate Statistics: Correlation and Regression 55
3.5.1 Correlation 56
3.5.2 Regression 57
3.6 Chi-Square Analysis 58
4
Cleaning Up Your Act: Screening Data
Prior to Analysis 60
4.1 ImportantIssues in Data Screening 61
4.1.1 Accuracy of Data File 61
4.1.2 Honest Correlations 61
4.1.2.1 Inflated Correlation 61
4.1.2.2 Deflated Correlation 61
4.1.3 Missing Data 62
4.1.3.1 Deleting Cases or Variables 63
4.1.3.2 Estimating Missing Data 66
4.1.3.3 Using a Missing Data Correlation Matrix 70
4.1.3.4 Treating Missing Data as Data 71
4.1.3.5 Repeating Analyses With and Without Missing Data 71
4.1.3.6 Choosing Among Methods for Dealing
With Missing Data 71
4.1.4 Outliers 72
4.1.4.1 Detecting Univariate and Multivariate Outliers 73
4.1.4.2 Describing Outliers 76
4.1.4.3 Reducing the Influence of Outliers 77
4.1.4.4 Outliers in a Solution 77
4.1.5 Normality, Linearity, and Homoscedasticity 78
4.1.5.1 Normality 79
4.1.5.2 Linearity 83
4.1.5.3 Homoscedasticity, Homogeneity of Variance, and
Homogeneity of Variance–Covariance Matrices 85