Name: Solution Manual for Using Multivariate Statistics 7th Edition Barbara G. Tabachnick, Linda S. Fidell
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ISBN-10 ‏ : ‎ 0134790545
ISBN-13 ‏ : ‎ 978-0134790541
Author: Barbara G. Tabachnick, Linda S. Fidell

Using Multivariate Statistics, 7th Edition presents complex statistical procedures in a way that is maximally useful and accessible to researchers who may not be statisticians. The authors focus on the benefits and limitations of applying a technique to a data set – when, why, and how to do it. Only a limited knowledge of higher-level mathematics is assumed.

Students using this text will learn to conduct numerous types of multivariate statistical analyses; find the best technique to use; understand limitations to applications; and learn how to use SPSS and SAS syntax and output.

Table of Content:

Chapter 1 Introduction
Learning Objectives
1.1 Multivariate Statistics: Why?
1.1.1 The Domain of Multivariate Statistics: Numbers of IVs and DVs
1.1.2 Experimental and Nonexperimental Research
1.1.3 Computers and Multivariate Statistics
1.1.4 Garbage In, Roses Out?
1.2 Some Useful Definitions
1.2.1 Continuous, Discrete, and Dichotomous Data
1.2.2 Samples and Populations
1.2.3 Descriptive and Inferential Statistics
1.2.4 Orthogonality: Standard and Sequential Analyses
1.3 Linear Combinations of Variables
1.4 Number and Nature of Variables to Include
1.5 Statistical Power
1.6 Data Appropriate for Multivariate Statistics
1.6.1 The Data Matrix
1.6.2 The Correlation Matrix
1.6.3 The Variance–Covariance Matrix
1.6.4 The Sum-of-Squares and Cross-Products Matrix
1.6.5 Residuals
1.7 Organization of the Book
Chapter 2 A Guide to Statistical Techniques Using the Book
Learning Objectives
2.1 Research Questions and Associated Techniques
2.1.1 Degree of Relationship Among Variables
2.1.1.1 Bivariate r
2.1.1.2 Multiple R
2.1.1.3 Sequential R
2.1.1.4 Canonical R
2.1.1.5 Multiway Frequency Analysis
2.1.1.6 Multilevel Modeling
2.1.2 Significance of Group Differences
2.1.2.1 One-Way ANOVA and t Test
2.1.2.2 One-Way ANCOVA
2.1.2.3 Factorial ANOVA
2.1.2.4 Factorial ANCOVA
2.1.2.5 Hotelling’s T2
2.1.2.6 One-Way MANOVA
2.1.2.7 One-Way MANCOVA
2.1.2.8 Factorial MANOVA
2.1.2.9 Factorial MANCOVA
2.1.2.10 Profile Analysis of Repeated Measures
2.1.3 Prediction of Group Membership
2.1.3.1 One-Way Discriminant Analysis
2.1.3.2 Sequential One-Way Discriminant Analysis
2.1.3.3 Multiway Frequency Analysis (Logit)
2.1.3.4 Logistic Regression
2.1.3.5 Sequential Logistic Regression
2.1.3.6 Factorial Discriminant Analysis
2.1.3.7 Sequential Factorial Discriminant Analysis
2.1.4 Structure
2.1.4.1 Principal Components
2.1.4.2 Factor Analysis
2.1.4.3 Structural Equation Modeling
2.1.5 Time Course of Events
2.1.5.1 Survival/Failure Analysis
2.1.5.2 Time-Series Analysis
2.2 Some Further Comparisons
2.3 A Decision Tree
2.4 Technique Chapters
2.5 Preliminary Check of the Data
Chapter 3 Review of Univariate and Bivariate Statistics
Learning Objectives
3.1 Hypothesis Testing
3.1.1 One-Sample z Test as Prototype
3.1.2 Power
3.1.3 Extensions of the Model
3.1.4 Controversy Surrounding Significance Testing
3.2 Analysis of Variance
3.2.1 One-Way Between-Subjects ANOVA
3.2.2 Factorial Between-Subjects ANOVA
3.2.3 Within-Subjects ANOVA
3.2.4 Mixed Between-Within-Subjects ANOVA6
3.2.5 Design Complexity
3.2.5.1 Nesting
3.2.5.2 Latin-Square Designs
3.2.5.3 Unequal n and Nonorthogonality
3.2.5.4 Fixed and Random Effects
3.2.6 Specific Comparisons
3.2.6.1 Weighting Coefficients for Comparisons
3.2.6.2 Orthogonality of Weighting Coefficients
3.2.6.3 Obtained F for Comparisons
3.2.6.4 Critical F for Planned Comparisons
3.2.6.5 Critical F for Post Hoc Comparisons
3.3 Parameter Estimation
3.4 Effect Size
3.5 Bivariate Statistics: Correlation and Regression
3.5.1 Correlation
3.5.2 Regression
3.6 Chi-Square Analysis
Chapter 4 Cleaning Up Your Act Screening Data Prior to Analysis
Learning Objectives
4.1 Important Issues in Data Screening
4.1.1 Accuracy of Data File
4.1.2 Honest Correlations
4.1.2.1 Inflated Correlation
4.1.2.2 Deflated Correlation
4.1.3 Missing Data
4.1.3.1 Deleting Cases or Variables
4.1.3.2 Estimating Missing Data
4.1.3.3 Using a Missing Data Correlation Matrix
4.1.3.4 Treating Missing Data as Data
4.1.3.5 Repeating Analyses With and Without Missing Data
4.1.3.6 Choosing Among Methods for Dealing With Missing Data
4.1.4 Outliers
4.1.4.1 Detecting Univariate and Multivariate Outliers
4.1.4.2 Describing Outliers
4.1.4.3 Reducing the Influence of Outliers
4.1.4.4 Outliers in a Solution
4.1.5 Normality, Linearity, and Homoscedasticity
4.1.5.1 Normality
4.1.5.2 Linearity
4.1.5.3 Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance–Covariance Matrices
4.1.6 Common Data Transformations
4.1.7 Multicollinearity and Singularity
4.1.8 A Checklist and Some Practical Recommendations
4.2 Complete Examples of Data Screening
4.2.1 Screening Ungrouped Data
4.2.1.1 Accuracy of Input, Missing Data, Distributions, and Univariate Outliers
4.2.1.2 Linearity and Homoscedasticity
4.2.1.3 Transformation
4.2.1.4 Detecting Multivariate Outliers
4.2.1.5 Variables Causing Cases to Be Outliers
4.2.1.6 Multicollinearity
4.2.2 Screening Grouped Data
4.2.2.1 Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers
4.2.2.2 Linearity
4.2.2.3 Multivariate Outliers
4.2.2.4 Variables Causing Cases to be Outliers
4.2.2.5 Multicollinearity
Chapter 5 Multiple Regression
Learning Objectives
5.1 General Purpose and Description
5.2 Kinds of Research Questions
5.2.1 Degree of Relationship
5.2.2 Importance of IVs
5.2.3 Adding IVs
5.2.4 Changing IVs
5.2.5 Contingencies Among IVs
5.2.6 Comparing Sets of IVs
5.2.7 Predicting DV Scores for Members of a New Sample
5.2.8 Parameter Estimates
5.3 Limitations to Regression Analyses
5.3.1 Theoretical Issues
5.3.2 Practical Issues
5.3.2.1 Ratio of Cases to IVs
5.3.2.2 Absence of Outliers Among the IVs and on the DV
5.3.2.3 Absence of Multicollinearity and Singularity
5.3.2.4 Normality, Linearity, and Homoscedasticity of Residuals
5.3.2.5 Independence of Errors
5.3.2.6 Absence of Outliers in the Solution
5.4 Fundamental Equations for Multiple Regression
5.4.1 General Linear Equations
5.4.2 Matrix Equations
5.4.3 Computer Analyses of Small-Sample Example
5.5 Major Types of Multiple Regression
5.5.1 Standard Multiple Regression
5.5.2 Sequential Multiple Regression
5.5.3 Statistical (Stepwise) Regression
5.5.4 Choosing Among Regression Strategies
5.6 Some Important Issues
5.6.1 Importance of IVs
5.6.1.1 Standard Multiple Regression
5.6.1.2 Sequential or Statistical Regression
5.6.1.3 Commonality Analysis
5.6.1.4 Relative Importance Analysis
5.6.2 Statistical Inference
5.6.2.1 Test for Multiple R
5.6.2.2 Test of Regression Components
5.6.2.3 Test of Added Subset of IVs
5.6.2.4 Confidence Limits
5.6.2.5 Comparing Two Sets of Predictors
5.6.3 Adjustment of R2
5.6.4 Suppressor Variables
5.6.5 Regression Approach to ANOVA
5.6.6 Centering When Interactions and Powers of IVs are Included
5.6.7 Mediation in Causal Sequence
5.7 Complete Examples of Regression Analysis
5.7.1 Evaluation of Assumptions
5.7.1.1 Ratio of Cases to IVs
5.7.1.2 Normality, Linearity, Homoscedasticity, and Independence of Residuals
5.7.1.3 Outliers
5.7.1.4 Multicollinearity and Singularity
5.7.2 Standard Multiple Regression
5.7.3 Sequential Regression
5.7.4 Example of Standard Multiple Regression with Missing Values Multiply Imputed
5.8 Comparison of Programs
5.8.1 IBM SPSS Package
5.8.2 SAS System
5.8.3 SYSTAT System
Chapter 6 Analysis of Covariance
Learning Objectives
6.1 General Purpose and Description
6.2 Kinds of Research Questions
6.2.1 Main Effects of IVs
6.2.2 Interactions Among IVs
6.2.3 Specific Comparisons and Trend Analysis
6.2.4 Effects of Covariates
6.2.5 Effect Size
6.2.6 Parameter Estimates
6.3 Limitations to Analysis of Covariance
6.3.1 Theoretical Issues
6.3.2 Practical Issues
6.3.2.1 Unequal Sample Sizes, Missing Data, and Ratio of Cases to IVs
6.3.2.2 Absence of Outliers
6.3.2.3 Absence of Multicollinearity and Singularity
6.3.2.4 Normality of Sampling Distributions
6.3.2.5 Homogeneity of Variance
6.3.2.6 Linearity
6.3.2.7 Homogeneity of Regression
6.3.2.8 Reliability of Covariates
6.4 Fundamental Equations for Analysis of Covariance
6.4.1 Sums of Squares and Cross-Products
6.4.2 Significance Test and Effect Size
6.4.3 Computer Analyses of Small-Sample Example
6.5 Some Important Issues
6.5.1 Choosing Covariates
6.5.2 Evaluation of Covariates
6.5.3 Test for Homogeneity of Regression
6.5.4 Design Complexity
6.5.4.1 Within-Subjects and Mixed Within-Between Designs
6.5.4.1.1 Same Covariate(s) for All Cells
6.5.4.1.2 Varying Covariate(s) Over Cells
6.5.4.2 Unequal Sample Sizes
6.5.4.3 Specific Comparisons and Trend Analysis
6.5.4.4 Effect Size
6.5.5 Alternatives to ANCOVA
6.6 Complete Example of Analysis of Covariance
6.6.1 Evaluation of Assumptions
6.6.1.1 Unequal n and Missing Data
6.6.1.2 Normality
6.6.1.3 Linearity
6.6.1.4 Outliers
6.6.1.5 Multicollinearity and Singularity
6.6.1.6 Homogeneity of Variance
6.6.1.7 Homogeneity of Regression
6.6.1.8 Reliability of Covariates
6.6.2 Analysis of Covariance
6.6.2.1 Main Analysis
6.6.2.2 Evaluation of Covariates
6.6.2.3 Homogeneity of Regression Run
6.7 Comparison of Programs
6.7.1 IBM SPSS Package
6.7.2 SAS System
6.7.3 SYSTAT System
Chapter 7 Multivariate Analysis of Variance and Covariance
Learning Objectives
7.1 General Purpose and Description
7.2 Kinds of Research Questions
7.2.1 Main Effects of IVs
7.2.2 Interactions Among IVs
7.2.3 Importance of DVs
7.2.4 Parameter Estimates
7.2.5 Specific Comparisons and Trend Analysis
7.2.6 Effect Size
7.2.7 Effects of Covariates
7.2.8 Repeated-Measures Analysis of Variance
7.3 Limitations to Multivariate Analysis of Variance and Covariance
7.3.1 Theoretical Issues
7.3.2 Practical Issues
7.3.2.1 Unequal Sample Sizes, Missing Data, and Power
7.3.2.2 Multivariate Normality
7.3.2.3 Absence of Outliers
7.3.2.4 Homogeneity of Variance–Covariance Matrices
7.3.2.5 Linearity
7.3.2.6 Homogeneity of Regression
7.3.2.7 Reliability of Covariates
7.3.2.8 Absence of Multicollinearity and Singularity
7.4 Fundamental Equations for Multivariate Analysis of Variance and Covariance
7.4.1 Multivariate Analysis of Variance
7.4.2 Computer Analyses of Small-Sample Example
7.4.3 Multivariate Analysis of Covariance
7.5 Some Important Issues
7.5.1 MANOVA Versus ANOVAs
7.5.2 Criteria for Statistical Inference
7.5.3 Assessing DVs
7.5.3.1 Univariate F
7.5.3.2 Roy–Bargmann Stepdown Analysis10
7.5.3.3 Using Discriminant Analysis
7.5.3.4 Choosing Among Strategies for Assessing DVs
7.5.4 Specific Comparisons and Trend Analysis
7.5.5 Design Complexity
7.5.5.1 Within-Subjects and Between-Within Designs
7.5.5.2 Unequal Sample Sizes
7.6 Complete Examples of Multivariate Analysis of Variance and Covariance
7.6.1 Evaluation of Assumptions
7.6.1.1 Unequal Sample Sizes and Missing Data
7.6.1.2 Multivariate Normality
7.6.1.3 Linearity
7.6.1.4 Outliers
7.6.1.5 Homogeneity of Variance–Covariance Matrices
7.6.1.6 Homogeneity of Regression
7.6.1.7 Reliability of Covariates
7.6.1.8 Multicollinearity and Singularity
7.6.2 Multivariate Analysis of Variance
7.6.3 Multivariate Analysis of Covariance
7.6.3.1 Assessing Covariates
7.6.3.2 Assessing DVs
7.7 Comparison of Programs
7.7.1 IBM SPSS Package
7.7.2 SAS System
7.7.3 SYSTAT System
Chapter 8 Profile Analysis: The Multivariate Approach to Repeated Measures
Learning Objectives
8.1 General Purpose and Description
8.2 Kinds of Research Questions
8.2.1 Parallelism of Profiles
8.2.2 Overall Difference Among Groups
8.2.3 Flatness of Profiles
8.2.4 Contrasts Following Profile Analysis
8.2.5 Parameter Estimates
8.2.6 Effect Size
8.3 Limitations to Profile Analysis
8.3.1 Theoretical Issues
8.3.2 Practical Issues
8.3.2.1 Sample Size, Missing Data, and Power
8.3.2.2 Multivariate Normality
8.3.2.3 Absence of Outliers
8.3.2.4 Homogeneity of Variance–Covariance Matrices
8.3.2.5 Linearity
8.3.2.6 Absence of Multicollinearity and Singularity
8.4 Fundamental Equations for Profile Analysis
8.4.1 Differences in Levels
8.4.2 Parallelism
8.4.3 Flatness
8.4.4 Computer Analyses of Small-Sample Example
8.5 Some Important Issues
8.5.1 Univariate Versus Multivariate Approach to Repeated Measures
8.5.2 Contrasts in Profile Analysis
8.5.2.1 Parallelism and Flatness Significant, Levels Not Significant (Simple-Effects Analysis)
8.5.2.2 Parallelism and Levels Significant, Flatness Not Significant (Simple-Effects Analysis)
8.5.2.3 Parallelism, Levels, and Flatness Significant (Interaction Contrasts)
8.5.2.4 Only Parallelism Significant
8.5.3 Doubly Multivariate Designs
8.5.4 Classifying Profiles
8.5.5 Imputation of Missing Values
8.6 Complete Examples of Profile Analysis
8.6.1 Profile Analysis of Subscales of the WISC
8.6.1.1 Evaluation of Assumptions
8.6.1.1.1 Unequal Sample Sizes and Missing Data
8.6.1.1.2 Multivariate Normality
8.6.1.1.3 Linearity
8.6.1.1.4 Outliers
8.6.1.1.5 Homogeneity of Variance–Covariance Matrices
8.6.1.1.6 Multicollinearity and Singularity
8.6.1.2 Profile Analysis
8.6.2 Doubly Multivariate Analysis of Reaction Time
8.6.2.1 Evaluation of Assumptions
8.6.2.1.1 Unequal Sample Sizes, Missing Data, Multivariate Normality, and Linearity
8.6.2.1.2 Outliers
8.6.2.1.3 Homogeneity of Variance–Covariance Matrices
8.6.2.1.4 Homogeneity of Regression
8.6.2.1.5 Reliability of DVs
8.6.2.1.6 Multicollinearity and Singularity
8.6.2.2 Doubly Multivariate Analysis of Slope and Intercept
8.7 Comparison of Programs
8.7.1 IBM SPSS Package
8.7.2 SAS System
8.7.3 SYSTAT System
Chapter 9 Discriminant Analysis
Learning Objectives
9.1 General Purpose and Description
9.2 Kinds of Research Questions
9.2.1 Significance of Prediction
9.2.2 Number of Significant Discriminant Functions
9.2.3 Dimensions of Discrimination
9.2.4 Classification Functions
9.2.5 Adequacy of Classification
9.2.6 Effect Size
9.2.7 Importance of Predictor Variables
9.2.8 Significance of Prediction with Covariates
9.2.9 Estimation of Group Means
9.3 Limitations to Discriminant Analysis
9.3.1 Theoretical Issues
9.3.2 Practical Issues
9.3.2.1 Unequal Sample Sizes, Missing Data, and Power
9.3.2.2 Multivariate Normality
9.3.2.3 Absence of Outliers
9.3.2.4 Homogeneity of Variance–Covariance Matrices
9.3.2.5 Linearity
9.3.2.6 Absence of Multicollinearity and Singularity
9.4 Fundamental Equations for Discriminant Analysis
9.4.1 Derivation and Test of Discriminant Functions
9.4.2 Classification
9.4.3 Computer Analyses of Small-Sample Example
9.5 Types of Discriminant Analyses
9.5.1 Direct Discriminant Analysis
9.5.2 Sequential Discriminant Analysis
9.5.3 Stepwise (Statistical) Discriminant Analysis
9.6 Some Important Issues
9.6.1 Statistical Inference
9.6.1.1 Criteria for Overall Statistical Significance
9.6.1.2 Stepping Methods
9.6.2 Number of Discriminant Functions
9.6.3 Interpreting Discriminant Functions
9.6.3.1 Discriminant Function Plots
9.6.3.2 Structure Matrix of Loadings
9.6.4 Evaluating Predictor Variables
9.6.5 Effect Size
9.6.6 Design Complexity: Factorial Designs
9.6.7 Use of Classification Procedures
9.6.7.1 Cross-Validation and New Cases
9.6.7.2 Jackknifed Classification
9.6.7.3 Evaluating Improvement in Classification
9.7 Complete Example of Discriminant Analysis
9.7.1 Evaluation of Assumptions
9.7.1.1 Unequal Sample Sizes and Missing Data
9.7.1.2 Multivariate Normality
9.7.1.3 Linearity
9.7.1.4 Outliers
9.7.1.5 Homogeneity of Variance–Covariance Matrices
9.7.1.6 Multicollinearity and Singularity
9.7.2 Direct Discriminant Analysis
9.8 Comparison of Programs
9.8.1 IBM SPSS Package
9.8.2 SAS System
9.8.3 SYSTAT System
Chapter 10 Logistic Regression
Learning Objectives
10.1 General Purpose and Description
10.2 Kinds of Research Questions
10.2.1 Prediction of Group Membership or Outcome
10.2.2 Importance of Predictors
10.2.3 Interactions Among Predictors
10.2.4 Parameter Estimates
10.2.5 Classification of Cases
10.2.6 Significance of Prediction with Covariates
10.2.7 Effect Size
10.3 Limitations to Logistic Regression Analysis
10.3.1 Theoretical Issues
10.3.2 Practical Issues
10.3.2.1 Ratio of Cases to Variables
10.3.2.2 Adequacy of Expected Frequencies and Power
10.3.2.3 Linearity in the Logit
10.3.2.4 Absence of Multicollinearity
10.3.2.5 Absence of Outliers in the Solution
10.3.2.6 Independence of Errors
10.4 Fundamental Equations for Logistic Regression
10.4.1 Testing and Interpreting Coefficients
10.4.2 Goodness of Fit
10.4.3 Comparing Models
10.4.4 Interpretation and Analysis of Residuals
10.4.5 Computer Analyses of Small-Sample Example
10.5 Types of Logistic Regression
10.5.1 Direct Logistic Regression
10.5.2 Sequential Logistic Regression
10.5.3 Statistical (Stepwise) Logistic Regression
10.5.4 Probit and Other Analyses
10.6 Some Important Issues
10.6.1 Statistical Inference
10.6.1.1 Assessing Goodness of Fit of Models
10.6.1.1.1 Constant-Only versus Full Model
10.6.1.1.2 Comparison with a Perfect (Hypothetical) Model
10.6.1.1.3 Deciles of Risk
10.6.1.2 Tests of Individual PREDICTORS
10.6.2 Effect Sizes
10.6.2.1 Effect Size for a Model
10.6.2.2 Effect Sizes for Predictors
10.6.3 Interpretation of Coefficients Using Odds
10.6.4 Coding Outcome and Predictor Categories
10.6.5 Number and Type of Outcome Categories
10.6.6 Classification of Cases
10.6.7 Hierarchical and Nonhierarchical Analysis
10.6.8 Importance of Predictors
10.6.9 Logistic Regression for Matched Groups
10.7 Complete Examples of Logistic Regression
10.7.1 Evaluation of Limitations
10.7.1.1 Ratio of Cases to Variables and Missing Data
10.7.1.2 Multicollinearity
10.7.1.3 Outliers in the Solution
10.7.2 Direct Logistic Regression with Two-Category Outcome and Continuous Predictors
10.7.2.1 Limitation: Linearity in the Logit
10.7.2.2 Direct Logistic Regression with Two-Category Outcome
10.7.3 Sequential Logistic Regression with Three Categories of Outcome
10.7.3.1 Limitations of Multinomial Logistic Regression
10.7.3.1.1 Adequacy of Expected Frequencies
10.7.3.1.2 Linearity in the Logit
10.7.3.2 Sequential Multinomial Logistic Regression
10.8 Comparison of Programs
10.8.1 IBM SPSS Package
10.8.2 SAS System
10.8.3 SYSTAT System
Chapter 11 Survival/Failure Analysis
Learning Objectives
11.1 General Purpose and Description
11.2 Kinds of Research Questions
11.2.1 Proportions Surviving at Various Times
11.2.2 Group Differences in Survival
11.2.3 Survival Time with Covariates
11.2.3.1 Treatment Effects
11.2.3.2 Importance of Covariates
11.2.3.3 Parameter Estimates
11.2.3.4 Contingencies Among Covariates
11.2.3.5 Effect Size and Power
11.3 Limitations to Survival Analysis
11.3.1 Theoretical Issues
11.3.2 Practical Issues
11.3.2.1 Sample Size and Missing Data
11.3.2.2 Normality of Sampling Distributions, Linearity, and Homoscedasticity
11.3.2.3 Absence of Outliers
11.3.2.4 Differences Between Withdrawn and Remaining Cases
11.3.2.5 Change in Survival Conditions over Time
11.3.2.6 Proportionality of Hazards
11.3.2.7 Absence of Multicollinearity
11.4 Fundamental Equations for Survival Analysis
11.4.1 Life Tables
11.4.2 Standard Error of Cumulative Proportion Surviving
11.4.3 Hazard and Density Functions
11.4.4 Plot of Life Tables
11.4.5 Test for Group Differences
11.4.6 Computer Analyses of Small-Sample Example
11.5 Types of Survival Analyses
11.5.1 Actuarial and Product-Limit Life Tables and Survivor Functions
11.5.2 Prediction of Group Survival Times from Covariates
11.5.2.1 Direct, Sequential, and Statistical Analysis
11.5.2.2 Cox Proportional-Hazards Model
11.5.2.3 Accelerated Failure-Time Models
11.5.2.4 Choosing a Method
11.6 Some Important Issues
11.6.1 Proportionality of Hazards
11.6.2 Censored Data
11.6.2.1 Right-Censored Data
11.6.2.2 Other Forms of Censoring
11.6.3 Effect Size and Power
11.6.4 Statistical Criteria
11.6.4.1 Test Statistics for Group Differences in Survival Functions
11.6.4.2 Test Statistics for Prediction From Covariates
11.6.5 Predicting Survival Rate
11.6.5.1 Regression Coefficients (Parameter Estimates)
11.6.5.2 Hazard Ratios
11.6.5.3 Expected Survival Rates
11.7 Complete Example of Survival Analysis
11.7.1 Evaluation of Assumptions
11.7.1.1 Accuracy of Input, Adequacy of Sample Size, Missing Data, and Distributions
11.7.1.2 Outliers
11.7.1.3 Differences Between Withdrawn and Remaining Cases
11.7.1.4 Change in Survival Experience over Time
11.7.1.5 Proportionality of Hazards
11.7.1.6 Multicollinearity
11.7.2 Cox Regression Survival Analysis
11.7.2.1 Effect of Drug Treatment
11.7.2.2 Evaluation of Other Covariates
11.8 Comparison of Programs
11.8.1 SAS System
11.8.2 IBM SPSS Package
11.8.3 SYSTAT System
Chapter 12 Canonical Correlation
Learning Objectives
12.1 General Purpose and Description
12.2 Kinds of Research Questions
12.2.1 Number of Canonical Variate Pairs
12.2.2 Interpretation of Canonical Variates
12.2.3 Importance of Canonical Variates and Predictors
12.2.4 Canonical Variate Scores
12.3 Limitations
12.3.1 Theoretical Limitations1
12.3.2 Practical Issues
12.3.2.1 Ratio of Cases to IVs
12.3.2.2 Normality, Linearity, and Homoscedasticity
12.3.2.3 Missing Data
12.3.2.4 Absence of Outliers
12.3.2.5 Absence of Multicollinearity and Singularity
12.4 Fundamental Equations for Canonical Correlation
12.4.1 Eigenvalues and Eigenvectors
12.4.2 Matrix Equations
12.4.3 Proportions of Variance Extracted
12.4.4 Computer Analyses of Small-Sample Example
12.5 Some Important Issues
12.5.1 Importance of Canonical Variates
12.5.2 Interpretation of Canonical Variates
12.6 Complete Example of Canonical Correlation
12.6.1 Evaluation of Assumptions
12.6.1.1 Missing Data
12.6.1.2 Normality, Linearity, and Homoscedasticity
12.6.1.3 Outliers
12.6.1.4 Multicollinearity and Singularity
12.6.2 Canonical Correlation
12.7 Comparison of Programs
12.7.1 SAS System
12.7.2 IBM SPSS Package
12.7.3 SYSTAT System
Chapter 13 Principal Components and Factor Analysis
Learning Objectives
13.1 General Purpose and Description
13.2 Kinds of Research Questions
13.2.1 Number of Factors
13.2.2 Nature of Factors
13.2.3 Importance of Solutions and Factors
13.2.4 Testing Theory in FA
13.2.5 Estimating Scores on Factors
13.3 Limitations
13.3.1 Theoretical Issues
13.3.2 Practical Issues
13.3.2.1 Sample Size and Missing Data
13.3.2.2 Normality
13.3.2.3 Linearity
13.3.2.4 Absence of Outliers Among Cases
13.3.2.5 Absence of Multicollinearity and Singularity
13.3.2.6 Factorability of R
13.3.2.7 Absence of Outliers Among Variables
13.4 Fundamental Equations for Factor Analysis
13.4.1 Extraction
13.4.2 Orthogonal Rotation
13.4.3 Communalities, Variance, and Covariance
13.4.4 Factor Scores
13.4.5 Oblique Rotation
13.4.6 Computer Analyses of Small-Sample Example
13.5 Major Types of Factor Analyses
13.5.1 Factor Extraction Techniques
13.5.1.1 PCA Versus FA
13.5.1.2 Principal Components
13.5.1.3 Principal Factors
13.5.1.4 Image Factor Extraction
13.5.1.5 Maximum Likelihood Factor Extraction
13.5.1.6 Unweighted Least Squares Factoring
13.5.1.7 Generalized (Weighted) Least Squares Factoring
13.5.1.8 Alpha Factoring
13.5.2 Rotation
13.5.2.1 Orthogonal Rotation
13.5.2.2 Oblique Rotation
13.5.2.3 Geometric Interpretation
13.5.3 Some Practical Recommendations
13.6 Some Important Issues
13.6.1 Estimates of Communalities
13.6.2 Adequacy of Extraction and Number of Factors
13.6.3 Adequacy of Rotation and Simple Structure
13.6.4 Importance and Internal Consistency of Factors
13.6.5 Interpretation of Factors
13.6.6 Factor Scores
13.6.7 Comparisons Among Solutions and Groups
13.7 Complete Example of FA
13.7.1 Evaluation of Limitations
13.7.1.1 Sample Size and Missing Data
13.7.1.2 Normality
13.7.1.3 Linearity
13.7.1.4 Outliers
13.7.1.5 Multicollinearity and Singularity
13.7.1.6 Factorability of R
13.7.1.7 Outliers Among Variables
13.7.2 Principal Factors Extraction with Varimax Rotation
13.8 Comparison of Programs
13.8.1 IBM SPSS Package
13.8.2 SAS System
13.8.3 SYSTAT System
Chapter 14 Structural Equation Modeling
Learning Objectives
14.1 General Purpose and Description
14.2 Kinds of Research Questions
14.2.1 Adequacy of the Model
14.2.2 Testing Theory
14.2.3 Amount of Variance in the Variables Accounted for by the Factors
14.2.4 Reliability of the Indicators
14.2.5 Parameter Estimates
14.2.6 Intervening Variables
14.2.7 Group Differences
14.2.8 Longitudinal Differences
14.2.9 Multilevel Modeling
14.2.10 Latent Class Analysis
14.3 Limitations to Structural Equation Modeling
14.3.1 Theoretical Issues
14.3.2 Practical Issues
14.3.2.1 Sample Size and Missing Data
14.3.2.2 Multivariate Normality and Outliers
14.3.2.3 Linearity
14.3.2.4 Absence of Multicollinearity and Singularity
14.3.2.5 Residuals
14.4 Fundamental Equations for Structural Equations Modeling
14.4.1 Covariance Algebra
14.4.2 Model Hypotheses
14.4.3 Model Specification
14.4.4 Model Estimation
14.4.5 Model Evaluation
14.4.6 Computer Analysis of Small-Sample Example
14.5 Some Important Issues
14.5.1 Model Identification
14.5.2 Estimation Techniques
14.5.2.1 Estimation Methods and Sample Size
14.5.2.2 Estimation Methods and Nonnormality
14.5.2.3 Estimation Methods and Dependence
14.5.2.4 Some Recommendations for Choice of Estimation Method
14.5.3 Assessing the Fit of the Model
14.5.3.1 Comparative Fit Indices
14.5.3.2 Absolute Fit Index
14.5.3.3 Indices of Proportion of Variance Accounted FOR
14.5.3.4 Degree of Parsimony Fit Indices
14.5.3.5 Residual-Based Fit Indices
14.5.3.6 Choosing among Fit Indices
14.5.4 Model Modification
14.5.4.1 Chi-Square Difference Test
14.5.4.2 Lagrange Multiplier (LM) Test
14.5.4.3 Wald Test
14.5.4.4 Some Caveats and Hints on Model Modification
14.5.5 Reliability and Proportion of Variance
14.5.6 Discrete and Ordinal Data
14.5.7 Multiple Group Models
14.5.8 Mean and Covariance Structure Models
14.6 Complete Examples of Structural Equation Modeling Analysis
14.6.1 Confirmatory Factor Analysis of the WISC
14.6.1.1 Model Specification for CFA
14.6.1.2 Evaluation of Assumptions for CFA
14.6.1.2.1 Sample Size and Missing Data
14.6.1.2.2 Normality and Linearity
14.6.1.2.3 Outliers
14.6.1.2.4 Multicollinearity and Singularity
14.6.1.2.5 Residuals
14.6.1.3 CFA Model Estimation and Preliminary Evaluation
14.6.1.4 Model Modification
The Hypothesized Model
Assumptions
Model Estimation
14.6.2 SEM of Health Data
14.6.2.1 SEM Model Specification
14.6.2.2 Evaluation of Assumptions for SEM
14.6.2.2.1 Sample Size and Missing Data
14.6.2.2.2 Normality and Linearity
14.6.2.2.3 Outliers
14.6.2.2.4 Multicollinearity and Singularity
14.6.2.2.5 Adequacy of Covariances
14.6.2.2.6 Residuals
14.6.2.3 SEM Model Estimation and Preliminary Evaluation
14.6.2.4 Model Modification
The Hypothesized Model
Assumptions
Model Estimation
Direct Effects
Indirect Effects
14.7 Comparison of Programs
14.7.1 EQS
14.7.2 LISREL
14.7.3 AMOS
14.7.4 SAS System
Chapter 15 Multilevel Linear Modeling
Learning Objectives
15.1 General Purpose and Description
15.2 Kinds of Research Questions
15.2.1 Group Differences in Means
15.2.2 Group Differences in Slopes
15.2.3 Cross-Level Interactions
15.2.4 Meta-Analysis
15.2.5 Relative Strength of Predictors at Various Levels
15.2.6 Individual and Group Structure
15.2.7 Effect Size
15.2.8 Path Analysis at Individual and Group Levels
15.2.9 Analysis of Longitudinal Data
15.2.10 Multilevel Logistic Regression
15.2.11 Multiple Response Analysis
15.3 Limitations to Multilevel Linear Modeling
15.3.1 Theoretical Issues
15.3.2 Practical Issues
15.3.2.1 Sample Size, Unequal-n, and Missing Data
15.3.2.2 Independence of Errors
15.3.2.3 Absence of Multicollinearity and Singularity
15.4 Fundamental Equations
15.4.1 Intercepts-Only Model
15.4.1.1 The Intercepts-Only Model: Level-1 Equation
15.4.1.2 The Intercepts-Only Model: Level-2 Equation
15.4.1.3 Computer Analyses of Intercepts-Only Model
15.4.2 Model with a First-Level Predictor
15.4.2.1 Level-1 Equation for a Model With a Level-1 Predictor
15.4.2.2 Level-2 Equations for a Model With a Level-1 Predictor
15.4.2.3 Computer Analysis of a Model With a Level-1 Predictor
15.4.3 Model with Predictors at First and Second Levels
15.4.3.1 Level-1 Equation for Model with Predictors at Both Levels
15.4.3.2 Level-2 Equations for Model with Predictors at Both Levels
15.4.3.3 Computer Analyses of Model With Predictors at First and Second Levels
15.5 Types of MLM
15.5.1 Repeated Measures
15.5.2 Higher-Order MLM
15.5.3 Latent Variables
15.5.4 Nonnormal Outcome Variables
15.5.5 Multiple Response Models
15.6 Some Important Issues
15.6.1 Intraclass Correlation
15.6.2 Centering Predictors and Changes in Their Interpretations
15.6.3 Interactions
15.6.4 Random and Fixed Intercepts and Slopes
15.6.5 Statistical Inference
15.6.5.1 Assessing Models
15.6.5.2 Tests of Individual Effects
15.6.6 Effect Size
15.6.7 Estimation Techniques and Convergence Problems
15.6.8 Exploratory Model Building
15.7 Complete Example of MLM
15.7.1 Evaluation of Assumptions
15.7.1.1 Sample Sizes, Missing Data, and Distributions
15.7.1.2 Outliers
15.7.1.3 Multicollinearity and Singularity
15.7.1.4 Independence of Errors: Intraclass Correlations
15.7.2 Multilevel Modeling
Hypothesized Model
Assumptions
Multilevel Modeling
15.8 Comparison of Programs
15.8.1 SAS System
15.8.2 IBM SPSS Package
15.8.3 HLM Program
15.8.4 MLwiN Program
15.8.5 SYSTAT System
Chapter 16 Multiway Frequency Analysis
Learning Objectives
16.1 General Purpose and Description
16.2 Kinds of Research Questions
16.2.1 Associations Among Variables
16.2.2 Effect on a Dependent Variable
16.2.3 Parameter Estimates
16.2.4 Importance of Effects
16.2.5 Effect Size
16.2.6 Specific Comparisons and Trend Analysis
16.3 Limitations to Multiway Frequency Analysis
16.3.1 Theoretical Issues
16.3.2 Practical Issues
16.3.2.1 Independence
16.3.2.2 Ratio of Cases to Variables
16.3.2.3 Adequacy of Expected Frequencies
16.3.2.4 Absence of Outliers in the Solution
16.4 Fundamental Equations for Multiway Frequency Analysis
16.4.1 Screening for Effects
16.4.1.1 Total Effect
16.4.1.2 First-Order Effects
16.4.1.3 Second-Order Effects
16.4.1.4 Third-Order Effect
16.4.2 Modeling
16.4.3 Evaluation and Interpretation
16.4.3.1 Residuals
16.4.3.2 Parameter Estimates
16.4.4 Computer Analyses of Small-Sample Example
16.5 Some Important Issues
16.5.1 Hierarchical and Nonhierarchical Models
16.5.2 Statistical Criteria
16.5.2.1 Tests of Models
16.5.2.2 Tests of Individual Effects
16.5.3 Strategies for Choosing a Model
16.5.3.1 IBM SPSS HILOGLINEAR (Hierarchical)
16.5.3.2 IBM SPSS GENLOG (General Log-Linear)
16.5.3.3 SAS CATMOD and IBM SPSS LOGLINEAR (General Log-Linear)
16.6 Complete Example of Multiway Frequency Analysis
16.6.1 Evaluation of Assumptions: Adequacy of Expected Frequencies
16.6.2 Hierarchical Log-Linear Analysis
16.6.2.1 Preliminary Model Screening
16.6.2.2 Stepwise Model Selection
16.6.2.3 Adequacy of Fit
16.6.2.4 Interpretation of the Selected Model
16.7 Comparison of Programs
16.7.1 IBM SPSS Package
16.7.2 SAS System
16.7.3 SYSTAT System
Chapter 17 Time-Series Analysis
Learning Objectives
17.1 General Purpose and Description
17.2 Kinds of Research Questions
17.2.1 Pattern of Autocorrelation
17.2.2 Seasonal Cycles and Trends
17.2.3 Forecasting
17.2.4 Effect of an Intervention
17.2.5 Comparing Time Series
17.2.6 Time Series with Covariates
17.2.7 Effect Size and Power
17.3 Assumptions of Time-Series Analysis
17.3.1 Theoretical Issues
17.3.2 Practical Issues
17.3.2.1 Normality of Distributions of Residuals
17.3.2.2 Homogeneity of Variance and Zero Mean of Residuals
17.3.2.3 Independence of Residuals
17.3.2.4 Absence of Outliers
17.3.2.5 Sample Size and Missing Data
17.4 Fundamental Equations for Time-Series ARIMA Models
17.4.1 Identification of ARIMA (p, d, q) Models
17.4.1.1 Trend Components, d: Making the Process Stationary
17.4.1.2 Auto-Regressive Components
17.4.1.3 Moving Average Components
17.4.1.4 Mixed Models
17.4.1.5 ACFs and PACFs
17.4.2 Estimating Model Parameters
17.4.3 Diagnosing a Model
17.4.4 Computer Analysis of Small-Sample Time-Series Example
17.5 Types of Time-Series Analyses
17.5.1 Models with Seasonal Components
17.5.2 Models with Interventions
17.5.2.1 Abrupt, Permanent Effects
17.5.2.2 Abrupt, Temporary Effects
17.5.2.3 Gradual, Permanent Effects
17.5.2.4 Models with Multiple Interventions
17.5.3 Adding Continuous Variables
17.6 Some Important Issues
17.6.1 Patterns of ACFs and PACFs
17.6.2 Effect Size
17.6.3 Forecasting
17.6.4 Statistical Methods for Comparing Two Models
17.7 Complete Examples of Time-Series Analysis
17.7.1 Time-Series Analysis of Introduction of Seat Belt Law
17.7.1.1 Evaluation of Assumptions
17.7.1.1.1 Normality of Sampling Distributions
17.7.1.1.2 Homogeneity of Variance
17.7.1.1.3 Outliers
17.7.1.2 Baseline Model Identification and Estimation
17.7.1.3 Baseline Model Diagnosis
17.7.1.4 Intervention Analysis
17.7.1.4.1 Model Diagnosis
17.7.1.4.2 Model Interpretation
17.7.2. Time-Series Analysis of Introduction of a Dashboard to an Educational Computer Game
17.7.2.1 Evaluation of Assumptions
17.7.2.1.1 Normality of Sampling Distributions and Homogeneity of Variance
17.7.2.1.2 Outliers
17.7.2.2 Baseline Model Identification and Diagnosis
17.7.2.3 Intervention Analysis
17.7.2.3.1 Model Diagnosis
17.7.2.3.2 Model Interpretation
17.8 Comparison of Programs
17.8.1 IBM SPSS Package
17.8.2 SAS System
17.8.3 SYSTAT System
Chapter 18 An Overview of the General Linear Model
Learning Objectives
18.1 Linearity and the General Linear Model
18.2 Bivariate to Multivariate Statistics and Overview of Techniques
18.2.1 Bivariate Form
18.2.2 Simple Multivariate Form
18.2.3 Full Multivariate Form
18.3 Alternative Research Strategies
Appendix A A Skimpy Introduction to Matrix Algebra
A.1 The Trace of a Matrix
A.2 Addition or Subtraction of a Constant to a Matrix
A.3 Multiplication or Division of a Matrix by a Constant
A.4 Addition and Subtraction of Two Matrices
A.5 Multiplication, Transposes, and Square Roots of Matrices
A.6 Matrix “Division” (Inverses and Determinants)
A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix
Appendix B Research Designs for Complete Examples
B.1 Women’s Health and Drug Study
Method
B.2 Sexual Attraction Study
Method
B.3 Learning Disabilities Data Bank
B.4 Reaction Time to Identify Figures
B.5 Field Studies of Noise-Induced Sleep Disturbance
B.6 Clinical Trial for Primary Biliary Cirrhosis
B.7 Impact of Seat Belt Law
B.8 The Selene Online Educational Game
Appendix C Statistical Tables
References
Index