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Using Multivariate Statistics

ISBN: 9780205459384 | 0205459382
Edition: 5th
Format: Paperback
Publisher: Pearson
Pub. Date: 2/21/2006

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SummaryTable of Contents
"Using Multivariate Statistics" provides practical guidelines for conducting numerous types of multivariate statistical analyses. It gives syntax and output for accomplishing many analyses through the most recent releases of SAS, SPSS, and SYSTAT, some not available in software manuals. The book maintains its practical approach, still focusing on the benefits and limitations of applications of a technique to a data set -- when, why, and how to do it. Overall, it provides advanced students with a timely and comprehensive introduction to today's ... MORE
Prefacexxvii
Introduction
1(16)
Multivariate Statistics: Why?
1(4)
... MOREThe Domain of Multivariate Statistics: Numbers of IVs and DVs
1(1)
Experimental and Nonexperimental Research
2(2)
Computers and Multivariate Statistics
4(1)
Garbage In, Roses Out?
5(1)
Some Useful Definitions
5(5)
Continuous, Discrete, and Dichotomous Data
5(2)
Samples and Populations
7(1)
Descriptive and Inferential Statistics
7(1)
Orthogonality: Standard and Sequential Analyses
8(2)
Linear Combinations of Variables
10(1)
Number and Nature of Variables to Include
11(1)
Statistical Power
11(1)
Data Appropriate for Multivariate Statistics
12(4)
The Data Matrix
12(1)
The Correlation Matrix
13(1)
The Variance-Covariance Matrix
14(1)
The Sum-of-Squares and Cross-Products Matrix
14(2)
Residuals
16(1)
Organization of the Book
16(1)
A Guide to Statistical Techniques: Using the Book
17(16)
Research Questions and Associated Techniques
17(10)
Degree of Relationship among Variables
17(1)
Bivariate r
17(1)
Multiple R
18(1)
Sequential R
18(1)
Canonical R
18(1)
Multiway Frequency Analysis
19(1)
Multilevel Modeling
19(1)
Significance of Group Differences
19(1)
One-Way ANOVA and t Test
19(1)
One-Way ANCOVA
20(1)
Factorial ANOVA
20(1)
Factorial ANCOVA
20(1)
Hotelling's T2
21(1)
One-Way MANOVA
21(1)
One-Way MANCOVA
21(1)
Factorial MANOVA
22(1)
Factorial MANCOVA
22(1)
Profile Analysis of Repeated Measures
23(1)
Prediction of Group Membership
23(1)
One-Way Discriminant
23(1)
Sequential One-Way Discriminant
24(1)
Multiway Frequency Analysis (Logit)
24(1)
Logistic Regression
24(1)
Sequential Logistic Regression
25(1)
Factorial Discriminant Analysis
25(1)
Sequential Factorial Discriminant Analysis
25(1)
Structure
25(1)
Principal Components
25(1)
Factor Analysis
26(1)
Structural Equation Modeling
26(1)
Time Course of Events
26(1)
Survival/Failure Analysis
26(1)
Time-Series Analysis
27(1)
Some Further Comparisons
27(1)
A Decision Tree
28(3)
Technique Chapters
31(1)
Preliminary Check of the Data
32(1)
Review of Univariate and Bivariate Statistics
33(27)
Hypothesis Testing
33(4)
One-Sample z Test as Prototype
33(3)
Power
36(1)
Extensions of the Model
37(1)
Controversy Surrounding Significance Testing
37(1)
Analysis of Variance
37(16)
One-Way Between-Subjects ANOVA
39(3)
Factorial Between-Subjects ANOVA
42(1)
Within-Subjects ANOVA
43(3)
Mixed Between-Within-Subjects ANOVA
46(1)
Design Complexity
47(1)
Nesting
47(1)
Latin-Square Designs
47(1)
Unequal n and Nonorthogonality
48(1)
Fixed and Random Effects
49(1)
Specific Comparisons
49(1)
Weighting Coefficients for Comparisons
50(1)
Orthogonality of Weighting Coefficients
50(1)
Obtained F for Comparisons
51(1)
Critical F for Planned Comparisons
52(1)
Critical F for Post Hoc Comparisons
53(1)
Parameter Estimation
53(1)
Effect Size
54(2)
Bivariate Statistics: Correlation and Regression
56(2)
Correlation
56(1)
Regression
57(1)
Chi-Square Analysis
58(2)
Cleaning Up Your Act: Screening Data Prior to Analysis
60(57)
Important Issues in Data Screening
61(31)
Accuracy of Data File
61(1)
Honest Correlations
61(1)
Inflated Correlation
61(1)
Deflated Correlation
61(1)
Missing Data
62(1)
Deleting Cases or Variables
63(3)
Estimating Missing Data
66(4)
Using a Missing Data Correlation Matrix
70(1)
Treating Missing Data as Data
71(1)
Repeating Analyses with and without Missing Data
71(1)
Choosing among Methods for Dealing with Missing Data
71(1)
Outliers
72(1)
Detecting Univariate and Multivariate Outliers
73(3)
Describing Outliers
76(1)
Reducing the Influence of Outliers
77(1)
Outliers in a Solution
77(1)
Normality, Linearity, and Homoscedasticity
78(1)
Normality
79(4)
Linearity
83(2)
Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance-Covariance Matrices
85(1)
Common Data Transformations
86(2)
Multicollinearity and Singularity
88(3)
A Checklist and Some Practical Recommendations
91(1)
Complete Examples of Data Screening
92(25)
Screening Ungrouped Data
92(1)
Accuracy of Input, Missing Data, Distributions, and Univariate Outliers
93(3)
Linearity and Homoscedasticity
96(2)
Transformation
98(1)
Detecting Multivariate Outliers
99(1)
Variables Causing Cases to Be Outliers
100(4)
Multicollinearity
104(1)
Screening Grouped Data
105(1)
Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers
105(5)
Linearity
110(1)
Multivariate Outliers
111(2)
Variables Causing Cases to Be Outliers
113(1)
Multicollinearity
114(3)
Multiple Regression
117(78)
General Purpose and Description
117(1)
Kinds of Research Questions
118(3)
Degree of Relationship
119(1)
Importance of IVs
119(1)
Adding IVs
119(1)
Changing IVs
120(1)
Contingencies among IVs
120(1)
Comparing Sets of IVs
120(1)
Predicting DV Scores for Members of a New Sample
120(1)
Parameter Estimates
121(1)
Limitations to Regression Analyses
121(7)
Theoretical Issues
122(1)
Practical Issues
123(1)
Ratio of Cases to IVs
123(1)
Absence of Outliers among the IVs and on the DV
124(1)
Absence of Multicollinearity and Singularity
124(1)
Normality, Linearity, Homoscedasticity of Residuals
125(3)
Independence of Errors
128(1)
Absence of Outliers in the Solution
128(1)
Fundamental Equations for Multiple Regression
128(8)
General Linear Equations
129(2)
Matrix Equations
131(3)
Computer Analyses of Small-Sample Example
134(2)
Major Types of Multiple Regression
136(8)
Standard Multiple Regression
136(2)
Sequential Multiple Regression
138(1)
Statistical (Stepwise) Regression
138(5)
Choosing among Regression Strategies
143(1)
Some Important Issues
144(17)
Importance of IVs
144(2)
Standard Multiple Regression
146(1)
Sequential or Statistical Regression
146(1)
Statistical Inference
146(1)
Test for Multiple R
147(1)
Test of Regression Components
148(1)
Test of Added Subset of IVs
149(1)
Confidence Limits around B and Multiple R2
150(2)
Comparing Two Sets of Predictors
152(1)
Adjustment of R2
153(1)
Suppressor Variables
154(1)
Regression Approach to ANOVA
155(2)
Centering when Interactions and Powers of IVs Are Included
157(2)
Mediation in Causal Sequences
159(2)
Complete Examples of Regression Analysis
161(27)
Evaluation of Assumptions
161(1)
Ratio of Cases to IVs
161(1)
Normality, Linearity, Homoscedasticity, and Independence of Residuals
161(4)
Outliers
165(2)
Multicollinearity and Singularity
167(1)
Standard Multiple Regression
167(7)
Sequential Regression
174(5)
Example of Standard Multiple Regression with Missing Values Multiply Imputed
179(9)
Comparison of Programs
188(7)
SPSS Package
188(3)
SAS System
191(3)
SYSTAT System
194(1)
Analysis of Covariance
195(48)
General Purpose and Description
195(3)
Kinds of Research Questions
198(2)
Main Effects of IVs
198(1)
Interactions among IVs
198(1)
Specific Comparisons and Trend Analysis
199(1)
Effects of Covariates
199(1)
Effect Size
199(1)
Parameter Estimates
199(1)
Limitations to Analysis of Covariance
200(3)
Theoretical Issues
200(1)
Practical Issues
201(1)
Unequal Sample Sizes, Missing Data, and Ratio of Cases to IVs
201(1)
Absence of Outliers
201(1)
Absence of Multicollinearity and Singularity
201(1)
Normality of Sampling Distributions
202(1)
Homogeneity of Variance
202(1)
Linearity
202(1)
Homogeneity of Regression
202(1)
Reliability of Covariates
203(1)
Fundamental Equations for Analysis of Covariance
203(8)
Sums of Squares and Cross Products
204(4)
Significance Test and Effect Size
208(1)
Computer Analyses of Small-Sample Example
209(2)
Some Important Issues
211(12)
Choosing Covariates
211(1)
Evaluation of Covariates
212(1)
Test for Homogeneity of Regression
213(1)
Design Complexity
213(1)
Within-Subjects and Mixed Within-Between Designs
214(3)
Unequal Sample Sizes
217(1)
Specific Comparisons and Trend Analysis
218(3)
Effect Size
221(1)
Alternatives to ANCOVA
221(2)
Complete Example of Analysis of Covariance
223(17)
Evaluation of Assumptions
223(1)
Unequal n and Missing Data
224(1)
Normality
224(1)
Linearity
224(1)
Outliers
224(3)
Multicollinearity and Singularity
227(1)
Homogeneity of Variance
228(2)
Homogeneity of Regression
230(1)
Reliability of Covariates
230(1)
Analysis of Covariance
230(1)
Main Analysis
230(5)
Evaluation of Covariates
235(2)
Homogeneity of Regression Run
237(3)
Comparison of Programs
240(3)
SPSS Package
240(1)
SAS System
240(1)
SYSTAT System
240(3)
Multivariate Analysis of Variance and Covariance
243(68)
General Purpose and Description
243(4)
Kinds of Research Questions
247(2)
Main Effects of IVs
247(1)
Interactions among IVs
247(1)
Importance of DVs
247(1)
Parameter Estimates
248(1)
Specific Comparisons and Trend Analysis
248(1)
Effect Size
248(1)
Effects of Covariates
248(1)
Repeated-Measures Analysis of Variance
249(1)
Limitations to Multivariate Analysis of Variance and Covariance
249(4)
Theoretical Issues
249(1)
Practical Issues
250(1)
Unequal Sample Sizes, Missing Data, and Power
250(1)
Multivariate Normality
251(1)
Absence of Outliers
251(1)
Homogeneity of Variance-Covariance Matrices
251(1)
Linearity
252(1)
Homogeneity of Regression
252(1)
Reliability of Covariates
253(1)
Absence of Multicollinearity and Singularity
253(1)
Fundamental Equations for Multivariate Analysis of Variance and Covariance
253(15)
Multivariate Analysis of Variance
253(8)
Computer Analyses of Small-Sample Example
261(3)
Multivariate Analysis of Covariance
264(4)
Some Important Issues
268(9)
MANOVA vs. ANOVAs
268(1)
Criteria for Statistical Inference
269(1)
Assessing DVs
270(1)
Univariate F
270(1)
Roy-Bargmann Stepdown Analysis
271(1)
Using Discriminant Analysis
272(1)
Choosing among Strategies for Assessing DVs
273(1)
Specific Comparisons and Trend Analysis
273(1)
Design Complexity
274(1)
Within-Subjects and Between-Within Designs
274(2)
Unequal Sample Sizes
276(1)
Complete Examples of Multivariate Analysis of Variance and Covariance
277(30)
Evaluation of Assumptions
277(1)
Unequal Sample Sizes and Missing Data
277(2)
Multivariate Normality
279(1)
Linearity
279(1)
Outliers
279(1)
Homogeneity of Variance-Covariance Matrices
280(1)
Homogeneity of Regression
281(3)
Reliability of Covariates
284(1)
Multicollinearity and Singularity
285(1)
Multivariate Analysis of Variance
285(11)
Multivariate Analysis of Covariance
296(1)
Assessing Covariates
296(1)
Assessing DVs
296(11)
Comparison of Programs
307(4)
SPSS Package
307(3)
SAS System
310(1)
SYSTAT System
310(1)
Profile Analysis: The Multivariate Approach to Repeated Measures
311(64)
General Purpose and Description
311(1)
Kinds of Research Questions
312(2)
Parallelism of Profiles
312(1)
Overall Difference among Groups
313(1)
Flatness of Profiles
313(1)
Contrasts Following Profile Analysis
313(1)
Parameter Estimates
313(1)
Effect Size
314(1)
Limitations to Profile Analysis
314(2)
Theoretical Issues
314(1)
Practical Issues
315(1)
Sample Size, Missing Data, and Power
315(1)
Multivariate Normality
315(1)
Absence of Outliers
315(1)
Homogeneity of Variance-Covariance Matrices
315(1)
Linearity
316(1)
Absence of Multicollinearity and Singularity
316(1)
Fundamental Equations for Profile Analysis
316(13)
Differences in Levels
316(2)
Parallelism
318(3)
Flatness
321(2)
Computer Analyses of Small-Sample Example
323(6)
Some Important Issues
329(17)
Univariate vs. Multivariate Approach to Repeated Measures
329(2)
Contrasts in Profile Analysis
331(2)
Parallelism and Flatness Significant, Levels Not Significant (Simple-effects Analysis)
333(3)
Parallelism and Levels Significant, Flatness Not Significant (Simple-effects Analysis)
336(3)
Parallelism, Levels, and Flatness Significant (Interaction Contrasts)
339(1)
Only Parallelism Significant
339(1)
Doubly-Multivariate Designs
339(6)
Classifying Profiles
345(1)
Imputation of Missing Values
345(1)
Complete Examples of Profile Analysis
346(25)
Profile Analysis of Subscales of the WISC
346(1)
Evaluation of Assumptions
346(5)
Profile Analysis
351(9)
Doubly-Multivariate Analysis of Reaction Time
360(1)
Evaluation of Assumptions
360(3)
Doubly-Multivariate Analysis of Slope and Intercept
363(8)
Comparison of Programs
371(4)
SPSS Package
373(1)
SAS System
373(1)
SYSTAT System
374(1)
Discriminant Analysis
375(62)
General Purpose and Description
375(3)
Kinds of Research Questions
378(3)
Significance of Prediction
378(1)
Number of Significant Discriminant Functions
378(1)
Dimensions of Discrimination
379(1)
Classification Functions
379(1)
Adequacy of Classification
379(1)
Effect Size
379(1)
Importance of Predictor Variables
380(1)
Significance of Prediction with Covariates
380(1)
Estimation of Group Means
380(1)
Limitations to Discriminant Analysis
381(3)
Theoretical Issues
381(1)
Practical Issues
381(1)
Unequal Sample Sizes, Missing Data, and Power
381(1)
Multivariate Normality
382(1)
Absence of Outliers
382(1)
Homogeneity of Variance-Covariance Matrices
382(1)
Linearity
383(1)
Absence of Multicollinearity and Singularity
383(1)
Fundamental Equations for Discriminant Analysis
384(11)
Derivation and Test of Discriminant Functions
384(3)
Classification
387(2)
Computer Analyses of Small-Sample Example
389(6)
Types of Discriminant Function Analyses
395(2)
Direct Discriminant Analysis
395(1)
Sequential Discriminant Analysis
396(1)
Stepwise (Statistical) Discriminant Analysis
396(1)
Some Important Issues
397(10)
Statistical Inference
397(1)
Criteria for Overall Statistical Significance
397(1)
Stepping Methods
397(1)
Number of Discriminant Functions
398(1)
Interpreting Discriminant Functions
398(1)
Discriminant Function Plots
398(2)
Structure Matrix of Loadings
400(1)
Evaluating Predictor Variables
401(1)
Effect Size
402(1)
Design Complexity: Factorial Designs
403(1)
Use of Classification Procedures
404(1)
Cross-Validation and New Cases
405(1)
Jackknifed Classification
405(1)
Evaluating Improvement in Classification
405(2)
Complete Example of Discriminant Analysis
407(23)
Evaluation of Assumptions
407(1)
Unequal Sample Sizes and Missing Data
407(1)
Multivariate Normality
408(1)
Linearity
408(1)
Outliers
408(3)
Homogeneity of Variance-Covariance Matrices
411(1)
Multicollinearity and Singularity
411(1)
Direct Discriminant Analysis
412(18)
Comparison of Programs
430(7)
SPSS Package
430(1)
SAS System
430(6)
SYSTAT System
436(1)
Logistic Regression
437(69)
General Purpose and Description
437(2)
Kinds of Research Questions
439(2)
Prediction of Group Membership or Outcome
439(1)
Importance of Predictors
439(1)
Interactions among Predictors
440(1)
Parameter Estimates
440(1)
Classification of Cases
440(1)
Significance of Prediction with Covariates
440(1)
Effect Size
441(1)
Limitations to Logistic Regression Analysis
441(3)
Theoretical Issues
441(1)
Practical Issues
442(1)
Ratio of Cases to Variables
442(1)
Adequacy of Expected Frequencies and Power
442(1)
Linearity in the Logit
443(1)
Absence of Multicollinearity
443(1)
Absence of Outliers in the Solution
443(1)
Independence of Errors
443(1)
Fundamental Equations for Logistic Regression
444(9)
Testing and Interpreting Coefficients
445(1)
Goodness-of-Fit
446(2)
Comparing Models
448(1)
Interpretation and Analysis of Residuals
448(1)
Computer Analyses of Small-Sample Example
449(4)
Types of Logistic Regression
453(4)
Direct Logistic Regression
454(1)
Sequential Logistic Regression
454(1)
Statistical (Stepwise) Logistic Regression
454(2)
Probit and Other Analyses
456(1)
Some Important Issues
457(12)
Statistical Inference
457(1)
Assessing Goodness-of-Fit of Models
457(2)
Tests of Individual Variables
459(1)
Effect Size for a Model
460(1)
Interpretation of Coefficients Using Odds
461(3)
Coding Outcome and Predictor Categories
464(1)
Number and Type of Outcome Categories
464(4)
Classification of Cases
468(1)
Hierarchical and Nonhierarchical Analysis
468(1)
Importance of Predictors
469(1)
Logistic Regression for Matched Groups
469(1)
Complete Examples of Logistic Regression
469(30)
Evaluation of Limitations
470(1)
Ratio of Cases to Variables and Missing Data
470(3)
Multicollinearity
473(1)
Outliers in the Solution
474(1)
Direct Logistic Regression with Two-Category Outcome and Continuous Predictors
474(1)
Limitation: Linearity in the Logit
474(1)
Direct Logistic Regression with Two-Category Outcome
474(7)
Sequential Logistic Regression with Three Categories of Outcome
481(1)
Limitations of Multinomial Logistic Regression
481(1)
Sequential Multinomial Logistic Regression
481(18)
Comparisons of Programs
499(7)
SPSS Package
499(5)
SAS System
504(1)
SYSTAT System
504(2)
Survival/Failure Analysis
506(61)
General Purpose and Description
506(1)
Kinds of Research Questions
507(2)
Proportions Surviving at Various Times
507(1)
Group Differences in Survival
508(1)
Survival Time with Covariates
508(1)
Treatment Effects
508(1)
Importance of Covariates
508(1)
Parameter Estimates
508(1)
Contingencies among Covariates
508(1)
Effect Size and Power
509(1)
Limitations to Survival Analysis
509(2)
Theoretical Issues
509(1)
Practical Issues
509(1)
Sample Size and Missing Data
509(1)
Normality of Sampling Distributions, Linearity, and Homoscedasticity
510(1)
Absence of Outliers
510(1)
Differences between Withdrawn and Remaining Cases
510(1)
Change in Survival Conditions over Time
510(1)
Proportionality of Hazards
510(1)
Absence of Multicollinearity
510(1)
Fundamental Equations for Survival Analysis
511(13)
Life Tables
511(2)
Standard Error of Cumulative Proportion Surviving
513(1)
Hazard and Density Functions
514(1)
Plot of Life Tables
515(1)
Test for Group Differences
515(2)
Computer Analyses of Small-Sample Example
517(7)
Types of Survival Analyses
524(11)
Actuarial and Product-Limit Life Tables and Survivor Functions
524(1)
Prediction of Group Survival Times from Covariates
524(3)
Direct, Sequential, and Statistical Analysis
527(1)
Cox Proportional-Hazards Model
527(2)
Accelerated Failure-Time Models
529(6)
Choosing a Method
535(1)
Some Important Issues
535(6)
Proportionality of Hazards
535(2)
Censored Data
537(1)
Right-Censored Data
537(1)
Other Forms of Censoring
537(1)
Effect Size and Power
538(1)
Statistical Criteria
539(1)
Test Statistics for Group Differences in Survival Functions
539(1)
Test Statistics for Prediction from Covariates
540(1)
Predicting Survival Rate
540(1)
Regression Coefficients (Parameter Estimates)
540(1)
Odds Ratios
540(1)
Expected Survival Rates
541(1)
Complete Example of Survival Analysis
541(18)
Evaluation of Assumptions
543(1)
Accuracy of Input, Adequacy of Sample Size, Missing Data, and Distributions
543(2)
Outliers
545(4)
Differences between Withdrawn and Remaining Cases
549(1)
Change in Survival Experience over Time
549(1)
Proportionality of Hazards
549(2)
Multicollinearity
551(1)
Cox Regression Survival Analysis
551(1)
Effect of Drug Treatment
552(1)
Evaluation of Other Covariates
552(7)
Comparison of Programs
559(8)
SAS System
559(1)
SPSS Package
559(7)
SYSTAT System
566(1)
Canonical Correlation
567(40)
General Purpose and Description
567(1)
Kinds of Research Questions
568(1)
Number of Canonical Variate Pairs
568(1)
Interpretation of Canonical Variates
569(1)
Importance of Canonical Variates
569(1)
Canonical Variate Scores
569(1)
Limitations
569(3)
Theoretical Limitations
569(1)
Practical Issues
570(1)
Ratio of Cases to IVs
570(1)
Normality, Linearity, and Homoscedasticity
570(1)
Missing Data
571(1)
Absence of Outliers
571(1)
Absence of Multicollinearity and Singularity
571(1)
Fundamental Equations for Canonical Correlation
572(14)
Eigenvalues and Eigenvectors
573(2)
Matrix Equations
575(4)
Proportions of Variance Extracted
579(1)
Computer Analyses of Small-Sample Example
580(6)
Some Important Issues
586(1)
Importance of Canonical Variates
586(1)
Interpretation of Canonical Variates
587(1)
Complete Example of Canonical Correlation
587(17)
Evaluation of Assumptions
588(1)
Missing Data
588(1)
Normality, Linearity, and Homoscedasticity
588(3)
Outliers
591(4)
Multicollinearity and Singularity
595(1)
Canonical Correlation
595(9)
Comparison of Programs
604(3)
SAS System
604(1)
SPSS Package
604(2)
SYSTAT System
606(1)
Principal Components and Factor Analysis
607(69)
General Purpose and Description
607(3)
Kinds of Research Questions
610(1)
Number of Factors
610(1)
Nature of Factors
611(1)
Importance of Solutions and Factors
611(1)
Testing Theory in FA
611(1)
Estimating Scores on Factors
611(1)
Limitations
611(4)
Theoretical Issues
611(1)
Practical Issues
612(1)
Sample Size and Missing Data
613(1)
Normality
613(1)
Linearity
613(1)
Absence of Outliers among Cases
613(1)
Absence of Multicollinearity and Singularity
614(1)
Factorability of R
614(1)
Absence of Outliers among Variables
614(1)
Fundamental Equations for Factor Analysis
615(18)
Extraction
616(4)
Orthogonal Rotation
620(1)
Communalities, Variance, and Covariance
621(1)
Factor Scores
622(3)
Oblique Rotation
625(3)
Computer Analyses of Small-Sample Example
628(5)
Major Types of Factor Analyses
633(10)
Factor Extraction Techniques
633(1)
PCA vs. FA
634(1)
Principal Components
635(1)
Principal Factors
636(1)
Image Factor Extraction
636(1)
Maximum Likelihood Factor Extraction
636(1)
Unweighted Least Squares Factoring
636(1)
Generalized (Weighted) Least Squares Factoring
637(1)
Alpha Factoring
637(1)
Rotation
637(1)
Orthogonal Rotation
638(1)
Oblique Rotation
638(2)
Geometric Interpretation
640(2)
Some Practical Recommendations
642(1)
Some Important Issues
643(8)
Estimates of Communalities
643(1)
Adequacy of Extraction and Number of Factors
644(2)
Adequacy of Rotation and Simple Structure
646(1)
Importance and Internal Consistency of Factors
647(2)
Interpretation of Factors
649(1)
Factor Scores
650(1)
Comparisons among Solutions and Groups
651(1)
Complete Example of FA
651(20)
Evaluation of Limitations
652(1)
Sample Size and Missing Data
652(1)
Normality
652(1)
Linearity
652(1)
Outliers
652(5)
Multicollinearity and Singularity
657(1)
Outliers among Variables
657(1)
Principal Factors Extraction with Varimax Rotation
657(14)
Comparison of Programs
671(5)
SPSS Package
674(1)
SAS System
675(1)
SYSTAT System
675(1)
Structural Equation Modeling
676(105)
General Purpose and Description
676(4)
Kinds of Research Questions
680(2)
Adequacy of the Model
680(1)
Testing Theory
680(1)
Amount of Variance in the Variables Accounted for by the Factors
680(1)
Reliability of the Indicators
680(1)
Parameter Estimates
680(1)
Intervening Variables
681(1)
Group Differences
681(1)
Longitudinal Differences
681(1)
Multilevel Modeling
681(1)
Limitations to Structural Equation Modeling
682(2)
Theoretical Issues
682(1)
Practical Issues
682(1)
Sample Size and Missing Data
682(1)
Multivariate Normality and Absence of Outliers
683(1)
Linearity
683(1)
Absence of Multicollinearity and Singularity
683(1)
Residuals
684(1)
Fundamental Equations for Structural Equations Modeling
684(25)
Covariance Algebra
684(2)
Model Hypotheses
686(2)
Model Specification
688(2)
Model Estimation
690(4)
Model Evaluation
694(2)
Computer Analysis of Small-Sample Example
696(13)
Some Important Issues
709(23)
Model Identification
709(4)
Estimation Techniques
713(1)
Estimation Methods and Sample Size
714(1)
Estimation Methods and Nonnormality
714(1)
Estimation Methods and Dependence
715(1)
Some Recommendations for Choice of Estimation Method
715(1)
Assessing the Fit of the Model
715(1)
Comparative Fit Indices
716(2)
Absolute Fit Index
718(1)
Indices of Proportion of Variance Accounted
718(1)
Degree of Parsimony Fit Indices
719(1)
Residual-Based Fit Indices
720(1)
Choosing among Fit Indices
720(1)
Model Modification
721(1)
Chi-Square Difference Test
721(1)
Lagrange Multiplier (LM) Test
721(2)
Wald Test
723(5)
Some Caveats and Hints on Model Modification
728(1)
Reliability and Proportion of Variance
728(1)
Discrete and Ordinal Data
729(1)
Multiple Group Models
730(1)
Mean and Covariance Structure Models
731(1)
Complete Examples of Structural Equation Modeling Analysis
732(41)
Confirmatory Factor Analysis of the WISC
732(1)
Model Specification for CFA
732(1)
Evaluation of Assumptions for CFA
733(1)
CFA Model Estimation and Preliminary Evaluation
734(9)
Model Modification
743(7)
SEM of Health Data
750(1)
SEM Model Specification
750(1)
Evaluation of Assumptions for SEM
751(4)
SEM Model Estimation and Preliminary Evaluation
755(4)
Model Modification
759(14)
Comparison of Programs
773(8)
EQS
773(1)
LISREL
773(7)
AMOS
780(1)
SAS System
780(1)
Multilevel Linear Modeling
781(77)
General Purpose and Description
781(3)
Kinds of Research Questions
784(2)
Group Differences in Means
784(1)
Group Differences in Slopes
784(1)
Cross-Level Interactions
785(1)
Meta-Analysis
785(1)
Relative Strength of Predictors at Various Levels
785(1)
Individual and Group Structure
785(1)
Path Analysis at Individual and Group Levels
786(1)
Analysis of Longitudinal Data
786(1)
Multilevel Logistic Regression
786(1)
Multiple Response Analysis
786(1)
Limitations to Multilevel Linear Modeling
786(3)
Theoretical Issues
786(1)
Practical Issues
787(1)
Sample Size, Unequal-n, and Missing Data
787(1)
Independence of Errors
788(1)
Absence of Multicollinearity and Singularity
789(1)
Fundamental Equations
789(25)
Intercepts-Only Model
792(1)
The Intercepts-Only Model: Level-1 Equation
793(1)
The Intercepts-Only Model: Level-2 Equation
793(1)
Computer Analysis of Intercepts-only Model
794(5)
Model with a First-Level Predictor
799(1)
Level-1 Equation for a Model with a Level-1 Predictor
799(2)
Level-2 Equations for a Model with a Level-1 Predictor
801(1)
Computer Analysis of a Model with a Level-1 Predictor
802(5)
Model with Predictors at First and Second Levels
807(1)
Level-1 Equation for Model with Predictors at Both Levels
807(1)
Level-2 Equations for Model with Predictors at Both Levels
807(1)
Computer Analyses of Model with Predictors at First and Second Levels
808(6)
Types of MLM
814(8)
Repeated Measures
814(5)
Higher-Order MLM
819(1)
Latent Variables
819(1)
Nonnormal Outcome Variables
820(1)
Multiple Response Models
821(1)
Some Important Issues
822(13)
Intraclass Correlation
822(1)
Centering Predictors and Changes in Their Interpretations
823(3)
Interactions
826(1)
Random and Fixed Intercepts and Slopes
826(4)
Statistical Inference
830(1)
Assessing Models
830(1)
Tests of Individual Effects
831(1)
Effect Size
832(1)
Estimation Techniques and Convergence Problems
833(1)
Exploratory Model Building
834(1)
Complete Example of MLM
835(17)
Evaluation of Assumptions
835(1)
Sample Sizes, Missing Data, and Distributions
835(3)
Outliers
838(1)
Multicollinearity and Singularity
839(1)
Independence of Errors: Intraclass Correlations
839(1)
Multilevel Modeling
840(12)
Comparison of Programs
852(6)
SAS System
852(4)
SPSS Package
856(1)
HLM Program
856(1)
MLwiN Program
857(1)
SYSTAT System
857(1)
Multiway Frequency Analysis
858(55)
General Purpose and Description
858(1)
Kinds of Research Questions
859(2)
Associations among Variables
859(1)
Effect on a Dependent Variable
860(1)
Parameter Estimates
860(1)
Importance of Effects
860(1)
Effect Size
860(1)
Specific Comparisons and Trend Analysis
860(1)
Limitations to Multiway Frequency Analysis
861(2)
Theoretical Issues
861(1)
Practical Issues
861(1)
Independence
861(1)
Ratio of Cases to Variables
861(1)
Adequacy of Expected Frequencies
862(1)
Absence of Outliers in the Solution
863(1)
Fundamental Equations for Multiway Frequency Analysis
863(24)
Screening for Effects
864(1)
Total Effect
865(1)
First-Order Effects
866(1)
Second-Order Effects
867(4)
Third-Order Effect
871(1)
Modeling
871(3)
Evaluation and Interpretation
874(1)
Residuals
874(1)
Parameter Estimates
874(6)
Computer Analyses of Small-Sample Example
880(7)
Some Important Issues
887(3)
Hierarchical and Nonhierarchical Models
887(1)
Statistical Criteria
888(1)
Tests of Models
888(1)
Tests of Individual Effects
888(1)
Strategies for Choosing a Model
889(1)
SPSS HILOGLINEAR (Hierarchical)
889(1)
SPSS GENLOG (General Log-Linear)
889(1)
SAS CATMOD and SPSS LOGLINEAR (General Log-Linear)
890(1)
Complete Example of Multiway Frequency Analysis
890(18)
Evaluation of Assumptions: Adequacy of Expected Frequencies
890(1)
Hierarchical Log-Linear Analysis
891(1)
Preliminary Model Screening
891(2)
Stepwise Model Selection
893(2)
Adequacy of Fit
895(6)
Interpretation of the Selected Model
901(7)
Comparison of Programs
908(5)
SPSS Package
911(1)
SAS System
912(1)
SYSTAT System
912(1)
An Overview of the General Linear Model
913
Linearity and the General Linear Model
913(1)
Bivariate to Multivariate Statistics and Overview of Techniques
913(5)
Bivariate Form
913(1)
Simple Multivariate Form
914(3)
Full Multivariate Form
917(1)
Alternative Research Strategies
918
Time-Series Analysis (available online at www.ablongman.com/tabachnick5e)
1(923)
General Purpose and Description
1(2)
Kinds of Research Questions
3(3)
Pattern of Autocorrelation
5(1)
Seasonal Cycles and Trends
5(1)
Forecasting
5(1)
Effect of an Intervention
5(1)
Comparing Time Series
5(1)
Time Series with Covariates
6(1)
Effect Size and Power
6(1)
Assumptions of Time-Series Analysis
6(1)
Theoretical Issues
6(1)
Practical Issues
6(1)
Normality of Distributions of Residuals
6(1)
Homogeneity of Variance and Zero Mean of Residuals
7(1)
Independence of Residuals
7(1)
Absence of Outliers
7(1)
Fundamental Equations for Time-Series ARIMA Models
7(20)
Identification ARIMA (p, d, q) Models
8(1)
Trend Components, d: Making the Process Stationary
8(3)
Auto-Regressive Components
11(1)
Moving Average Components
12(1)
Mixed Models
13(1)
ACFs and PACFs
13(3)
Estimating Model Parameters
16(3)
Diagnosing a Model
19(1)
Computer Analysis of Small-Sample Time-Series Example
19(8)
Types of Time-Series Analyses
27(14)
Models with Seasonal Components
27(3)
Models with Interventions
30(2)
Abrupt, Permanent Effects
32(1)
Abrupt, Temporary Effects
32(6)
Gradual, Permanent Effects
38(1)
Models with Multiple Interventions
38(1)
Adding Continuous Variables
38(3)
Some Important Issues
41(6)
Patterns of ACFs and PACFs
41(3)
Effect Size
44(1)
Forecasting
45(1)
Statistical Methods for Comparing Two Models
45(2)
Complete Example of a Time-Series Analysis
47(13)
Evaluation of Assumptions
48(1)
Normality of Sampling Distributions
48(1)
Homogeneity of Variance
48(1)
Outliers
48(1)
Baseline Model Identification and Estimation
48(1)
Baseline Model Diagnosis
49(6)
Intervention Analysis
55(1)
Model Diagnosis
55(1)
Model Interpretation
56(4)
Comparison of Programs
60(864)
SPSS Package
61(1)
SAS System
61(1)
SYSTAT System
61(863)
Appendix A A Skimpy Introduction to Matrix Algebra
924(10)
A.1 The Trace of a Matrix
925(1)
A.2 Addition or Subtraction of a Constant to a Matrix
925(1)
A.3 Multiplication or Division of a Matrix by a Constant
925(1)
A.4 Addition and Subtraction of Two Matrices
926(1)
A.5 Multiplication, Transposes, and Square Roots of Matrices
927(2)
A.6 Matrix ``Division'' (Inverses and Determinants)
929(1)
A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix
930(4)
Appendix B Research Designs for Complete Examples
934(7)
B.1 Women's Health and Drug Study
934(1)
B.2 Sexual Attraction Study
935(3)
B.3 Learning Disabilities Data Bank
938(1)
B.4 Reaction Time to Identify Figures
939(1)
B.5 Field Studies of Noise-Induced Sleep Disturbance
939(1)
B.6 Clinical Trial for Primary Biliary Cirrhosis
940(1)
B.7 Impact of Seat Belt Law
940(1)
Appendix C Statistical Tables
941(12)
C.1 Normal Curve Areas
942(1)
C.2 Critical Values of the t Distribution for a = .05 and .01, Two-Tailed Test
943(1)
C.3 Critical Values of the F Distribution
944(5)
C.4 Critical Values of Chi Square (χ2)
949(1)
C.5 Critical Values for Squared Multiple Correlation (R2) in Forward Stepwise Selection
950(2)
C.6 Critical Values for FMAX (S2MAX/S2MIN) Distribution for a = .05 and .01
952(1)
References953(10)
Index963

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