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  • Izdošanas datums: 28-Oct-2012
  • Izdevniecība: Pearson
  • ISBN-10: 0205885667
  • ISBN-13: 9780205885664
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A Practical Approach to using Multivariate Analyses

Using Multivariate Statistics, 6th edition provides advanced undergraduate as well as graduate students with a timely and comprehensive introduction to today's most commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge of higher-level mathematics. This text’s practical approach focuses on the benefits and limitations of applications of a technique to a data set — when, why, and how to do it.

Learning Goals

Upon completing this book, readers should be able to:

  • Learn to conduct numerous types of multivariate statistical analyses
  • Find the best technique to use
  • Understand Limitations to applications
  • Learn how to use SPSS and SAS syntax and output

Note: MySearchLab with eText does not come automatically packaged with this text. To purchase MySearchLab with eText, please visitwww.mysearchlab.com or you can purchase a ValuePack of the text + MySearchLab with eText (at no additional cost). ValuePack ISBN-10: 0205885667 / ValuePack ISBN-13: 9780205885664

Preface xxxi
1 Introduction
1(16)
1.1 Multivariate Statistics: Why?
1(4)
1.1.1 The Domain of Multivariate Statistics: Numbers of IVs and DVs
1(1)
1.1.2 Experimental and Nonexperimental Research
2(1)
1.1.3 Computers and Multivariate Statistics
3(2)
1.1.4 Garbage In, Roses Out?
5(1)
1.2 Some Useful Definitions
5(5)
1.2.1 Continuous, Discrete, and Dichotomous Data
5(2)
1.2.2 Samples and Populations
7(1)
1.2.3 Descriptive and Inferential Statistics
7(1)
1.2.4 Orthogonality: Standard and Sequential Analyses
8(2)
1.3 Linear Combinations of Variables
10(1)
1.4 Number and Nature of Variables to Include
11(1)
1.5 Statistical Power
11(1)
1.6 Data Appropriate for Multivariate Statistics
12(4)
1.6.1 The Data Matrix
12(1)
1.6.2 The Correlation Matrix
13(1)
1.6.3 The Variance-Covariance Matrix
14(1)
1.6.4 The Sum-of-Squares and Cross-Products Matrix
14(2)
1.6.5 Residuals
16(1)
1.7 Organization of the Book
16(1)
2 A Guide to Statistical Techniques: Using the Book
17(16)
2.1 Research Questions and Associated Techniques
17(10)
2.1.1 Degree of Relationship Among Variables
17(1)
2.1.1.1 Bivariate r
17(1)
2.1.1.2 Multiple R
18(1)
2.1.1.3 Sequential R
18(1)
2.1.1.4 Canonical R
18(1)
2.1.1.5 Multiway Frequency Analysis
19(1)
2.1.1.6 Multilevel Modeling
19(1)
2.1.2 Significance of Group Differences
19(1)
2.1.2.1 One-Way ANOVA and t Test
19(1)
2.1.2.2 One-Way ANCOVA
19(1)
2.1.2.3 Factorial ANOVA
20(1)
2.1.2.4 Factorial ANCOVA
20(1)
2.1.2.5 Hotelling's T2
20(1)
2.1.2.6 One-Way MANOVA
21(1)
2.1.2.7 One-Way MANCOVA
21(1)
2.1.2.8 Factorial MANOVA
22(1)
2.1.2.9 Factorial MANCOVA
22(1)
2.1.2.10 Profile Analysis of Repeated Measures
22(1)
2.1.3 Prediction of Group Membership
23(1)
2.1.3.1 One-Way Discriminant Analysis
23(1)
2.1.3.2 Sequential One-Way Discriminant Analysis
24(1)
2.1.3.3 Multiway Frequency Analysis (Logit)
24(1)
2.1.3.4 Logistic Regression
24(1)
2.1.3.5 Sequential Logistic Regression
24(1)
2.1.3.6 Factorial Discriminant Analysis
25(1)
2.1.3.7 Sequential Factorial Discriminant Analysis
25(1)
2.1.4 Structure
25(1)
2.1.4.1 Principal Components
25(1)
2.1.4.2 Factor Analysis
25(1)
2.1.4.3 Structural Equation Modeling
26(1)
2.1.5 Time Course of Events
26(1)
2.1.5.1 Survival/Failure Analysis
26(1)
2.1.5.2 Time-Series Analysis
26(1)
2.2 Some Further Comparisons
27(1)
2.3 A Decision Tree
28(3)
2.4 Technique
Chapters
31(1)
2.5 Preliminary Check of the Data
32(1)
3 Review of Univariate and Bivariate Statistics
33(27)
3.1 Hypothesis Testing
33(4)
3.1.1 One-Sample z Test as Prototype
33(3)
3.1.2 Power
36(1)
3.1.3 Extensions of the Model
37(1)
3.1.4 Controversy Surrounding Significance Testing
37(1)
3.2 Analysis of Variance
37(16)
3.2.1 One-Way Between-Subjects ANOVA
39(3)
3.2.2 Factorial Between-Subjects ANOVA
42(1)
3.2.3 Within-Subjects ANOVA
43(3)
3.2.4 Mixed Between-Within-Subjects ANOVA
46(1)
3.2.5 Design Complexity
47(1)
3.2.5.1 Nesting
47(1)
3.2.5.2 Latin-Square Designs
47(1)
3.2.5.3 Unequal n and Nonorthogonality
48(1)
3.2.5.4 Fixed and Random Effects
49(1)
3.2.6 Specific Comparisons
49(1)
3.2.6.1 Weighting Coefficients for Comparisons
50(1)
3.2.6.2 Orthogonality of Weighting Coefficients
50(1)
3.2.6.3 Obtained F for Comparisons
51(1)
3.2.6.4 Critical F for Planned Comparisons
52(1)
3.2.6.5 Critical F for Post Hoc Comparisons
52(1)
3.3 Parameter Estimation
53(1)
3.4 Effect Size
54(1)
3.5 Bivariate Statistics: Correlation and Regression
55(3)
3.5.1 Correlation
56(1)
3.5.2 Regression
57(1)
3.6 Chi-Square Analysis
58(2)
4 Cleaning Up Your Act: Screening Data Prior to Analysis
60(57)
4.1 Important-Issues in Data Screening
61(31)
4.1.1 Accuracy of Data File
61(1)
4.1.2 Honest Correlations
61(1)
4.1.2.1 Inflated Correlation
61(1)
4.1.2.2 Deflated Correlation
61(1)
4.1.3 Missing Data
62(1)
4.1.3.1 Deleting Cases or Variables
63(3)
4.1.3.2 Estimating Missing Data
66(4)
4.1.3.3 Using a Missing Data Correlation Matrix
70(1)
4.1.3.4 Treating Missing Data as Data
71(1)
4.1.3.5 Repeating Analyses With and Without Missing Data
71(1)
4.1.3.6 Choosing Among Methods for Dealing With Missing Data
71(1)
4.1.4 Outliers
72(1)
4.1.4.1 Detecting Univariate and Multivariate Outliers
73(3)
4.1.4.2 Describing Outliers
76(1)
4.1.4.3 Reducing the Influence of Outliers
77(1)
4.1.4.4 Outliers in a Solution
77(1)
4.1.5 Normality, Linearity, and Homoscedasticity
78(1)
4.1.5.1 Normality
79(4)
4.1.5.2 Linearity
83(2)
4.1.5.3 Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance-Covariance Matrices
85(1)
4.1.6 Common Data Transformations
86(2)
4.1.7 Multicollinearity and Singularity
88(3)
4.1.8 A Checklist and Some Practical Recommendations
91(1)
4.2 Complete Examples of Data Screening
92(25)
4.2.1 Screening Ungrouped Data
92(1)
4.2.1.1 Accuracy of Input, Missing Data, Distributions, and Univariate Outliers
93(4)
4.2.1.2 Linearity and Homoscedasticity
97(1)
4.2.1.3 Transformation
98(1)
4.2.1.4 Detecting Multivariate Outliers
99(1)
4.2.1.5 Variables Causing Cases to Be Outliers
100(4)
4.2.1.6 Multicollinearity
104(1)
4.2.2 Screening Grouped Data
105(1)
4.2.2.1 Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers
105(5)
4.2.2.2 Linearity
110(1)
4.2.2.3 Multivariate Outliers
111(2)
4.2.2.4 Variables Causing Cases to Be Outliers
113(1)
4.2.2.5 Multicollinearity
114(3)
5 Multiple Regression
117(80)
5.1 General Purpose and Description
117(2)
5.2 Kinds of Research Questions
119(3)
5.2.1 Degree of Relationship
119(1)
5.2.2 Importance of IVs
120(1)
5.2.3 Adding IVs
120(1)
5.2.4 Changing IVs
120(1)
5.2.5 Contingencies Among IVs
120(1)
5.2.6 Comparing Sets of IVs
121(1)
5.2.7 Predicting DV Scores for Members of a New Sample
121(1)
5.2.8 Parameter Estimates
121(1)
5.3 Limitations to Regression Analyses
122(7)
5.3.1 Theoretical Issues
122(1)
5.3.2 Practical Issues
123(1)
5.3.2.1 Ratio of Cases to IVs
123(1)
5.3.2.2 Absence of Outliers Among the IVs and on the DV
124(1)
5.3.2.3 Absence of Multicollinearity and Singularity
125(1)
5.3.2.4 Normality, Linearity, and Homoscedasticity of Residuals
125(3)
5.3.2.5 Independence of Errors
128(1)
5.3.2.6 Absence of Outliers in the Solution
128(1)
5.4 Fundamental Equations for Multiple Regression
129(7)
5.4.1 General Linear Equations
129(2)
5.4.2 Matrix Equations
131(2)
5.4.3 Computer Analyses of Small-Sample Example
133(3)
5.5 Major Types of Multiple Regression
136(8)
5.5.1 Standard Multiple Regression
136(1)
5.5.2 Sequential Multiple Regression
137(1)
5.5.3 Statistical (Stepwise) Regression
138(5)
5.5.4 Choosing Among Regression Strategies
143(1)
5.6 Some Important Issues
144(17)
5.6.1 Importance of IVs
144(1)
5.6.1.1 Standard Multiple Regression
144(1)
5.6.1.2 Sequential or Statistical Regression
145(1)
5.6.1.3 Commonality Analysis
146(3)
5.6.2 Statistical Inference
149(1)
5.6.2.1 Test for Multiple R
149(1)
5.6.2.2 Test of Regression Components
150(1)
5.6.2.3 Test of Added Subset of IVs
151(1)
5.6.2.4 Confidence Limits Around B and Multiple R2
151(2)
5.6.2.5 Comparing Two Sets of Predictors
153(1)
5.6.3 Adjustment of R2
154(1)
5.6.4 Suppressor Variables
155(1)
5.6.5 Regression Approach to ANOVA
156(2)
5.6.6 Centering When Interactions and Powers of IVs Are Included
158(2)
5.6.7 Mediation in Causal Sequence
160(1)
5.7 Complete Examples of Regression Analysis
161(29)
5.7.1 Evaluation of Assumptions
162(1)
5.7.1.1 Ratio of Cases to IVs
162(1)
5.7.1.2 Normality, Linearity, Homoscedasticity, and Independence of Residuals
162(5)
5.7.1.3 Outliers
167(1)
5.7.1.4 Multicollinearity and Singularity
168(1)
5.7.2 Standard Multiple Regression
169(6)
5.7.3 Sequential Regression
175(6)
5.7.4 Example of Standard Multiple Regression With Missing Values Multiply Imputed
181(9)
5.8 Comparison of Programs
190(7)
5.8.1 IBM SPSS Package
190(5)
5.8.2 SAS System
195(1)
5.8.3 SYSTAT System
196(1)
6 Analysis of Covariance
197(48)
6.1 General Purpose and Description
197(3)
6.2 Kinds of Research Questions
200(2)
6.2.1 Main Effects of IVs
200(1)
6.2.2 Interactions Among IVs
200(1)
6.2.3 Specific Comparisons and Trend Analysis
201(1)
6.2.4 Effects of Covariates
201(1)
6.2.5 Effect Size
201(1)
6.2.6 Parameter Estimates
201(1)
6.3 Limitations to Analysis of Covariance
202(3)
6.3.1 Theoretical Issues
202(1)
6.3.2 Practical Issues
203(1)
6.3.2.1 Unequal Sample Sizes, Missing Data, and Ratio of Cases to IVs
203(1)
6.3.2.2 Absence of Outliers
203(1)
6.3.2.3 Absence of Multicollinearity and Singularity
203(1)
6.3.2.4 Normality of Sampling Distributions
204(1)
6.3.2.5 Homogeneity of Variance
204(1)
6.3.2.6 Linearity
204(1)
6.3.2.7 Homogeneity of Regression
204(1)
6.3.2.8 Reliability of Covariates
205(1)
6.4 Fundamental Equations for Analysis of Covariance
205(8)
6.4.1 Sums of Squares and Cross-Products
206(4)
6.4.2 Significance Test and Effect Size
210(1)
6.4.3 Computer Analyses of Small-Sample Example
211(2)
6.5 Some Important Issues
213(12)
6.5.1 Choosing Covariates
213(1)
6.5.2 Evaluation of Covariates
214(1)
6.5.3 Test for Homogeneity of Regression
215(1)
6.5.4 Design Complexity
215(1)
6.5.4.1 Within-Subjects and Mixed Within-Between Designs
216(3)
6.5.4.2 Unequal Sample Sizes
219(1)
6.5.4.3 Specific Comparisons and Trend Analysis
220(3)
6.5.4.4 Effect Size
223(1)
6.5.5 Alternatives to ANCOVA
223(2)
6.6 Complete Example of Analysis of Covariance
225(17)
6.6.1 Evaluation of Assumptions
225(1)
6.6.1.1 Unequal n and Missing Data
226(1)
6.6.1.2 Normality
226(1)
6.6.1.3 Linearity
226(1)
6.6.1.4 Outliers
226(4)
6.6.1.5 Multicollinearity and Singularity
230(1)
6.6.1.6 Homogeneity of Variance
230(2)
6.6.1.7 Homogeneity of Regression
232(1)
6.6.1.8 Reliability of Covariates
232(1)
6.6.2 Analysis of Covariance
232(1)
6.6.2.1 Main Analysis
232(2)
6.6.2.2 Evaluation of Covariates
234(5)
6.6.2.3 Homogeneity of Regression Run
239(3)
6.7 Comparison of Programs
242(3)
6.7.1 SPSS Package
242(1)
6.7.2 SAS System
242(1)
6.7.3 SYSTAT System
242(3)
7 Multivariate Analysis of Variance and Covariance
245(69)
7.1 General Purpose and Description
245(3)
7.2 Kinds of Research Questions
248(3)
7.2.1 Main Effects of IVs
249(1)
7.2.2 Interactions Among IVs
249(1)
7.2.3 Importance of DVs
249(1)
7.2.4 Parameter Estimates
250(1)
7.2.5 Specific Comparisons and Trend Analysis
250(1)
7.2.6 Effect Size
250(1)
7.2.7 Effects of Covariates
250(1)
7.2.8 Repeated-Measures Analysis of Variance
251(1)
7.3 Limitations to Multivariate Analysis of Variance and Covariance
251(4)
7.3.1 Theoretical Issues
251(1)
7.3.2 Practical Issues
252(1)
7.3.2.1 Unequal Sample Sizes, Missing Data, and Power
252(1)
7.3.2.2 Multivariate Normality
252(1)
7.3.2.3 Absence of Outliers
253(1)
7.3.2.4 Homogeneity of Variance-Covariance Matrices
253(1)
7.3.2.5 Linearity
254(1)
7.3.2.6 Homogeneity of Regression
254(1)
7.3.2.7 Reliability of Covariates
255(1)
7.3.2.8 Absence of Multicollinearity and Singularity
255(1)
7.4 Fundamental Equations for Multivariate Analysis of Variance and Covariance
255(15)
7.4.1 Multivariate Analysis of Variance
255(8)
7.4.2 Computer Analyses of Small-Sample Example
263(3)
7.4.3 Multivariate Analysis of Covariance
266(4)
7.5 Some Important Issues
270(9)
7.5.1 MANOVA versus ANOVAs
270(1)
7.5.2 Criteria for Statistical Inference
270(1)
7.5.3 Assessing DVs
271(1)
7.5.3.1 Univariate F
272(1)
7.5.3.2 Roy-Bargmann Stepdown Analysis
273(1)
7.5.3.3 Using Discriminant Analysis
274(1)
7.5.3.4 Choosing Among Strategies for Assessing DVs
275(1)
7.5.4 Specific Comparisons and Trend Analysis
275(1)
7.5.5 Design Complexity
276(1)
7.5.5.1 Within-Subjects and Between-Within Designs
276(2)
7.5.5.2 Unequal Sample Sizes
278(1)
7.6 Complete Examples of Multivariate Analysis of Variance and Covariance
279(31)
7.6.1 Evaluation of Assumptions
279(1)
7.6.1.1 Unequal Sample Sizes and Missing Data
279(2)
7.6.1.2 Multivariate Normality
281(1)
7.6.1.3 Linearity
281(1)
7.6.1.4 Outliers
282(1)
7.6.1.5 Homogeneity of Variance--Covariance Matrices
282(1)
7.6.1.6 Homogeneity of Regression
283(3)
7.6.1.7 Reliability of Covariates
286(1)
7.6.1.8 Multicollinearity and Singularity
287(1)
7.6.2 Multivariate Analysis of Variance
287(11)
7.6.3 Multivariate Analysis of Covariance
298(1)
7.6.3.1 Assessing Covariates
298(2)
7.6.3.2 Assessing DVs
300(10)
7.7 Comparison of Programs
310(4)
7.7.1 IBM SPSS Package
310(3)
7.7.2 SAS System
313(1)
7.7.3 SYSTAT System
313(1)
8 Profile Analysis: The Multivariate Approach to Repeated Measures
314(63)
8.1 General Purpose and Description
314(1)
8.2 Kinds of Research Questions
315(2)
8.2.1 Parallelism of Profiles
315(1)
8.2.2 Overall Difference Among Groups
316(1)
8.2.3 Flatness of Profiles
316(1)
8.2.4 Contrasts Following Profile Analysis
316(1)
8.2.5 Parameter Estimates
316(1)
8.2.6 Effect Size
316(1)
8.3 Limitations to Profile Analysis
317(2)
8.3.1 Theoretical Issues
317(1)
8.3.2 Practical Issues
317(1)
8.3.2.1 Sample Size, Missing Data, and Power
317(1)
8.3.2.2 Multivariate Normality
318(1)
8.3.2.3 Absence of Outliers
318(1)
8.3.2.4 Homogeneity of Variance--Covariance Matrices
318(1)
8.3.2.5 Linearity
318(1)
8.3.2.6 Absence of Multicollinearity and Singularity
319(1)
8.4 Fundamental Equations for Profile Analysis
319(12)
8.4.1 Differences in Levels
320(1)
8.4.2 Parallelism
321(3)
8.4.3 Flatness
324(1)
8.4.4 Computer Analyses of Small-Sample Example
325(6)
8.5 Some Important Issues
331(17)
8.5.1 Univariate Versus Multivariate Approach to Repeated Measures
331(2)
8.5.2 Contrasts in Profile Analysis
333(2)
8.5.2.1 Parallelism and Flatness Significant, Levels Not Significant (Simple-Effects Analysis)
335(2)
8.5.2.2 Parallelism and Levels Significant, Flatness Not Significant (Simple-Effects Analysis)
337(4)
8.5.2.3 Parallelism, Levels, and Flatness Significant (Interaction Contrasts)
341(1)
8.5.2.4 Only Parallelism Significant
341(2)
8.5.3 Doubly Multivariate Designs
343(4)
8.5.4 Classifying Profiles
347(1)
8.5.5 Imputation of Missing Values
347(1)
8.6 Complete Examples of Profile Analysis
348(25)
8.6.1 Profile Analysis of Subscales of the WISC
348(1)
8.6.1.1 Evaluation of Assumptions
349(4)
8.6.1.2 Profile Analysis
353(9)
8.6.2 Doubly Multivariate Analysis of Reaction Time
362(1)
8.6.2.1 Evaluation of Assumptions
362(3)
8.6.2.2 Doubly Multivariate Analysis of Slope and Intercept
365(8)
8.7 Comparison of Programs
373(4)
8.7.1 IBM SPSS Package
374(1)
8.7.2 SAS System
374(2)
8.7.3 SYSTAT System
376(1)
9 Discriminant Analysis
377(62)
9.1 General Purpose and Description
377(3)
9.2 Kinds of Research Questions
380(3)
9.2.1 Significance of Prediction
380(1)
9.2.2 Number of Significant Discriminant Functions
380(1)
9.2.3 Dimensions of Discrimination
381(1)
9.2.4 Classification Functions
381(1)
9.2.5 Adequacy of Classification
381(1)
9.2.6 Effect Size
381(1)
9.2.7 Importance of Predictor Variables
382(1)
9.2.8 Significance of Prediction With Covariates
382(1)
9.2.9 Estimation of Group Means
382(1)
9.3 Limitations to Discriminant Analysis
383(3)
9.3.1 Theoretical Issues
383(1)
9.3.2 Practical Issues
383(1)
9.3.2.1 Unequal Sample Sizes, Missing Data, and Power
383(1)
9.3.2.2 Multivariate Normality
384(1)
9.3.2.3 Absence of Outliers
384(1)
9.3.2.4 Homogeneity of Variance--Covariance Matrices
384(1)
9.3.2.5 Linearity
385(1)
9.3.2.6 Absence of Multicollinearity and Singularity
385(1)
9.4 Fundamental Equations for Discriminant Analysis
386(11)
9.4.1 Derivation and Test of Discriminant Functions
386(3)
9.4.2 Classification
389(2)
9.4.3 Computer Analyses of Small-Sample Example
391(6)
9.5 Types of Discriminant Analyses
397(2)
9.5.1 Direct Discriminant Analysis
397(1)
9.5.2 Sequential Discriminant Analysis
398(1)
9.5.3 Stepwise (Statistical) Discriminant Analysis
398(1)
9.6 Some Important Issues
399(10)
9.6.1 Statistical Inference
399(1)
9.6.1.1 Criteria for Overall Statistical Significance
399(1)
9.6.1.2 Stepping Methods
399(1)
9.6.2 Number of Discriminant Functions
400(1)
9.6.3 Interpreting Discriminant Functions
400(1)
9.6.3.1 Discriminant Function Plots
400(2)
9.6.3.2 Structure Matrix of Loadings
402(1)
9.6.4 Evaluating Predictor Variables
403(1)
9.6.5 Effect Size
404(1)
9.6.6 Design Complexity: Factorial Designs
405(1)
9.6.7 Use of Classification Procedures
406(1)
9.6.7.1 Cross-Validation and New Cases
407(1)
9.6.7.2 Jackknifed Classification
407(1)
9.6.7.3 Evaluating Improvement in Classification
407(2)
9.7 Complete Example of Discriminant Analysis
409(23)
9.7.1 Evaluation of Assumptions
409(1)
9.7.1.1 Unequal Sample Sizes and Missing Data
409(1)
9.7.1.2 Multivariate Normality
410(1)
9.7.1.3 Linearity
410(1)
9.7.1.4 Outliers
410(3)
9.7.1.5 Homogeneity of Variance-Covariance Matrices
413(1)
9.7.1.6 Multicollinearity and Singularity
413(1)
9.7.2 Direct Discriminant Analysis
414(18)
9.8 Comparison of Programs
432(7)
9.8.1 IBM SPSS Package
432(1)
9.8.2 SAS System
432(6)
9.8.3 SYSTAT System
438(1)
10 Logistic Regression
439(71)
10.1 General Purpose and Description
439(2)
10.2 Kinds of Research Questions
441(2)
10.2.1 Prediction of Group Membership or Outcome
441(1)
10.2.2 Importance of Predictors
441(1)
10.2.3 Interactions among Predictors
442(1)
10.2.4 Parameter Estimates
442(1)
10.2.5 Classification of Cases
442(1)
10.2.6 Significance of Prediction with Covariates
442(1)
10.2.7 Effect Size
443(1)
10.3 Limitations to Logistic Regression Analysis
443(3)
10.3.1 Theoretical Issues
443(1)
10.3.2 Practical Issues
444(1)
10.3.2.1 Ratio of Cases to Variables
444(1)
10.3.2.2 Adequacy of Expected Frequencies and Power
444(1)
10.3.2.3 Linearity in the Logit
445(1)
10.3.2.4 Absence of Multicollinearity
445(1)
10.3.2.5 Absence of Outliers in the Solution
445(1)
10.3.2.6 Independence of Errors
445(1)
10.4 Fundamental Equations for Logistic Regression
446(9)
10.4.1 Testing and Interpreting Coefficients
447(1)
10.4.2 Goodness of Fit
448(2)
10.4.3 Comparing Models
450(1)
10.4.4 Interpretation and Analysis of Residuals
450(1)
10.4.5 Computer Analyses of Small-Sample Example
451(4)
10.5 Types of Logistic Regression
455(4)
10.5.1 Direct Logistic Regression
456(1)
10.5.2 Sequential Logistic Regression
456(1)
10.5.3 Statistical (Stepwise) Logistic Regression
456(2)
10.5.4 Probit and Other Analyses
458(1)
10.6 Some Important Issues
459(13)
10.6.1 Statistical Inference
459(1)
10.6.1.1 Assessing Goodness of Fit of Models
459(2)
10.6.1.2 Tests of Individual Variables
461(1)
10.6.2 Effect Size for a Model
462(1)
10.6.3 Interpretation of Coefficients Using Odds
463(2)
10.6.4 Coding Outcome and Predictor Categories
465(1)
10.6.5 Number and Type of Outcome Categories
466(3)
10.6.6 Classification of Cases
469(1)
10.6.7 Hierarchical and Nonhierarchical Analysis
470(2)
10.6.8 Importance of Predictors
472(1)
10.6.9 Logistic Regression for Matched Groups
472(1)
10.7 Complete Examples of Logistic Regression
472(30)
10.7.1 Evaluation of Limitations
473(1)
10.7.1.1 Ratio of Cases to Variables and Missing Data
473(3)
10.7.1.2 Multicollinearity
476(1)
10.7.1.3 Outliers in the Solution
477(1)
10.7.2 Direct Logistic Regression with Two-Category Outcome and Continuous Predictors
477(1)
10.7.2.1 Limitation: Linearity in the Logit
477(1)
10.7.2.2 Direct Logistic Regression With Two-Category Outcome
477(7)
10.7.3 Sequential Logistic Regression with Three Categories of Outcome
484(1)
10.7.3.1 Limitations of Multinomial Logistic Regression
484(1)
10.7.3.2 Sequential Multinomial Logistic Regression
484(18)
10.8 Comparison of Programs
502(8)
10.8.1 IBM SPSS Package
502(6)
10.8.2 SAS System
508(1)
10.8.3 SYSTAT System
509(1)
11 Survival/Failure Analysis
510(61)
11.1 General Purpose and Description
510(2)
11.2 Kinds of Research Questions
512(1)
11.2.1 Proportions Surviving at Various Times
512(1)
11.2.2 Group Differences in Survival
512(1)
11.2.3 Survival Time With Covariates
512(1)
11.2.3.1 Treatment Effects
512(1)
11.2.3.2 Importance of Covariates
512(1)
11.2.3.3 Parameter Estimates
513(1)
11.2.3.4 Contingencies Among Covariates
513(1)
11.2.3.5 Effect Size and Power
513(1)
11.3 Limitations to Survival Analysis
513(2)
11.3.1 Theoretical Issues
513(1)
11.3.2 Practical Issues
513(1)
11.3.2.1 Sample Size and Missing Data
514(1)
11.3.2.2 Normality of Sampling Distributions, Linearity, and Homoscedasticity
514(1)
11.3.2.3 Absence of Outliers
514(1)
11.3.2.4 Differences Between Withdrawn and Remaining Cases
514(1)
11.3.2.5 Change in Survival Conditions over Time
514(1)
11.3.2.6 Proportionality of Hazards
515(1)
11.3.2.7 Absence of Multicollinearity
515(1)
11.4 Fundamental Equations for Survival Analysis
515(13)
11.4.1 Life Tables
516(2)
11.4.2 Standard Error of Cumulative Proportion Surviving
518(1)
11.4.3 Hazard and Density Functions
518(1)
11.4.4 Plot of Life Tables
519(1)
11.4.5 Test for Group Differences
520(2)
11.4.6 Computer Analyses of Small-Sample Example
522(6)
11.5 Types of Survival Analyses
528(11)
11.5.1 Actuarial and Product-Limit Life Tables and Survivor Functions
528(1)
11.5.2 Prediction of Group Survival Times From Covariates
529(2)
11.5.2.1 Direct, Sequential, and Statistical Analysis
531(1)
11.5.2.2 Cox Proportional-Hazards Model
531(1)
11.5.2.3 Accelerated Failure-Time Models
532(7)
11.5.2.4 Choosing a Method
539(1)
11.6 Some Important Issues
539(6)
11.6.1 Proportionality of Hazards
539(2)
11.6.2 Censored Data
541(1)
11.6.2.1 Right-Censored Data
541(1)
11.6.2.2 Other Forms of Censoring
541(1)
11.6.3 Effect Size and Power
542(1)
11.6.4 Statistical Criteria
543(1)
11.6.4.1 Test Statistics for Group Differences in Survival Functions
543(1)
11.6.4.2 Test Statistics for Prediction From Covariates
544(1)
11.6.5 Predicting Survival Rate
544(1)
11.6.5.1 Regression Coefficients (Parameter Estimates)
544(1)
11.6.5.2 Hazard Ratios
544(1)
11.6.5.3 Expected Survival Rates
545(1)
11.7 Complete Example of Survival Analysis
545(18)
11.7.1 Evaluation of Assumptions
547(1)
11.7.1.1 Accuracy of Input, Adequacy of Sample Size, Missing Data, and Distributions
547(2)
11.7.1.2 Outliers
549(4)
11.7.1.3 Differences Between Withdrawn and Remaining Cases
553(1)
11.7.1.4 Change in Survival Experience over Time
553(1)
11.7.1.5 Proportionality of Hazards
553(2)
11.7.1.6 Multicollinearity
555(1)
11.7.2 Cox Regression Survival Analysis
555(1)
11.7.2.1 Effect of Drug Treatment
556(1)
11.7.2.2 Evaluation of Other Covariates
556(7)
11.8 Comparison of Programs
563(8)
11.8.1 SAS System
563(6)
11.8.2 IBM SPSS Package
569(1)
11.8.3 SYSTAT System
570(1)
12 Canonical Correlation
571(41)
12.1 General Purpose and Description
571(2)
12.2 Kinds of Research Questions
573(1)
12.2.1 Number of Canonical Variate Pairs
573(1)
12.2.2 Interpretation of Canonical Variates
573(1)
12.2.3 Importance of Canonical Variates
573(1)
12.2.4 Canonical Variate Scores
574(1)
12.3 Limitations
574(2)
12.3.1 Theoretical Limitations
574(1)
12.3.2 Practical Issues
575(1)
12.3.2.1 Ratio of Cases to IVs
575(1)
12.3.2.2 Normality, Linearity, and Homoscedasticity
575(1)
12.3.2.3 Missing Data
576(1)
12.3.2.4 Absence of Outliers
576(1)
12.3.2.5 Absence of Multicollinearity and Singularity
576(1)
12.4 Fundamental Equations for Canonical Correlation
576(15)
12.4.1 Eigenvalues and Eigenvectors
578(2)
12.4.2 Matrix Equations
580(4)
12.4.3 Proportions of Variance Extracted
584(1)
12.4.4 Computer Analyses of Small-Sample Example
585(6)
12.5 Some Important Issues
591(1)
12.5.1 Importance of Canonical Variates
591(1)
12.5.2 Interpretation of Canonical Variates
592(1)
12.6 Complete Example of Canonical Correlation
592(17)
12.6.1 Evaluation of Assumptions
593(1)
12.6.1.1 Missing Data
593(1)
12.6.1.2 Normality, Linearity, and Homoscedasticity
593(2)
12.6.1.3 Outliers
595(1)
12.6.1.4 Multicollinearity and Singularity
595(1)
12.6.2 Canonical Correlation
595(14)
12.7 Comparison of Programs
609(3)
12.7.1 SAS System
609(1)
12.7.2 IBM SPSS Package
609(2)
12.7.3 SYSTAT System
611(1)
13 Principal Components and Factor Analysis
612(69)
13.1 General Purpose and Description
612(3)
13.2 Kinds of Research Questions
615(1)
13.2.1 Number of Factors
615(1)
13.2.2 Nature of Factors
616(1)
13.2.3 Importance of Solutions and Factors
616(1)
13.2.4 Testing Theory in FA
616(1)
13.2.5 Estimating Scores on Factors
616(1)
13.3 Limitations
616(4)
13.3.1 Theoretical Issues
616(1)
13.3.2 Practical Issues
617(1)
13.3.2.1 Sample Size and Missing Data
618(1)
13.3.2.2 Normality
618(1)
13.3.2.3 Linearity
618(1)
13.3.2.4 Absence of Outliers Among Cases
619(1)
13.3.2.5 Absence of Multicollinearity and Singularity
619(1)
13.3.2.6 Factorability of R?
619(1)
13.3.2.7 Absence of Outliers Among Variables
620(1)
13.4 Fundamental Equations for Factor Analysis
620(17)
13.4.1 Extraction
622(3)
13.4.2 Orthogonal Rotation
625(1)
13.4.3 Communalities, Variance, and Covariance
626(1)
13.4.4 Factor Scores
627(3)
13.4.5 Oblique Rotation
630(2)
13.4.6 Computer Analyses of Small-Sample Example
632(5)
13.5 Major Types of Factor Analyses
637(10)
13.5.1 Factor Extraction Techniques
637(2)
13.5.1.1 PCA Versus FA
639(1)
13.5.1.2 Principal Components
640(1)
13.5.1.3 Principal Factors
640(1)
13.5.1.4 Image Factor Extraction
641(1)
13.5.1.5 Maximum Likelihood Factor Extraction
641(1)
13.5.1.6 Unweighted Least Squares Factoring
641(1)
13.5.1.7 Generalized (Weighted) Least Squares Factoring
641(1)
13.5.1.8 Alpha Factoring
642(1)
13.5.2 Rotation
642(1)
13.5.2.1 Orthogonal Rotation
642(2)
13.5.2.2 Oblique Rotation
644(1)
13.5.2.3 Geometric Interpretation
645(2)
13.5.3 Some Practical Recommendations
647(1)
13.6 Some Important Issues
647(9)
13.6.1 Estimates of Communalities
648(1)
13.6.2 Adequacy of Extraction and Number of Factors
648(3)
13.6.3 Adequacy of Rotation and Simple Structure
651(1)
13.6.4 Importance and Internal Consistency of Factors
652(2)
13.6.5 Interpretation of Factors
654(1)
13.6.6 Factor Scores
655(1)
13.6.7 Comparisons Among Solutions and Groups
656(1)
13.7 Complete Example of FA
656(20)
13.7.1 Evaluation of Limitations
657(1)
13.7.1.1 Sample Size and Missing Data
657(1)
13.7.1.2 Normality
657(1)
13.7.1.3 Linearity
657(1)
13.7.1.4 Outliers
658(3)
13.7.1.5 Multicollinearity and Singularity
661(1)
13.7.1.6 Factorability of R
661(1)
13.7.1.7 Outliers Among Variables
661(1)
13.7.2 Principal Factors Extraction With Varimax Rotation
661(15)
13.8 Comparison of Programs
676(5)
13.8.1 IBM SPSS Package
676(1)
13.8.2 SAS System
676(4)
13.8.3 SYSTAT System
680(1)
14 Structural Equation Modeling
681(105)
Jodie B. Ullman
14.1 General Purpose and Description
681(4)
14.2 Kinds of Research Questions
685(2)
14.2.1 Adequacy of the Model
685(1)
14.2.2 Testing Theory
685(1)
14.2.3 Amount of Variance in the Variables Accounted for by the Factors
685(1)
14.2.4 Reliability of the Indicators
685(1)
14.2.5 Parameter Estimates
685(1)
14.2.6 Intervening Variables
686(1)
14.2.7 Group Differences
686(1)
14.2.8 Longitudinal Differences
686(1)
14.2.9 Multilevel Modeling
687(1)
14.2.10 Latent Class Analysis
687(1)
14.3 Limitations to Structural Equation Modeling
687(2)
14.3.1 Theoretical Issues
687(1)
14.3.2 Practical Issues
688(1)
14.3.2.1 Sample Size and Missing Data
688(1)
14.3.2.2 Multivariate Normality and Outliers
688(1)
14.3.2.3 Linearity
689(1)
14.3.2.4 Absence of Multicollinearity and Singularity
689(1)
14.3.2.5 Residuals
689(1)
14.4 Fundamental Equations for Structural Equations Modeling
689(25)
14.4.1 Covariance Algebra
689(2)
14.4.2 Model Hypotheses
691(2)
14.4.3 Model Specification
693(2)
14.4.4 Model Estimation
695(4)
14.4.5 Model Evaluation
699(2)
14.4.6 Computer Analysis of Small-Sample Example
701(13)
14.5 Some Important Issues
714(23)
14.5.1 Model Identification
714(3)
14.5.2 Estimation Techniques
717(2)
14.5.2.1 Estimation Methods and Sample Size
719(1)
14.5.2.2 Estimation Methods and Nonnormality
719(1)
14.5.2.3 Estimation Methods and Dependence
720(1)
14.5.2.4 Some Recommendations for Choice of Estimation Method
720(1)
14.5.3 Assessing the Fit of the Model
720(1)
14.5.3.1 Comparative Fit Indices
721(2)
14.5.3.2 Absolute Fit Index
723(1)
14.5.3.3 Indices of Proportion of Variance Accounted
723(1)
14.5.3.4 Degree of Parsimony Fit Indices
724(1)
14.5.3.5 Residual-Based Fit Indices
725(1)
14.5.3.6 Choosing Among Fit Indices
725(1)
14.5.4 Model Modification
726(1)
14.5.4.1 Chi-Square Difference Test
726(1)
14.5.4.2 Lagrange Multiplier (LM) Test
726(2)
14.5.4.3 Wald Test
728(5)
14.5.4.4 Some Caveats and Hints on Model Modification
733(1)
14.5.5 Reliability and Proportion of Variance
733(1)
14.5.6 Discrete and Ordinal Data
734(1)
14.5.7 Multiple Group Models
735(1)
14.5.8 Mean and Covariance Structure Models
736(1)
14.6 Complete Examples of Structural Equation Modeling Analysis
737(41)
14.6.1 Confirmatory Factor Analysis of the WISC
737(1)
14.6.1.1 Model Specification for CFA
737(1)
14.6.1.2 Evaluation of Assumptions for CFA
738(1)
14.6.1.3 CFA Model Estimation and Preliminary Evaluation
739(9)
14.6.1.4 Model Modification
748(7)
14.6.2 SEM of Health Data
755(1)
14.6.2.1 SEM Model Specification
755(1)
14.6.2.2 Evaluation of Assumptions for SEM
756(4)
14.6.2.3 SEM Model Estimation and Preliminary Evaluation
760(4)
14.6.2.4 Model Modification
764(14)
14.7 Comparison of Programs
778(8)
14.7.1 EQS
778(1)
14.7.2 LISREL
778(7)
14.7.3 AMOS
785(1)
14.7.4 SAS System
785(1)
15 Multilevel Linear Modeling
786(76)
15.1 General Purpose and Description
786(3)
15.2 Kinds of Research Questions
789(2)
15.2.1 Group Differences in Means
789(1)
15.2.2 Group Differences in Slopes
789(1)
15.2.3 Cross-Level Interactions
789(1)
15.2.4 Meta-Analysis
790(1)
15.2.5 Relative Strength of Predictors at Various Levels
790(1)
15.2.6 Individual and Group Structure
790(1)
15.2.7 Effect Size
790(1)
15.2.8 Path Analysis at Individual and Group Levels
790(1)
15.2.9 Analysis of Longitudinal Data
791(1)
15.2.10 Multilevel Logistic Regression
791(1)
15.2.11 Multiple Response Analysis
791(1)
15.3 Limitations to Multilevel Linear Modeling
791(3)
15.3.1 Theoretical Issues
791(1)
15.3.2 Practical Issues
792(1)
15.3.2.1 Sample Size, Unequal-n, and Missing Data
792(1)
15.3.2.2 Independence of Errors
793(1)
15.3.2.3 Absence of Multicollinearity and Singularity
794(1)
15.4 Fundamental Equations
794(24)
15.4.1 Intercepts-Only Model
797(1)
15.4.1.1 The Intercepts-Only Model: Level-1 Equation
798(1)
15.4.1.2 The Intercepts-Only Model: Level-2 Equation
798(1)
15.4.1.3 Computer Analyses of Intercepts-Only Model
799(3)
15.4.2 Model With a First-Level Predictor
802(1)
15.4.2.1 Level-1 Equation for a Model With a Level-1 Predictor
803(1)
15.4.2.2 Level-2 Equations for a Model With a Level-1 Predictor
804(2)
15.4.2.3 Computer Analysis of a Model With a Level-1 Predictor
806(5)
15.4.3 Model With Predictors at First and Second Levels
811(1)
15.4.3.1 Level-1 Equation for Model With Predictors at Both Levels
811(1)
15.4.3.2 Level-2 Equations for Model With Predictors at Both Levels
811(1)
15.4.3.3 Computer Analyses of Model With Predictors at First and Second Levels
812(6)
15.5 Types of MLM
818(8)
15.5.1 Repeated Measures
818(5)
15.5.2 Higher-Order MLM
823(1)
15.5.3 Latent Variables
823(1)
15.5.4 Nonnormal Outcome Variables
824(1)
15.5.5 Multiple Response Models
825(1)
15.6 Some Important Issues
826(13)
15.6.1 Intraclass Correlation
826(1)
15.6.2 Centering Predictors and Changes in Their Interpretations
827(3)
15.6.3 Interactions
830(1)
15.6.4 Random and Fixed-Intercepts and Slopes
830(4)
15.6.5 Statistical Inference
834(1)
15.6.5.1 Assessing Models
834(1)
15.6.5.2 Tests of Individual Effects
835(1)
15.6.6 Effect Size
836(1)
15.6.7 Estimation Techniques and Convergence Problems
837(1)
15.6.8 Exploratory Model Building
838(1)
15.7 Complete Example of MLM
839(17)
15.7.1 Evaluation of Assumptions
839(1)
15.7.1.1 Sample Sizes, Missing Data, and Distributions
839(3)
15.7.1.2 Outliers
842(1)
15.7.1.3 Multicollinearity and Singularity
843(1)
15.7.1.4 Independence of Errors: Intraclass Correlations
843(1)
15.7.2 Multilevel Modeling
844(12)
15.8 Comparison of Programs
856(6)
15.8.1 SAS System
856(4)
15.8.2 IBM SPSS Package
860(1)
15.8.3 HLM Program
860(1)
15.8.4 MLwiN Program
861(1)
15.8.5 SYSTAT System
861(1)
16 Multiway Frequency Analysis
862(53)
16.1 General Purpose and Description
862(1)
16.2 Kinds of Research Questions
863(2)
16.2.1 Associations Among Variables
863(1)
16.2.2 Effect on a Dependent Variable
864(1)
16.2.3 Parameter Estimates
864(1)
16.2.4 Importance of Effects
864(1)
16.2.5 Effect Size
864(1)
16.2.6 Specific Comparisons and Trend Analysis
865(1)
16.3 Limitations to Multiway Frequency Analysis
865(2)
16.3.1 Theoretical Issues
865(1)
16.3.2 Practical Issues
865(1)
16.3.2.1 Independence
865(1)
16.3.2.2 Ratio of Cases to Variables
866(1)
16.3.2.3 Adequacy of Expected Frequencies
866(1)
16.3.2.4 Absence of Outliers in the Solution
867(1)
16.4 Fundamental Equations for Multiway Frequency Analysis
867(23)
16.4.1 Screening for Effects
868(1)
16.4.1.1 Total Effect
869(1)
16.4.1.2 First-Order Effects
870(1)
16.4.1.3 Second-Order Effects
871(4)
16.4.1.4 Third-Order Effect
875(1)
16.4.2 Modeling
875(3)
16.4.3 Evaluation and Interpretation
878(1)
16.4.3.1 Residuals
878(1)
16.4.3.2 Parameter Estimates
879(4)
16.4.4 Computer Analyses of Small-Sample Example
883(7)
16.5 Some Important Issues
890(3)
16.5.1 Hierarchical and Nonhierarchical Models
890(1)
16.5.2 Statistical Criteria
890(1)
16.5.2.1 Tests of Models
891(1)
16.5.2.2 Tests of Individual Effects
891(1)
16.5.3 Strategies for Choosing a Model
891(1)
16.5.3.1 IBM SPSS HILOGLINEAR (Hierarchical)
892(1)
16.5.3.2 IBM SPSS GENLOG (General Log-Linear)
892(1)
16.5.3.3 SAS CATMOD and IBM SPSS Loglinear (General Log-Linear)
893(1)
16.6 Complete Example of Multiway Frequency Analysis
893(17)
16.6.1 Evaluation of Assumptions: Adequacy of Expected Frequencies
893(1)
16.6.2 Hierarchical Log-Linear Analysis
893(1)
16.6.2.1 Preliminary Model Screening
893(2)
16.6.2.2 Stepwise Model Selection
895(2)
16.6.2.3 Adequacy of Fit
897(4)
16.6.2.4 Interpretation of the Selected Model
901(9)
16.7 Comparison of Programs
910(5)
16.7.1 IBM SPSS Package
913(1)
16.7.2 SAS System
914(1)
16.7.3 SYSTAT System
914(1)
17 An Overview of the General Linear Model
915(12)
17.1 Linearity and the General Linear Model
915(1)
17.2 Bivariate to Multivariate Statistics and Overview of Techniques
915(7)
17.2.1 Bivariate Form
915(1)
17.2.2 Simple Multivariate Form
916(3)
17.2.3 Full Multivariate Form
919(3)
17.3 Alternative Research Strategies
922(5)
Appendix A A Skimpy Introduction to Matrix Algebra
927(10)
A.1 The Trace of a Matrix
928(1)
A.2 Addition or Subtraction of a Constant to a Matrix
928(1)
A.3 Multiplication or Division of a Matrix by a Constant
928(1)
A.4 Addition and Subtraction of Two Matrices
929(1)
A.5 Multiplication, Transposes, and Square Roots of Matrices
929(2)
A.6 Matrix "Division" (Inverses and Determinants)
931(2)
A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance From a Matrix
933(4)
Appendix B Research Designs for Complete Examples
937(7)
B.1 Women's Health and Drug Study
937(1)
B.2 Sexual Attraction Study
938(3)
B.3 Learning Disabilities Data Bank
941(1)
B.4 Reaction Time to Identify Figures
942(1)
B.5 Field Studies of Noise-Induced Sleep Disturbance
942(1)
B.6 Clinical Trial for Primary Biliary Cirrhosis
943(1)
B.7 Impact of Seat Belt Law
943(1)
Appendix C Statistical Tables
944(12)
C.1 Normal Curve Areas
945(1)
C.2 Critical Values of the t Distribution for α = .05 and .01, Two-Tailed Test
946(1)
C.3 Critical Values of the F Distribution
947(5)
C.4 Critical Values of Chi Square (χ2)
952(1)
C.5 Critical Values for Squared Multiple Correlation (R2) in Forward Stepwise Selection: α = .05
953(2)
C.6 Critical Values for Fmax (S2max/S2min) Distribution for α = .05 and .01
955(1)
References 956(9)
Index 965
Barbara Tabachnick is Professor Emerita of Psychology at California State University, Northridge, and co-author with Linda Fidell of Using Multivariate Statistics and Experimental Designs Using ANOVA. She has published over 70 articles and technical reports and participated in over 50 professional presentations, many invited.   She currently presents workshops in computer applications in univariate and multivariate data analysis and consults in a variety of research areas, including professional ethics in and beyond academia, effects of such factors as age and substances on driving and performance, educational computer games, effects of noise on annoyance and sleep, and fetal alcohol syndrome.  She is the recipient of the 2012 Western Psychological Association Lifetime Achievement Award.