Using Multivariate Statistics

by Tabachnick, Barbara G.; Fidell, Linda S.

• ISBN13: 9780321056771
• ISBN10: 0321056779
• Edition: 4th
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Allyn & Bacon

Summary

This book takes a practical approach to multivariate data analysis, with an introduction to the most commonly encountered statistical and multivariate techniques.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 users 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.For those interested in statistical analysis.

Table of Contents

Preface	xxv
Introduction	1	(16)
Multivariate Statistics: Why?	1	(4)
The Domain of Multivariate Statistics: Numbers of IVs and DVs	1	(1)
Experimental and Nonexperimental Research	2	(1)
Multivariate Statistics in Nonexperimental Research	3	(1)
Multivariate Statistics in Experimental Research	3	(1)
Computers and Multivariate Statistics	4	(1)
Program Updates	4	(1)
Garbage In, Roses Out?	5	(1)
Why Not?	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	8	(1)
Standard and Sequential Analysis	9	(1)
Combining 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 Corelation 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	(14)
Research Questions and Associated Techniques	17	(9)
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)
Significance of Group Differences	19	(1)
One-Way ANOVA and t Test	19	(1)
One-Way ANCOVA	19	(1)
Factorial ANOVA	20	(1)
Factorial ANCOVA	20	(1)
Hotelling's T2	20	(1)
One-Way MANOVA	21	(1)
One-Way MANCOVA	21	(1)
Factorial MANOVA	21	(1)
Factorial MANCOVA	22	(1)
Profile Analysis	22	(1)
Prediction of Group Membership	23	(1)
One-Way Discriminant Function	23	(1)
Sequential One-Way Discriminant Function	23	(1)
Multiway Frequency Analysis (Logit)	24	(1)
Logistic Regression	24	(1)
Sequential Logistic Regression	24	(1)
Factorial Discriminant Function	24	(1)
Sequential Factorial Discriminant Function	25	(1)
Structure	25	(1)
Principal Components	25	(1)
Factor Analysis	25	(1)
Structural Equation Modeling	26	(1)
Time Course of Events	26	(1)
Survival/Failure Analysis	26	(1)
Time-Series Analysis	26	(1)
A Decision Tree	26	(3)
Technique Chapters	29	(1)
Preliminary Check of the Data	30	(1)
Review of Univariate and Bivariate Statistics	31	(25)
Hypothesis Testing	31	(4)
One-Sample z Test as Prototype	31	(3)
Power	34	(1)
Extensions of the Model	35	(1)
Analysis of Variance	35	(16)
One-Way Between-Subjects ANOVA	36	(4)
Factorial Between-Subjects ANOVA	40	(1)
Within-Subjects ANOVA	41	(3)
Mixed Between-Within-Subjects ANOVA	44	(1)
Design Complexity	45	(1)
Nesting	45	(1)
Latin-Square Designs	46	(1)
Unequal n and Nonorthogonality	46	(1)
Fixed and Random Effects	47	(1)
Specific Comparisons	47	(1)
Weighting Coefficients for Comparisons	48	(1)
Orthogonality of Weighting Coefficients	48	(1)
Obtained F for Comparisons	49	(1)
Critical F for Planned Comparisons	50	(1)
Critical F for Post Hoc Comparisons	50	(1)
Parameter Estimation	51	(1)
Strength of Association	52	(1)
Bivariate Statistics: Correlation and Regression	53	(2)
Correlation	53	(1)
Regression	54	(1)
Chi-Square Analysis	55	(1)
Cleaning Up Your Act: Screening Data Prior to Analysis	56	(55)
Important Issues in Data Screening	57	(29)
Accuracy of Data File	57	(1)
Honest Correlations	57	(1)
Inflated Correlation	57	(1)
Deflated Correlation	57	(1)
Missing Data	58	(1)
Deleting Cases or Variables	59	(1)
Estimating Missing Data	60	(4)
Using a Missing Data Correlation Matrix	64	(1)
Treating Missing Data as Data	65	(1)
Repeating Analyses with and without Missing Data	65	(1)
Choosing among Methods for Dealing with Missing Data	65	(1)
Outliers	66	(1)
Detecting Univariate and Multivariate Outliers	67	(3)
Describing Outliers	70	(1)
Reducing the Influence of Outliers	71	(1)
Outliers in a Solution	71	(1)
Normality, Linearity, and Homoscedasticity	72	(1)
Normality	73	(4)
Linearity	77	(2)
Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance-Covariance Matrices	79	(1)
Common Data Transformations	80	(2)
Multicollinearity and Singularity	82	(3)
A Checklist and Some Practical Recommendations	85	(1)
Complete Examples of Data Screening	86	(25)
Screening Ungrouped Data	86	(1)
Accuracy of Input, Missing Data, Distributions, and Univariate Outliers	87	(3)
Linearity and Homoscedasticity	90	(2)
Transformation	92	(1)
Detecting Multivariate Outliers	92	(2)
Variables Causing Cases to be Outliers	94	(4)
Multicollinearity	98	(1)
Screening Grouped Data	99	(1)
Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers	99	(3)
Linearity	102	(2)
Multivariate Outliers	104	(3)
Variables Causing Cases to be Outliers	107	(1)
Multicollinearity	108	(3)
Multiple Regression	111	(66)
General Purpose and Description	111	(1)
Kinds of Research Questions	112	(3)
Degree of Relationship	113	(1)
Importance of IVs	113	(1)
Adding IVs	113	(1)
Changing IVs	113	(1)
Contingencies among IVs	114	(1)
Comparing Sets of IVs	114	(1)
Predicting DV Scores for Members of a New Sample	114	(1)
Parameter Estimates	115	(1)
Limitations to Regression Analyses	115	(7)
Theoretical Issues	115	(1)
Practical Issues	116	(1)
Ratio of Cases to IVs	117	(1)
Absence of Outliers among the IVs and on the DV	117	(1)
Absence of Multicollinearity and Singularity	118	(1)
Normality, Linearity, Homoscedasticity of Residuals	119	(2)
Independence of Errors	121	(1)
Outliers in the Solution	122	(1)
Fundamental Equations for Multiple Regression	122	(9)
General Linear Equations	123	(1)
Matrix Equations	124	(4)
Computer Analyses of Small-Sample Example	128	(3)
Major Types of Multiple Regression	131	(8)
Standard Multiple Regression	131	(1)
Sequential Multiple Regression	131	(2)
Statistical (Stepwise) Regression	133	(5)
Choosing among Regression Strategies	138	(1)
Some Important Issues	139	(14)
Importance of IVs	139	(1)
Standard Multiple Regression	140	(2)
Sequential or Statistical Regression	142	(1)
Statistical Inference	142	(1)
Test for Multiple R	142	(1)
Test of Regression Components	143	(1)
Test of Added Subset of IVs	144	(1)
Confidence Limits around B	145	(1)
Comparing Two Sets of Predictors	145	(2)
Adjustment of R2	147	(1)
Suppressor Variables	148	(1)
Regression Approach to ANOVA	149	(2)
Centering when Interactions and Powers of IVs Are Included	151	(2)
Complete Examples of Regression Analysis	153	(17)
Evaluation of Assumptions	154	(1)
Ratio of Cases to IVs	154	(1)
Normality, Linearity, Homoscedasticity, and Independence of Residuals	154	(3)
Outliers	157	(1)
Multicollinearity and Singularity	157	(2)
Standard Multiple Regression	159	(6)
Sequential Regression	165	(5)
Comparison of Programs	170	(7)
SPSS Package	170	(5)
SAS System	175	(1)
SYSTAT System	176	(1)
Canonical Correlation	177	(42)
General Purpose and Description	177	(1)
Kinds of Research Questions	178	(1)
Number of Canonical Variate Pairs	178	(1)
Interpretation of Canonical Variates	178	(1)
Importance of Canonical Variates	178	(1)
Canonical Variate Scores	178	(1)
Limitations	178	(4)
Theoretical Limitations	178	(2)
Practical Issues	180	(1)
Ratio of Cases to IVs	180	(1)
Normality, Linearity, and Homoscedasticity	180	(1)
Missing Data	181	(1)
Absence of Outliers	181	(1)
Absence of Multicollinearity and Singularity	181	(1)
Fundamental Equations for Canonical Correlation	182	(16)
Eigenvalues and Eigenvectors	183	(2)
Matrix Equations	185	(4)
Proportions of Variance Extracted	189	(1)
Computer Analyses of Small-Sample Example	190	(8)
Some Important Issues	198	(1)
Importance of Canonical Variates	198	(1)
Interpretation of Canonical Variates	199	(1)
Complete Example of Canonical Correlation	199	(17)
Evaluation of Assumptions	200	(1)
Missing Data	200	(1)
Normality, Linearity, and Homoscedasticity	200	(3)
Outliers	203	(4)
Multicollinearity and Singularity	207	(9)
Canonical Correlation	216	(1)
Comparison of Programs	216	(3)
SAS System	216	(1)
SPSS Package	216	(2)
SYSTAT System	218	(1)
Multiway Frequency Analysis	219	(56)
General Purpose and Description	219	(1)
Kinds of Research Questions	220	(2)
Associations among Variables	220	(1)
Effect on a Dependent Variable	221	(1)
Parameter Estimates	221	(1)
Importance of Effects	221	(1)
Strength of Association	221	(1)
Specific Comparisons and Trend Analysis	222	(1)
Limitations to Multiway Frequency Analysis	222	(2)
Theoretical Issues	222	(1)
Practical Issues	222	(1)
Independence	222	(1)
Ratio of Cases to Variables	223	(1)
Adequacy of Expected Frequencies	223	(1)
Outliers in the Solution	224	(1)
Fundamental Equations for Multiway Frequency Analysis	224	(26)
Screening for Effects	225	(1)
Total Effect	226	(1)
First-Order Effects	227	(1)
Second-Order Effects	228	(4)
Third-Order Effect	232	(1)
Modeling	233	(2)
Evaluation and Interpretation	235	(1)
Residuals	235	(1)
Parameter Estimates	236	(5)
Computer Analyses of Small-Sample Example	241	(9)
Some Important Issues	250	(3)
Hierarchical and Nonhierarchical Models	250	(1)
Statistical Criteria	251	(1)
Tests of Models	251	(1)
Test of Individual Effects	251	(1)
Strategies for Choosing a Model	252	(1)
SPSS HILOGLINEAR (Hierachical)	252	(1)
SPSS GENLOG (General Log-linear)	253	(1)
SAS CATMOD, SYSTAT LOGLINEAR, and SYSTAT LOGLIN (General Log-linear)	253	(1)
Complete Example of Multiway Frequency Analysis	253	(17)
Evaluation of Assumptions: Adequacy of Expected Frequencies	253	(1)
Hierarchical Log-linear Analysis	254	(1)
Preliminary Model Screening	254	(2)
Stepwise Model Selection	256	(2)
Adequacy of Fit	258	(6)
Interpretation of the Selected Model	264	(6)
Comparison of Programs	270	(5)
SPSS Package	273	(1)
SAS System	274	(1)
SYSTAT System	274	(1)
Analysis of Covariance	275	(47)
General Purpose and Description	275	(2)
Kinds of Research Questions	277	(2)
Main Effects of IVs	278	(1)
Interactions among IVs	278	(1)
Specific Comparisons and Trend Analysis	278	(1)
Effects of Covariates	278	(1)
Strength of Association	279	(1)
Parameter Estimates	279	(1)
Limitations to Analysis of Covariance	279	(4)
Theoretical Issues	279	(1)
Practical Issues	280	(1)
Unequal Sample Sizes, Missing Data, and Ratio of Cases to IVs	280	(1)
Absence of Outliers	281	(1)
Absence of Multicollinearity and Singularity	281	(1)
Normality of Sampling Distributions	281	(1)
Homogeneity of Variance	281	(1)
Linearity	282	(1)
Homogeneity of Regression	282	(1)
Reliability of Covariates	283	(1)
Fundamental Equations for Analysis of Covariance	283	(8)
Sums of Squares and Cross-Products	284	(4)
Significance Test and Strength of Association	288	(1)
Computer Analyses of Small-Sample Example	289	(2)
Some Important Issues	291	(13)
Test for Homogeneity of Regression	291	(2)
Design Complexity	293	(1)
Within-Subjects and Mixed Within-Between Designs	293	(3)
Unequal Sample Sizes	296	(2)
Specific Comparisons and Trend Analysis	298	(3)
Strength of Association	301	(1)
Evaluation of Covariates	302	(1)
Choosing Covariates	302	(1)
Alternatives to ANCOVA	303	(1)
Complete Example of Analysis of Covariance	304	(15)
Evaluation of Assumptions	305	(1)
Unequal n and Missing Data	305	(1)
Normality	305	(1)
Linearity	305	(1)
Outliers	305	(4)
Multicollinearity and Singularity	309	(1)
Homogeneity of Variance	309	(1)
Homogeneity of Regression	310	(1)
Reliability of Covariates	310	(1)
Analysis of Covariance	310	(1)
Main Analysis	310	(3)
Evaluation of Covariates	313	(2)
Homogeneity of Regression Run	315	(4)
Comparison of Programs	319	(3)
SPSS Package	319	(1)
SYSTAT System	319	(2)
SAS System	321	(1)
Multivariate Analysis of Variance and Covariance	322	(69)
General Purpose and Description	322	(3)
Kinds of Research Questions	325	(3)
Main Effects of IVs	325	(1)
Interactions among IVs	326	(1)
Importance of DVs	326	(1)
Parameter Estimates	326	(1)
Specific Comparisons and Trend Analysis	327	(1)
Strength of Association	327	(1)
Effects of Covariates	327	(1)
Repeated-Measures Analysis of Variance	327	(1)
Limitations to Multivariate Analysis of Variance and Covariance	328	(4)
Theoretical Issues	328	(1)
Practical Issues	328	(1)
Unequal Sample Sizes, Missing Data, and Power	329	(1)
Multivariate Normality	329	(1)
Absence of Outliers	330	(1)
Homogeneity of Variance-Covariance Matrices	330	(1)
Linearity	330	(1)
Homogeneity of Regression	331	(1)
Reliability of Covariates	331	(1)
Absence of Multicollinearity and Singularity	331	(1)
Fundamental Equations for Multivariate Analysis of Variance and Covariance	332	(15)
Multivariate Analysis of Variance	332	(7)
Computer Analyses of Small-Sample Example	339	(1)
Multivariate Analysis of Covariance	340	(7)
Some Important Issues	347	(10)
Criteria for Statistical Inference	347	(1)
Assessing DVs	348	(1)
Univariate F	348	(2)
Roy-Bargmann Stepdown Analysis	350	(1)
Using Discriminant Function Analysis	351	(1)
Choosing among Strategies for Assessing DVs	351	(1)
Specific Comparisons and Trend Analysis	352	(4)
Design Complexity	356	(1)
Within-Subjects and Between-Within Designs	356	(1)
Unequal Sample Sizes	356	(1)
MANOVA vs. ANOVAs	357	(1)
Complete Examples of Multivariate Analysis of Variance and Covariance	357	(29)
Evaluation of Assumptions	358	(1)
Unequal Sample Sizes and Missing Data	358	(2)
Multivariate Normality	360	(1)
Linearity	360	(1)
Outliers	360	(1)
Homogeneity of Variance-Covariance Matrices	361	(1)
Homogeneity of Regression	362	(3)
Reliability of Covariates	365	(1)
Multicollinearity and Singularity	365	(1)
Multivariate Analysis of Variance	365	(11)
Multivariate Analysis of Covariance	376	(1)
Assessing Covariates	377	(1)
Assessing DVs	377	(9)
Comparison of Programs	386	(5)
SPSS package	389	(1)
SYSTAT System	389	(1)
SAS System	390	(1)
Profile Analysis: The Multivariate Approach to Repeated Measures	391	(65)
General Purpose and Description	391	(1)
Kinds of Research Questions	392	(2)
Parallelism of Profiles	392	(1)
Overall Difference among Groups	393	(1)
Flatness of Profiles	393	(1)
Contrasts Following Profile Analysis	393	(1)
Parameter Estimates	393	(1)
Strength of Association	394	(1)
Limitations to Profile Analysis	394	(2)
Theoretical Issues	394	(1)
Practical Issues	394	(1)
Sample Size, Missing Data, and Power	394	(1)
Multivariate Normality	395	(1)
Absence of Outliers	395	(1)
Homogeneity of Variance-Covariance Matrices	395	(1)
Linearity	395	(1)
Absence of Multicollinearity and Singularity	396	(1)
Fundamental Equations for Profile Analysis	396	(14)
Differences in Levels	396	(2)
Parallelism	398	(3)
Flatness	401	(2)
Computer Analyses of Small-Sample Example	403	(7)
Some Important Issues	410	(20)
Contrasts in Profile Analysis	410	(3)
Parallelism and Flatness Significant, Levels Not Significant (Simple-Effects Analysis)	413	(1)
Parallelism and Levels Significant, Flatness Not Significant (Simple-Effects Analysis)	414	(2)
Parallelism, Levels, and Flatness Significant (Interaction Contrasts)	416	(5)
Only Parallelism Significant	421	(1)
Univariate vs. Multivariate Approach to Repeated Measures	421	(2)
Doubly-Multivariate Designs	423	(6)
Classifying Profiles	429	(1)
Imputation of Missing Values	429	(1)
Complete Examples of Profile Analysis	430	(23)
Profile Analysis of Subscales of the WISC	430	(1)
Evaluation of Assumptions	431	(4)
Profile Analysis	435	(7)
Doubly-Multivariate Analysis of Reaction Time	442	(1)
Evaluation of Assumptions	442	(4)
Doubly-Multivariate Analysis of Slope and Intercept	446	(7)
Comparison of Programs	453	(3)
SPSS Package	453	(2)
SAS System	455	(1)
SYSTAT System	455	(1)
Discriminant Function Analysis	456	(61)
General Purpose and Description	456	(2)
Kinds of Research Questions	458	(3)
Significance of Prediction	458	(1)
Number of Significant Discriminant Functions	458	(1)
Dimensions of Discrimination	459	(1)
Classification Functions	459	(1)
Adequacy of Classification	459	(1)
Strength of Association	460	(1)
Importance of Predictor Variables	460	(1)
Significance of Prediction with Covariates	460	(1)
Estimation of Group Means	460	(1)
Limits to Discriminant Function Analysis	461	(2)
Theoretical Issues	461	(1)
Practical Issues	461	(1)
Unequal Sample Sizes, Missing Data, and Power	461	(1)
Multivariate Normality	462	(1)
Absence of Outliers	462	(1)
Homogeneity of Variance-Covariance Matrices	462	(1)
Linearity	463	(1)
Absence of Multicollinearity and Singularity	463	(1)
Fundamental Equations for Discriminant Function Analysis	463	(14)
Derivation and Test of Discriminant Functions	464	(3)
Classification	467	(2)
Computer Analyses of Small-Sample Example	469	(8)
Types of Discriminant Function Analysis	477	(4)
Direct Discriminant Function Analysis	478	(1)
Sequential Discriminant Function Analysis	478	(3)
Stepwise (Statistical) Discriminant Function Analysis	481	(1)
Some Important Issues	481	(11)
Statistical Inference	481	(1)
Criteria for Overall Statistical Significance	481	(1)
Stepping Methods	482	(1)
Number of Discriminant Functions	482	(1)
Interpreting Discriminant Functions	483	(1)
Discriminant Function Plots	483	(1)
Loading Matrices	484	(1)
Evaluating Predictor Variables	485	(3)
Design Complexity: Factorial Designs	488	(1)
Use of Classification Procedures	489	(1)
Cross-Validation and New Cases	489	(1)
Jackknifed Classification	490	(1)
Evaluating Improvement in Classification	490	(2)
Complete Example of Discriminant Function Analysis	492	(17)
Evaluation of Assumptions	492	(1)
Unequal Sample Sizes and Missing Data	492	(1)
Multivariate Normality	492	(1)
Linearity	493	(1)
Outliers	493	(1)
Homogeneity of Variance-Covariance Matrices	493	(1)
Multicollinearity and Singularity	493	(4)
Direct Discriminant Function Analysis	497	(12)
Comparison of Programs	509	(8)
SPSS Package	515	(1)
SYSTAT System	516	(1)
SAS System	516	(1)
Logistic Regression	517	(65)
General Purpose and Description	517	(1)
Kinds of Research Questions	518	(3)
Prediction of Group Membership or Outcome	518	(1)
Importance of Predictors	518	(1)
Interactions among Predictors	518	(2)
Parameter Estimates	520	(1)
Classification of Cases	520	(1)
Significance of Prediction with Covariates	520	(1)
Strength of Association	520	(1)
Limitations to Logistic Regression Analysis	521	(2)
Theoretical Issues	521	(1)
Practical Issues	521	(1)
Ratio of Cases to Variables	521	(1)
Adequacy of Expected Frequencies and Power	522	(1)
Linearity in the Logit	522	(1)
Absence of Multicollinearity	522	(1)
Absence of Outliers in the Solution	523	(1)
Independence of Errors	523	(1)
Fundamental Equations for Logistic Regression	523	(10)
Testing and Interpreting Coefficients	524	(1)
Goodness-of-Fit	525	(2)
Comparing Models	527	(1)
Interpretation and Analysis of Residuals	527	(1)
Computer Analyses of Small-Sample Example	527	(6)
Types of Logistic Regression	533	(3)
Direct Logistic Regression	533	(1)
Sequential Logistic Regression	533	(2)
Stepwise (Statistical) Logistic Regression	535	(1)
Probit and Other Analyses	535	(1)
Some Important Issues	536	(14)
Statistical Inference	536	(1)
Assessing Goodness-of-Fit of Models	537	(2)
Tests of Individual Variables	539	(1)
Number and Type of Outcome Categories	539	(1)
Unordered Response Categories with SYSTAT LOGIT	540	(2)
Ordered Response Categories with SAS LOGISTIC	542	(3)
Strength of Association for a Model	545	(1)
Coding Outcome and Predictor Categories	546	(1)
Classification of Cases	547	(1)
Hierarchical and Nonhierarchical Analysis	548	(1)
Interpretation of Coefficients using Odds	548	(1)
Importance of Predictors	549	(1)
Logistic Regression for Matched Groups	550	(1)
Complete Examples of Logistic Regression	550	(25)
Evaluation of Limitations	551	(1)
Ratio of Cases to Variables and Missing Data	551	(3)
Adequacy of Expected Frequencies	554	(4)
Linearity in the Logit	558	(1)
Multicollinearity	558	(1)
Outliers in the Solution	559	(1)
Direct Logistic Regression with Two-Category Outcome	559	(4)
Sequential Logistic Regression with Three Categories of Outcome	563	(12)
Comparisons of Programs	575	(7)
SPSS Package	575	(5)
SAS System	580	(1)
SYSTAT System	581	(1)
Principal Components and Factor Analysis	582	(71)
General Purpose and Description	582	(3)
Kinds of Research Questions	585	(1)
Number of Factors	585	(1)
Nature of Factors	586	(1)
Importance of Solutions and Factors	586	(1)
Testing Theory in FA	586	(1)
Estimating Scores on Factors	586	(1)
Limitations	586	(4)
Theoretical Issues	586	(1)
Practical Issues	587	(1)
Sample Size and Missing Data	588	(1)
Normality	588	(1)
Linearity	588	(1)
Absence of Outliers among Cases	588	(1)
Absence of Multicollinearity and Singularity	589	(1)
Factorability of R	589	(1)
Absence of Outliers among Variables	589	(1)
Fundamental Equations for Factor Analysis	590	(19)
Extraction	591	(4)
Orthogonal Rotation	595	(1)
Communalities, Variance, and Covariance	596	(1)
Factor Scores	597	(3)
Oblique Rotation	600	(3)
Computer Analyses of Small-Sample Example	603	(6)
Major Types of Factor Analysis	609	(10)
Factor Extraction Techniques	609	(1)
PCA vs. FA	610	(2)
Principal Components	612	(1)
Principal Factors	612	(1)
Image Factor Extraction	612	(1)
Maximum Likelihood Factor Extraction	613	(1)
Unweighted Least Squares Factoring	613	(1)
Generalized (Weighted) Least Squares Factoring	613	(1)
Alpha Factoring	613	(1)
Rotation	614	(1)
Orthogonal Rotation	614	(2)
Oblique Rotation	616	(1)
Geometric Interpretation	616	(2)
Some Practical Recommendations	618	(1)
Some Important Issues	619	(8)
Estimates of Communalities	619	(1)
Adequacy of Extraction and Number of Factors	620	(2)
Adequacy of Rotation and Simple Structure	622	(1)
Importance and Internal Consistency of Factors	623	(2)
Interpretation of Factors	625	(1)
Factor Scores	626	(1)
Comparisons among Solutions and Groups	627	(1)
Complete Example of FA	627	(21)
Evaluation of Limitations	628	(1)
Sample Size and Missing Data	628	(1)
Normality	628	(1)
Linearity	628	(1)
Outliers	628	(5)
Multicollinearity and Singularity	633	(1)
Factorability of R	633	(1)
Outliers among Variables	633	(1)
Principal Factors Extraction with Varimax Rotation	633	(15)
Comparison of Programs	648	(5)
SPSS Package	648	(4)
SAS System	652	(1)
SYSTAT System	652	(1)
Structural Equation Modeling	653	(119)
Jodie B. Ullman
General Purpose and Description	653	(4)
Kinds of Research Questions	657	(2)
Adequacy of the Model	657	(1)
Testing Theory	657	(1)
Amount of Variance in the Variables Accounted for by the Factors	657	(1)
Reliability of the Indicators	657	(1)
Parameter Estimates	657	(1)
Mediation	658	(1)
Group Differences	658	(1)
Longitudinal Differences	658	(1)
Multilevel Modeling	658	(1)
Limitations to Structural Equation Modeling	659	(2)
Theoretical Issues	659	(1)
Practical Issues	659	(1)
Sample Size and Missing Data	659
Multivariate Normality and Absence of Outliers	600	(60)
Linearity	660	(1)
Absence of Multicollinearity and Singularity	660	(1)
Residuals	661	(1)
Fundamental Equations for Structural Equations Modeling	661	(30)
Covariance Algebra	661	(2)
Model Hypotheses	663	(2)
Model Specification	665	(2)
Model Estimation	667	(5)
Model Evaluation	672	(2)
Computer Analysis of Small-Sample Example	674	(17)
Some Important Issues	691	(28)
Model Identification	691	(3)
Estimation Techniques	694	(2)
Estimation Methods and Sample Size	696	(1)
Estimation Methods and Nonnormality	697	(1)
Estimation Methods and Dependence	697	(1)
Some Recommendations for Choice of Estimation Method	697	(1)
Assessing the Fit of the Model	697	(1)
Comparative Fit Indices	698	(2)
Absolute Fit Index	700	(1)
Indices of Proportion of Variance Accounted	700	(1)
Degree of Parsimony Fit Indices	701	(1)
Residual-Based Fit Indices	702	(1)
Choosing among Fit Indices	702	(1)
Model Modification	703	(1)
Chi-Square Difference Test	703	(1)
Lagrange Multiplier Test (LM)	703	(10)
Wald Test	713	(2)
Some Caveats and Hints on Model Modification	715	(1)
Reliability and Proportion of Variance	715	(1)
Discrete and Ordinal Data	716	(1)
Multiple Group Models	717	(1)
Mean and Covariance Structure Models	718	(1)
Complete Examples of Structural Equation Modeling Analysis	719	(45)
Confirmatory Factor Analysis of the WISC	719	(1)
Model Specification for CFA	719	(1)
Evaluation of Assumptions for CFA	719	(2)
CFA Model Estimation and Preliminary Evaluation	721	(9)
Model Modification	730	(7)
SEM of Health Data	737	(1)
SEM Model Specification	737	(1)
Evaluation of Assumptions for SEM	738	(4)
Model Estimation and Preliminary Evaluation	742	(3)
Model Modification	745	(19)
Comparison of Programs	764	(8)
EQS	764	(1)
LISREL	764	(7)
SAS	771	(1)
AMOS	771	(1)
Survival/Failure Analysis	772	(65)
General Purpose and Description	772	(1)
Kinds of Research Questions	773	(2)
Proportions Surviving at Various Times	773	(1)
Group Differences in Survival	774	(1)
Survival Time with Covariates	774	(1)
Treatment Effects	774	(1)
Importance of Covariates	774	(1)
Parameter Estimates	774	(1)
Contingencies among Covariates	774	(1)
Strength of Association and Power	774	(1)
Limitations to Survival Analysis	775	(1)
Theoretical Issues	775	(1)
Practical Issues	775	(1)
Sample Size and Missing Data	775	(1)
Normality of Sampling Distributions, Linearity, and Homoscedasticity	775	(1)
Absence of Outliers	775	(1)
Differences between Withdrawn and Remaining Cases	776	(1)
Change in Survival Conditions over Time	776	(1)
Proportionality of Hazards	776	(1)
Absence of Multicollinearity	776	(1)
Fundamental Equations for Survival Analysis	776	(15)
Life Tables	777	(1)
Standard Error of Cumulative Proportion Surviving	778	(1)
Hazard and Density Functions	779	(1)
Plot of Life Tables	780	(1)
Test for Group Differences	781	(2)
Computer Analyses of Small-Sample Example	783	(8)
Types of Survival Analysis	791	(14)
Actuarial and Product-Limit Life Tables and Survivor Functions	791	(5)
Prediction of Group Survival Times from Covariates	796	(1)
Direct, Sequential, and Statistical Analysis	796	(1)
Cox Proportional-Hazards Model	797	(1)
Accelerated Failure-Time Model	797	(7)
Choosing a Method	804	(1)
Some Important Issues	805	(8)
Proportionality of Hazards	805	(2)
Censored Data	807	(1)
Right-Censored Data	807	(1)
Other Forms of Censoring	808	(1)
Strength of Association and Power	808	(1)
Statistical Criteria	809	(1)
Test Statistics for Group Differences in Survival Functions	809	(1)
Test Statistics for Prediction from Covariates	809	(2)
Odds Ratios	811	(2)
Complete Example of Survival Analysis	813	(16)
Evaluation of Assumptions	814	(1)
Accuracy of Input, Adequacy of Sample Size, Missing Data, and Distributions	814	(1)
Outliers	814	(2)
Differences between Withdrawn and Remaining Cases	816	(3)
Change in Survival Experience over Time	819	(1)
Proportionality of Hazards	820	(1)
Multicollinearity	821	(1)
Cox Regression Survival Analysis	822	(1)
Effect of Drug Treatment	822	(3)
Evaluation of Other Covariates	825	(4)
Comparison of Programs	829	(8)
SAS System	829	(1)
SYSTAT System	829	(7)
SPSS Package	836	(1)
Time-Series Analysis	837	(64)
General Purpose and Description	837	(2)
Kinds of Research Questions	839	(3)
Pattern of Autocorrelation	841	(1)
Seasonal Cycles and Trends	841	(1)
Forecasting	841	(1)
Effect of an Intervention	841	(1)
Comparing Time Series	841	(1)
Time Series with Covariates	842	(1)
Strength of Association and Power	842	(1)
Assumptions of Time-Series Analysis	842	(1)
Theoretical Issues	842	(1)
Practical Issues	842	(1)
Normality of Distributions of Residuals	842	(1)
Homogeneity of Variance and Zero Mean of Residuals	843	(1)
Independence of Residuals	843	(1)
Absence of Outliers	843	(1)
Fundamental Equations for Time-Series ARIMA Models	843	(22)
Identification of ARIMA (p, d, q) Models	844	(1)
Trend Components, d: Making the Process Stationary	844	(3)
Auto-Regressive Components	847	(1)
Moving Average Components	848	(1)
Mixed Models	848	(1)
ACFs and PACFs	849	(5)
Estimating Model Parameters	854	(1)
Diagnosing a Model	855	(1)
Computer Analysis of Small-Sample Time-Series Example	855	(10)
Types of Time-Series Analysis	865	(13)
Models with Seasonal Components	865	(4)
Models with Interventions	869	(1)
Abrupt, Permanent Effects	870	(1)
Abrupt, Temporary Effects	870	(2)
Gradual, Permanent Effects	872	(5)
Models with Multiple Interventions	877	(1)
Adding Continuous Variables	877	(1)
Some Important Issues	878	(6)
Patterns of ACFs and PACFs	878	(3)
Strength of Association	881	(1)
Forecasting	882	(2)
Statistical Methods for Comparing Two Models	884	(1)
Complete Example of a Time-Series Analysis	884	(13)
Evaluation of Assumptions	884	(1)
Normality of Sampling Distributions	884	(1)
Homogeneity of Variance	885	(1)
Outliers	885	(1)
Baseline Model Identification and Estimation	885	(7)
Baseline Model Diagnosis	892	(1)
Intervention Analysis	893	(1)
Model Diagnosis	893	(1)
Model Interpretation	893	(4)
Comparison of Programs	897	(4)
SPSS Package	897	(1)
SAS System	897	(3)
SYSTAT System	900	(1)
An Overview of the General Linear Model	901	(7)
Linearity and the General Linear Model	901	(1)
Bivariate to Multivariate Statistics and Overview of Techniques	901	(6)
Bivariate Form	901	(1)
Simple Multivariate Form	902	(2)
Full Multivariate Form	904	(3)
Alternative Research Strategies	907	(1)
Appendix A A Skimpy Introduction to Matrix Algebra	908	(10)
A.1 The Trace of a Matrix	909	(1)
A.2 Addition or Subtraction of a Constant to a Matrix	909	(1)
A.3 Multiplication or Division of a Matrix by a Constant	909	(1)
A.4 Addition and Subtraction of Two Matrices	910	(1)
A.5 Multiplication, Transposes, and Square Roots of Matrices	911	(2)
A.6 Matrix ``Division'' (Inverses and Determinants)	913	(1)
A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix	914	(4)
Appendix B Research Designs for Complete Examples	918	(7)
B.1 Women's Health and Drug Study	918	(1)
B.2 Sexual Attraction Study	919	(3)
B.3 Learning Disabilities Data Bank	922	(1)
B.4 Reaction Time to Identify Figures	923	(1)
B.5 Clinical Trial for Primary Biliary Cirrhosis	923	(1)
B.6 Impact of Seat Belt Law	924	(1)
Appendix C Statistical Tables	925	(12)
C.1 Normal Curve Areas	926	(1)
C.2 Critical Values of the t Distribution for α = .05 and .01, Two-Tailed Test	927	(1)
C.3 Critical Values of the F Distribution	928	(5)
C.4 Critical Values of Chi Square (x2)	933	(1)
C.5 Critical Values for Square Multiple Correlation (R2) in Forward Stepwise Selection α = .05	934	(2)
C.6 Critical Values for Fmax (S2max/S2min) Distribution for α = .05 and .01	936	(1)
References	937	(8)
Index	945