Using Multivariate Statistics

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

• ISBN13: 9780205459384
• ISBN10: 0205459382
• Edition: 5th
• Format: Paperback
• Copyright: 2006-02-21
• Publisher: Pearson

Summary

Using Multivariate Statistics provides advanced students with a timely and comprehensive introduction to todayrs"s most commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge of higher level mathematics. This long-awaited revision reflects extensive updates throughout, especially in the areas of Data Screening (Chapter 4), Multiple Regression (Chapter 5), and Logistic Regression (Chapter 12). A brand new chapter (Chapter 15) on Multilevel Linear Modeling explains techniques for dealing with hierarchical data sets. Also included are syntax and output for accomplishing many analyses through the most recent releases of SAS and SPSS. As in past EDITIONs, each technique chapter: bull; discusses tests for assumptions of analysis (and procedures for dealing with their violation) bull; presents a small example, hand-worked for the most basic analysis bull; describes varieties of analysis bull; discusses important issues (such as effect size) bull; provides an example with a real data set from tests of assumptions to write-up of a results section bull; compares features of relevant programs

Table of Contents

Preface	xxvii
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	(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)
References	953	(10)
Index	963