Barbara G Tabachnick; Linda S Fidell
|ISBN:||9780205465255 0205459382 9780205459384 0205465250|
|描述：||XXVIII, 980 S. : ill., graph. Darst.|
|内容：||1. Introduction. 1.1 Multivariate Statistics: Why? 1.1.1 The Domain of Multivariate Statistics: Numbers of IVs and DVs. 1.1.2 Experimental and Nonexperimental Research. 1.1.3 Computers and Multivariate Statistics. 1.1.4 Words of Caution. 1.2 Some Useful Definitions. 1.2.1 Continuous, Discrete, and Dichotomous Data. 1.2.2 Samples and Populations. 1.2.3 Descriptive and Inferential Statistics. 1.2.4 Orthogonality: Standard and Sequential Analyses. 1.3 Linear Combinations of Variables. 1.4 Number and Nature of Variables to Include. 1.5 Statistical Power. 1.6 Data Appropriate for Multivariate Statistics. 1.6.1 The Data Matrix. 1.6.2 The Correlation Matrix. 1.6.3 The Variance-Covariance Matrix. 1.6.4 The Sum-Of-Squares and Cross-Products Matrix. 1.6.5 Residuals. 1.7 Organization of the Book. 2. A Guide to Statistical Techniques: Using the Book. 2.1 Research Questions and Associated Techniques. 2.1.1 Degree of Relationship among Variables. 126.96.36.199 Bivariate r. 188.8.131.52 Multiple R. 184.108.40.206 Sequential R. 220.127.116.11 Canonical R. 18.104.22.168 Multiway Frequency Analysis. 22.214.171.124 Multilevel Modeling. 2.1.2 Significance of Group Differences. 126.96.36.199 One-Way ANOVA and t Test. 188.8.131.52 One-Way ANCOVA. 184.108.40.206 Factorial ANOVA. 220.127.116.11 Factorial ANCOVA. 18.104.22.168 Hotelling=s T². 22.214.171.124 One-Way MANOVA. 126.96.36.199 One-Way MANCOVA. 188.8.131.52 Factorial MANOVA. 184.108.40.206 Factorial MANCOVA. 220.127.116.11 Profile Analysis of Repeated Measures. 2.1.3 Prediction of Group Membership. 18.104.22.168 One-Way Discriminant. 22.214.171.124 Sequential One-Way Discriminant. 126.96.36.199 Multiway Frequency Analysis (Logit). 188.8.131.52 Logistic Regression. 184.108.40.206 Sequential Logistic Regression. 220.127.116.11 Factorial Discriminantanalysis. 18.104.22.168 Sequential Factorial Discriminant Analysis. 2.1.4 Structure. 22.214.171.124 Principal Components. 126.96.36.199 Factor Analysis. 188.8.131.52 Structural Equation Modeling. 2.1.5 Time Course of Events. 184.108.40.206 Survival/Failure Analysis. 220.127.116.11 Time-Series Analysis. 2.2 Some Further Comparisons. 2.3 A Decision Tree. 2.4 Technique Chapters. 2.5 Preliminary Check of the Data. 3. Review of Univariate and Bivariate Statistics. 3.1 Hypothesis Testing. 3.1.1 One-Sample z Test as Prototype. 3.1.2 Power. 3.1.3 Extensions of the Model. 3.1.4 Controversy Surrounding Significance Testing. 3.2 Analysis of Variance. 3.2.1 One-Way Between-Subjects ANOVA. 3.2.2 Factorial Between-Subjects ANOVA. 3.2.3 Within-Subjects ANOVA. 3.2.4 Mixed Between-Within-Subjects ANOVA. 3.2.5 Design Complexity. 18.104.22.168 Nesting. 22.214.171.124 Latin-Square Designs. 126.96.36.199 Unequal n and Nonorthogonality. 188.8.131.52 Fixed and Random Effects. 3.2.6 Specific Comparisons. 184.108.40.206 Weighting Coefficients for Comparisons. 220.127.116.11 Orthogonality of Weighting Coefficients. 18.104.22.168 Obtained F for Comparisons. 22.214.171.124 Critical F for Planned Comparisons. 126.96.36.199 Critical F for Post Hoc Comparisons. 3.3 Parameter Estimation. 3.4 Effect Size. 3.5 Bivariate Statistics: Correlation and Regression. 3.5.1 Correlation. 3.5.2 Regression. 3.6 Chi-Square Analysis. 4. Cleaning Up Your Act: Screening Data Prior to Analysis. 4.1 Important Issues in Data Screening. 4.1.1 Accuracy of Data File. 4.1.2 Honest Correlations. 188.8.131.52 Inflated Correlation. 184.108.40.206 Deflated Correlation. 4.1.3 Missing Data. 220.127.116.11 Deleting Cases or Variables. 18.104.22.168 Estimating Missing Data. 22.214.171.124 Using a Missing Data Correlation Matrix. 126.96.36.199 Treating Missing Data as Data. 188.8.131.52 Repeating Analyses with and Without Missing Data. 184.108.40.206 Choosing among Methods for Dealing with Missing Data. 4.1.4 Outliers. 220.127.116.11 Detecting Univariate and Multivariate Outliers. 18.104.22.168 Describing Outliers. 22.214.171.124 Reducing the Influence of Outliers. 126.96.36.199 Outliers in a Solution. 4.1.5 Normality, Linearity, and Homoscedasticity. 188.8.131.52 Normality. 184.108.40.206 Linearity. 220.127.116.11 Homoscedasticity, Homogeneity of Variance, and Homogeneity of Variance-Covariance Matrices. 4.1.6 Common Data Transformations. 4.1.7 Multicollinearity and Singularity. 4.1.8 A Checklist and Some Practical Recommendation. 4.2 Complete Examples of Data Screening. 4.2.1 Screening Ungrouped Data. 18.104.22.168 Accuracy of Input, Missing Data, Distributions, and Univariate Outliers. 22.214.171.124 Linearity and Homoscedasticity. 126.96.36.199 Transformation. 188.8.131.52 Detecting Multivariate Outliers. 184.108.40.206 Variables Causing Cases to Be Outliers. 220.127.116.11 Multicollinearity. 4.2.2 Screening Grouped Data. 18.104.22.168 Accuracy of Input, Missing Data, Distributions, Homogeneity of Variance, and Univariate Outliers. 22.214.171.124 Linearity. 126.96.36.199 Multivariate Outliers. 188.8.131.52 Variables Causing Cases to Be Outliers. 184.108.40.206 Multicollinearity. 5. Multiple Regression. 5.1 General Purpose and Description. 5.2 Kinds of Research Questions. 5.2.1 Degree of Relationship. 5.2.2 Importance of IVs. 5.2.3 Adding IVs. 5.2.4 Changing IVs. 5.2.5 Contingencies among IVs. 5.2.6 Comparing Sets of IVs. 5.2.7 Predicting DV Scores for Members of a New Sample. 5.2.8 Parameter Estimates. 5.3 Limitations to Regression Analyses. 5.3.1 Theoretical Issues. 5.3.2 Practical Issues. 220.127.116.11 Ratio of Cases to IVs. 18.104.22.168 Absence of Outliers among the IVs and on the DV. 22.214.171.124 Absence of Multicollinearity and Singularity. 126.96.36.199 Normality, Linearity, Homoscedasticity of Residuals. 188.8.131.52 Independence of Errors. 184.108.40.206 Outliers in the Solution. 5.4 Fundamental Equations for Multiple Regression. 5.4.1 General Linear Equations. 5.4.2 Matrix Equations. 5.4.3 Computer Analyses of Small-Sample Example. 5.5 Major Types of Multiple Regression. 5.5.1 Standard Multiple Regression. 5.5.2 Sequential Multiple Regression. 5.5.3 Statistical (Stepwise) Regression. 5.5.4 Choosing among Regression Strategies. 5.6 Some Important Issues. 5.6.1 Importance of IVs. 220.127.116.11 Standard Multiple Regression. 18.104.22.168 Sequential or Statistical Regression. 5.6.2 Statistical Inference. 22.214.171.124 Test for Multiple R. 126.96.36.199 Test of Regression Components. 188.8.131.52 Test of Added Subset of IVs. 184.108.40.206 Confidence Limits around B. 220.127.116.11 Comparing Two Sets of Predictors. 5.6.3 Adjustment of R2. 5.6.4 Suppressor Variables. 5.6.5 Regression Approach to ANOVA. 5.6.6 Centering When Interactions and Powers of IVs Are Included. 5.6.7 Mediation in Causal Sequences. 5.7 Complete Examples of Regression Analysis. 5.7.1 Evaluation of Assumptions. 18.104.22.168 Ratio of Cases to IVs. 22.214.171.124 Normality, Linearity, Homoscedasticity, and Independence of Residuals. 126.96.36.199 Outliers. 188.8.131.52 Multicollinearity and Singularity. 5.7.2 Standard Multiple Regression. 5.7.3 Sequential Regression. 5.8 Comparison of Programs. 5.8.1 SPSS Package. 5.8.2 SAS System. 5.8.3 SYSTAT System. 6. Analysis of Covariance. 6.1 General Purpose and Description. 6.2 Kinds of Research Questions. 6.2.1 Main Effects of IVs. 6.2.2 Interactions among IVs. 6.2.3 Specific Comparisons and Trend Analysis. 6.2.4 Effects of Covariates. 6.2.5 Effect Size. 6.2.6 Parameter Estimates. 6.3 Limitations to Analysis of Covariance. 6.3.1 Theoretical Issues. 6.3.2 Practical Issues. 184.108.40.206 Unequal Sample Sizes, Missing Data, and Ratio of Cases to IVs. 220.127.116.11 Absence of Outliers. 18.104.22.168 Absence of Multicollinearity and Singularity. 22.214.171.124 Normality of Sampling Distributions. 126.96.36.199 Homogeneity of Variance. 188.8.131.52 Linearity. 184.108.40.206 Homogeneity of Regression. 220.127.116.11 Reliability of Covariates. 6.4 Fundamental Equations for Analysis of Covariance. 6.4.1 Sums of Squares and Cross Products. 6.4.2 Significance Test and Effect Size. 6.4.3 Computer Analyses of Small-Sample Example. 6.5 Some Important Issues. 6.5.1 Choosing Covariates. 6.5.2 Evaluation of Covariates. 6.5.3 Test for Homogeneity of Regression. 6.5.4 Design Complexity. 18.104.22.168 Within-Subjects and Mixed Within-Between Designs. 22.214.171.124.1 Same Covariate(S) for All Cells. 126.96.36.199.2 Varying Covariate(S) Over Cells. 188.8.131.52 Unequal Sample Sizes. 184.108.40.206 Specific Comparisons and Trend Analysis. 220.127.116.11 Effect Size. 6.5.5 Alternatives to ANCOVA. 6.6 Complete Example of Analysis of Covariance. 6.6.1 Evaluation of Assumptions. 18.104.22.168 Unequal n and Missing Data. 22.214.171.124 Normality. 126.96.36.199 Linearity. 188.8.131.52 Outliers. 184.108.40.206 Multicollinearity and Singularity. 220.127.116.11 Homogeneity of Variance. 18.104.22.168 Homogeneity of Regression. 22.214.171.124 Reliability of Covariates. 6.6.2 Analysis of Covariance. 126.96.36.199 Main Analysis. 188.8.131.52 Evaluation of Covariates. 184.108.40.206 Homogeneity of Regression Run. 6.7 Comparison of Programs. 6.7.1 SPSS Package. 6.7.2 SAS System. 6.7.3 SYSTAT System. 7. Multivariate Analysis of Variance and Covariance. 7.1 General Purpose and Description. 7.2 Kinds of Research Questions. 7.2.1 Main Effects of IVs. 7.2.2 Interactions among IVs. 7.2.3 Importance of DVs. 7.2.4 Parameter Estimates. 7.2.5 Specific Comparisons and Trend Analysis. 7.2.6 Effect Size. 7.2.7 Effects of Covariates. 7.3 Limitations to Multivariate Analysis of Variance and Covariance. 7.3.1 Theoretical Issues. 7.3.2 Practical Issues. 220.127.116.11 Unequal Sample Sizes, Missing Data, and Power. 18.104.22.168 Multivariate Normality. 22.214.171.124 Absence of Outliers. 126.96.36.199 Homogeneity of Variance-Covariance Matrices. 188.8.131.52 Linearity. 184.108.40.206 Homogeneity of Regression. 220.127.116.11 Reliability of Covariates. 18.104.22.168 Absence of Multicollinearity and Singularity. 7.4 Fundamental Equations for Multivariate Analysis of Variance and Covariance. 7.4.1 Multivariate Analysis of Variance. 7.4.2 Computer Analyses of Small-Sample Example. 7.4.3 Multivariate Analysis of Covariance. 7.5 Some Important Issues. 7.5.1 MANOVA vs. ANOVAs. 7.5.2 Criteria for Statistical Inference. 7.5.3 Assessing DVs. 22.214.171.124 Univariate F. 126.96.36.199 Roy-Bargmann Stepdown Analysis. 188.8.131.52 Using Discriminant Function Analysis. 184.108.40.206 Choosing among Strategies for Assessing DVs. 7.5.4 Specific Comparisons and Trend Analysis. 7.5.5 Design Complexity. 220.127.116.11 Within-Subjects and Between-Within Designs. 18.104.22.168 Unequal Sample Sizes. 7.6 Complete Examples of Multivariate Analysis of Variance and Covariance. 7.6.1 Evaluation of Assumptions. 22.214.171.124 Unequal Sample Sizes and Missing Data. 126.96.36.199 Multivariate Normality. 188.8.131.52 Linearity. 184.108.40.206 Outliers. 220.127.116.11 Homogeneity of Variance-Covariance Matrices. 18.104.22.168 Homogeneity of Regression. 22.214.171.124 Reliability of Covariates. 126.96.36.199 Multicollinearity and Singularity. 7.6.2 Multivariate Analysis of Variance. 7.6.3 Multivariate Analysis of Covariance. 7.7 Comparison of Programs. 7.7.1 SPSS Package. 7.7.2 SAS System. 7.7.3 SYSTAT System. 8. Profile Analysis: The Multivariate Approach to Repeated Measures. 8.1 General Purpose and Description. 8.2 Kinds of Research Questions. 8.2.1 Parallelism of Profiles. 8.2.2 Overall Difference among Groups. 8.2.3 Flatness of Profiles. 8.2.4 Contrasts Following Profile Analysis. 8.2.5 Parameter Estimates. 8.2.6 Effect Size. 8.3 Limitations to Profile Analysis. 8.3.1 Theoretical Issues. 8.3.2 Practical Issues. 188.8.131.52 Sample Size, Missing Data, and Power. 184.108.40.206 Multivariate Normality. 220.127.116.11 Absence of Outliers. 18.104.22.168 Homogeneity of Variance-Covariance Matrices. 22.214.171.124 Linearity. 126.96.36.199 Absence of Multicollinearity and Singularity. 8.4 Fundamental Equations for Profile Analysis. 8.4.1 Parallelism. 8.4.2 Flatness. 8.4.3 Computer Analyses of Small-Sample Example. 8.5 Some Important Issues. 8.5.1 Univariate Vs. Multivariate Approach to Repeated Measures. 8.5.2 Contrasts in Profile Analysis. 188.8.131.52 Parallelism and Flatness Significant, Levels Not Significant (Simple- Effects Analysis). 184.108.40.206 Parallelism and Levels Significant, Flatness Not Significant (Simple- Effects Analysis). 220.127.116.11parallelism, Levels, and Flatness Significant (Interaction Contrasts). 18.104.22.168 Only Parallelism Significant. 8.5.3 Doubly-Multivariate Designs. 8.5.4 Classifying Profiles. 8.5.5 Imputation of Missing Values. 8.6 Complete Examples of Profile Analysis. 8.6.1 Profile Analysis of Subscales of the Wisc. 22.214.171.124 Evaluation of Assumptions. 126.96.36.199.1 Unequal Sample Sizes and Missing Data. 188.8.131.52.2 Multivariate Normality. 184.108.40.206.3 Linearity. 220.127.116.11.4 Outliers. 18.104.22.168.5 Homogeneity of Variance-Covariance Matrices. 22.214.171.124.6 Multicollinearity and Singularity. 126.96.36.199 Profile Analysis. 8.6.2 Doubly-Multivariate Analysis of Reaction Time. 188.8.131.52 Evaluation of Assumptions. 184.108.40.206.1 Unequal Sample Sizes, Missing Data, Multivariate Normality, and Linearity. 220.127.116.11.2 Outliers. 18.104.22.168.3 Homogeneity of Variance-Covariance Matrices. 22.214.171.124.4 Homogeneity of Regression. 126.96.36.199.5 Reliability of DVs. 188.8.131.52.6 Multicollinearity and Singularity. 184.108.40.206 Doubly-Multivariate Analysis of Slope and Intercept. 8.7 Comparison of Programs. 8.7.1 SPSS Package. 8.7.2 SAS System. 8.7.3 SYSTAT System. 9. Discriminant Analysis. 9.1 General Purpose and Description. 9.2 Kinds of Research Questions. 9.2.1 Significance of Prediction. 9.2.2 Number of Significant Discriminant Functions. 9.2.3 Dimensions of Discrimination. 9.2.4 Classification Functions. 9.2.5 Adequacy of Classification. 9.2.6 Effect Size. 9.2.7 Importance of Predictor Variables. 9.2.8 Significance of Prediction with Covariates. 9.2.9 Estimation of Group Means. 9.3 Limitations to Discriminant Analysis. 9.3.1 Theoretical Issues. 9.3.2 Practical Issues. 220.127.116.11 Unequal Sample Sizes, Missing Data, and Power. 18.104.22.168 Multivariate Normality. 22.214.171.124 Absence of Outliers. 126.96.36.199 Homogeneity of Variance-Covariance Matrices. 188.8.131.52 Linearity. 184.108.40.206 Absence of Multicollinearity and Singularity. 9.4 Fundamental Equations for Discriminantanalysis. 9.4.1 Derivation and Test of Discriminant Functions. 9.4.2 Classification. 9.4.3 Computer Analyses of Small-Sample Example. 9.5 Types of Discriminant Analysis. 9.5.1 Direct Discriminant Analysis. 9.5.2 Sequential Discriminant Analysis. 9.5.3 Stepwise (Statistical) Discriminant Analysis. 9.6 Some Important Issues. 9.6.1 Statistical Inference. 220.127.116.11 Criteria for Overall Statistical Significance. 18.104.22.168 Stepping Methods. 9.6.2 Number of Discriminant Functions. 9.6.3 Interpreting Discriminant Functions. 22.214.171.124 Discriminant Function Plots. 126.96.36.199 Loading Matrices. 9.6.4 Evaluating Predictor Variables. 9.6.5 Effect Size. 9.6.6 Design Complexity: Factorial Designs. 9.6.7 Use of Classification Procedures. 188.8.131.52 Cross-Validation and New Cases. 184.108.40.206 Jackknifed Classification. 220.127.116.11 Evaluating Improvement in Classification. 9.7 Comparison of Programs. 9.7.1 SPSS Package. 9.7.2 SAS System. 9.7.3 SYSTAT System. 10. Logistic Regression. 10.1 General Purpose and Description. 10.2 Kinds of Research Questions. 10.2.1 Prediction of Group Membership or Outcome. 10.2.2 Importance of Predictors. 10.2.3 Interactions among Predictors. 10.2.4 Parameter Estimates. 10.2.5 Classification of Cases. 10.2.6 Significance of Prediction with Covariates. 10.2.7 Effect Size. 10.3 Limitations to Logistic Regression Analysis. 10.3.1 Theoretical Issues. 10.3.2 Practical Issues. 10.3.2.1 Ratio of Cases to Variables. 10.3.2.2 Adequacy of Expected Frequencies and Power. 10.3.2.3 Linearity in the Logit. 10.3.2.4 Absence of Multicollinearity. 10.3.2.5 Absence of Outliers in the Solution. 10.4 Fundamental Equations for Logistic Regression. 10.4.1 Testing and Interpreting Coefficients. 10.4.2 Goodness-of-Fit. 10.4.3 Comparing Models. 10.4.4 Interpretation and Analysis of Residuals. 10.4.5 Computer Analyses of Small-Sample Example. 10.5 Types of Logistic Regression. 10.5.1 Direct Logistic Regression. 10.5.2 Sequential Logistic Regression. 10.5.3 Statistical (Stepwise) Logistic Regression. 10.5.4 Probit and Other Analyses. 10.6 Some Important Issues. 10.6.1 Statistical Inference. 10.6.1.1 Assessing Goodness-Of-Fit of Models. 10.6.1.1.1 Constant-Only Vs. Full Model. 10.5.1.1.2 Comparison with a Perfect (Hypothetical) Model. 10.6.1.1.3 Deciles of Risk. 10.6.1.2 Tests of Individual Variables. 10.6.2 Effect Size for a Model. 10.6.3 Interpretation of Coefficients Using Odds. 10.6.4 Coding Outcome and Predictor Categories. 10.6.5 Number and Type of Outcome Categories. 10.6.6 Classification of Cases. 10.6.7 Hierarchical and Nonhierarchical Analysis. 10.6.8 Importance of Predictors. 10.6.9 Logistic Regression for Matched Groups. 10.7 Complete Examples of Logistic Regression. 10.7.1 Evaluation of Limitations. 10.7.1.1 Ratio of Cases to Variables and Missing Data. 10.7.1.2 Multicollinearity. 10.7.1.3 Outliers in the Solution. 10.7.2 Direct Logistic Regression with Two-Category Outcome and Continuous Predictors. 10.7.3 Sequential Logistic Regression with Three Categories of Outcome. 10.7.3.1 Limitations of Multinomial Logistic Regression. 10.7.3.1.1 Adequacy of Expected Frequencies. 10.7.3.1.2 Linearity in the Logit. 10.7.3.2 Sequential Multinomial Logistic Regression. 10.8 Comparison of Programs. 10.8.1 SPSS Package. 10.8.2 SAS System. 10.8.3 SYSTAT System. 11. Survival/Failure Analysis. 11.1 General Purpose and Description. 11.2 Kinds of Research Questions. 11.2.1 Proportions Surviving at Various Times. 11.2.2 Group Differences in Survival. 11.2.3 Survival Time with Covariates. 18.104.22.168 Treatment Effects. 22.214.171.124 Importance of Covariates. 126.96.36.199 Parameter Estimates. 188.8.131.52 Contingencies among Covariates. 184.108.40.206 Effect Size and Power. 11.3 Limitations to Survival Analysis. 11.3.1 Theoretical Issues. 11.3.2 Practical Issues. 220.127.116.11 Sample Size and Missing Data. 18.104.22.168 Normality of Sampling Distributions, Linearity, and Homoscedasticity. 22.214.171.124 Absence of Outliers. 126.96.36.199 Differences Between Withdrawn and Remaining Cases. 188.8.131.52 Change in Survival Conditions Over Time. 184.108.40.206 Proportionality of Hazards. 220.127.116.11 Absence of Multicollinearity. 11.4 Fundamental Equations for Survival Analysis. 11.4.1 Life Tables. 11.4.2 Standard Error of Cumulative Proportion Surviving. 11.4.3 Hazard and Density Functions. 11.4.4 Plot of Life Tables. 11.4.5 Test for Group Differences. 11.4.6 Computer Analyses of Small-Sample Example. 11.5 Types of Survival Analysis. 11.5.1 Actuarial and Product-Limit Life Tables and Survivor Functions. 11.5.2 Prediction of Group Survival Times from Covariates. 18.104.22.168 Direct, Sequential, and Statistical Analysis. 22.214.171.124 Cox Proportional-Hazards Model. 126.96.36.199 Accelerated Failure-Time Model. 188.8.131.52 Choosing a Method. 11.6 Some Important Issues. 11.6.1 Proportionality of Hazards. 11.6.2 Censored Data. 184.108.40.206 Right-Censored Data. 220.127.116.11 Other Forms of Censoring. 11.6.3 Effect Size and Power. 11.6.4 Statistical Criteria. 18.104.22.168 Test Statistics for Group Differences in Survival Functions. 22.214.171.124 Test Statistics for Prediction from Covariates. 11.6.5 Predicting Survival Rate. 126.96.36.199 Regression Coefficients (Parameter Estimates). 188.8.131.52 Odds Ratios. 184.108.40.206 Expected Survival Rates. 11.7 Complete Example of Survival Analysis. 11.7.1 Evaluation of Assumptions. 220.127.116.11 Accuracy of Input, Adequacy of Sample Size, Missing Data, and Distributions. 18.104.22.168 Outliers. 22.214.171.124 Differences Between Withdrawn and Remaining Cases. 126.96.36.199 Change in Survival Experience Over Time. 188.8.131.52 Proportionality of Hazards. 184.108.40.206 Multicollinearity. 11.7.2 Cox Regression Survival Analysis. 220.127.116.11 Effect of Drug Treatment. 18.104.22.168 Evaluation of Other Covariates. 11.8 Comparison of Programs. 11.8.1 SAS System. 11.8.2 SPSS Package. 11.8.3 SYSTAT System. 12. Canonical Correlation. 12.1 General Purpose and Description. 12.2 Kinds of Research Questions. 12.2.1 Number of Canonical Variate Pairs. 12.2.2 Interpretation of Canonical Variates. 12.2.3 Importance of Canonical Variates. 12.2.4 Canonical Variate Scores. 12.3 Limitations. 12.3.1 Theoretical Limitations. 12.3.2 Practical Issues. 22.214.171.124 Ratio of Cases to IVs. 126.96.36.199 Normality, Linearity, and Homoscedasticity. 188.8.131.52 Missing Data. 184.108.40.206 Absence of Outliers. 220.127.116.11 Absence of Multicollinearity and Singularity. 12.4 Fundamental Equations for Canonical Correlation\. 12.4.1 Eigenvalues and Eigenvectors. 12.4.2 Matrix Equations. 12.4.3 Proportions of Variance Extracted. 12.4.4 Computer Analyses of Small-Sample Example. 12.5 Some Important Issues. 12.5.1 Importance of Canonical Variates. 12.5.2 Interpretation of Canonical Variates. 12.6 Complete Example of Canonical Correlation. 12.6.1 Evaluation of Assumptions. 18.104.22.168 Missing Data. 22.214.171.124 Normality, Linearity, and Homoscedasticity. 126.96.36.199 Outliers. 188.8.131.52 Multicollinearity and Singularity. 12.6.2 Canonical Correlation. 12.7 Comparison of Programs. 12.7.1 SAS System. 12.7.2 SPSS Package. 12.7.3 SYSTAT System. 13. Principal Components and Factor Analysis. 13.1 General Purpose and Description. 13.2 Kinds of Research Questions. 13.2.1 Number of Factors. 13.2.2 Nature of Factors. 13.2.3 Importance of Solutions and Factors. 13.2.4 Testing Theory in FA. 13.2.5 Estimating Scores on Factors. 13.3 Limitations. 13.3.1 Theoretical Issues. 13.3.2 Practical Issues. 184.108.40.206 Sample Size and Missing Data. 220.127.116.11 Normality. 18.104.22.168 Linearity. 22.214.171.124 Absence of Outliers among Cases. 126.96.36.199 Absence of Multicollinearity and Singularity. 188.8.131.52 Factorability of R. 184.108.40.206 Absence of Outliers among Variables. 13.4 Fundamental Equations for Factor Analysis. 13.4.1 Extraction. 13.4.2 Orthogonal Rotation. 13.4.3 Communalities, Variance, and Covariance. 13.4.4 Factor Scores. 13.4.5 Oblique Rotation. 13.4.6 Computer Analyses of Small-Sample Example. 13.5 Major Types of Factor Analysis. 13.5.1 Factor Extraction Techniques. 220.127.116.11 PCA vs. FA. 18.104.22.168 Principal Components. 22.214.171.124 Principal Factors. 126.96.36.199 Image Factor Extraction. 188.8.131.52 Maximum Likelihood Factor Extraction. 184.108.40.206 Unweighted Least Squares Factoring. 220.127.116.11 Generalized (Weighted) Least Squares Factoring. 18.104.22.168 Alpha Factoring. 13.5.2 Rotation. 22.214.171.124 Orthogonal Rotation. 126.96.36.199 Oblique Rotation. 188.8.131.52 Geometric Interpretation. 13.5.3 Some Practical Recommendations. 13.6 Some Important Issues. 13.6.1 Estimates of Communalities. 13.6.2 Adequacy of Extraction and Number of Factors. 13.6.3 Adequacy of Rotation and Simple Structure. 13.6.4 Importance and Internal Consistency of Factors. 13.6.5 Interpretation of Factors. 13.6.6 Factor Scores. 13.6.7 Comparisons among Solutions and Groups. 13.7 Complete Example of FA. 13.7.1 Evaluation of Limitations. 184.108.40.206 Sample Size and Missing Data. 220.127.116.11 Normality. 18.104.22.168 Linearity. 22.214.171.124 Multicollinearity and Singularity. 126.96.36.199 Outliers among Variables. 13.7.2 Principal Factors Extraction with Varimax Rotation. 13.8 Comparison of Programs. 13.8.1 SPSS Package. 13.8.2 SAS System. 13.8.3 SYSTAT System. 14. Structural Equation Modeling. General Purpose and Description. Kinds of Research Questions. Adequacy of the Model. Testing Theory. Amount of Variance in the Variables Accounted for by the Factors. Reliability of the Indicators. Parameter Estimates. 14.2.6 Indirect Effects. Group Differences. Longitudinal Differences. Multilevel Modeling. Limitations to Structural Equation Modeling. Theoretical Issues. Practical Issues. Fundamental Equations for Structural Equations Modeling. Covariance Algebra. Model Hypotheses. Model Specification. Model Estimation. Model Evaluation. Computer Analysis of Small Sample Example. Some Important Issues. Model Identification. Estimation Techniques. Assessing the Fit of the Model. Model Modification. Reliability and Proportion of Variance. Discrete and Ordinal Data. Multiple Group Models. Mean and Covariance Structure Models. Complete Examples of Structural Equation Modeling Analysis. Model Specification for CFA. Evaluation of Assumptions for CFA. Model Modification. SEM Model Specification. SEM Model Estimation and Preliminary Evaluation. Model Modification. Comparison of Programs. EQS. LISREL. SAS System. AMOS. 15. Multilevel Linear Modeling. 15.1 General Purpose and Description. 15.2 Kinds of Research Questions. 15.2.1 Group Differences in Means. 15.2.2 Group Differences in Slopes. 15.2.3 Cross-Level Interactions. 15.2.4 Meta-Analysis. 15.2.5 Relative Strength of Predictors at Various Levels. 15.2.6 Individual and Group Structure. 15.2.7 Path Analysis at Individual and Group Levels. 15.2.8 Analysis of Longitudinal Data. 15.2.9 Multilevel Logistic Regression. 15.2.10 Multiple Response Analysis. 15.3 Limitations to Multilevel Linear Modeling. 15.3.1 Theoretical Issues. 15.3.2 Practical Issues. 188.8.131.52 Sample Size, Unequal-N, and Missing Data. 184.108.40.206 Independence of Errors. 220.127.116.11 Absence of Multicollinearity and Singularity. 15.4 Fundamental Equations. 15.4.1 Intercepts-Only Model. 18.104.22.168 The Intercepts-Only Model: Level-1 Equation. 22.214.171.124 The Intercepts-Only Model: Level 2 Equation. 126.96.36.199 Computer Analyses of Intercepts-Only Model. 15.4.2 Model with a First-Level Predictor. 188.8.131.52 Level-1 Equation for a Model with Level-1 Predictor. 184.108.40.206 Level-2 Equations for a Model with a Level-1 Predictor. 220.127.116.11 Computer Analyses of Model with a Level-1 Predictor. 15.4.3 Model with Predictors at First and Second Levels. 18.104.22.168 Level-1 Equation for Model with Predictors at Both Levels. 22.214.171.124 Level-2 Equations for Model with Predictors at Both Levels. 126.96.36.199 Computer Analyses of Model with Predictors at First and Second Levels. 15.5 Types of Mlm. 15.5.1 Repeated Measures. 15.5.2 Higher-Order Mlm. 15.5.3 Latent Variables. 15.5.4 Nonnormal Outcome Variables. 15.5.5 Multiple Response Models. 15.6 Some Important Issues. 15.6.1 Intraclass Correlation. 15.6.2 Centering Predictors and Changes in Their Interpretation. 15.6.3 Interactions. 15.6.4 Random and Fixed Intercepts and Slopes. 15.6.5 Statistical Inference. 188.8.131.52 Assessing Models. 184.108.40.206 Tests of Individual Effects. 15.6.6 Effect Size. 15.6.7 Estimation Techniques and Convergence Problems. 15.6.8 Exploratory Model Building. 15.7 Complete Example of MLM. 15.7.1 Evaluation of Assumptions. 220.127.116.11 Sample Sizes, Missing Data, and Distributions. 18.104.22.168 Outliers. 22.214.171.124 Multicollinearity and Singularity. 126.96.36.199 Independence of Errors: Intraclass Correlations. 15.7.2 Multilevel Modeling. 15.8 Comparison of Programs. 15.8.1 SAS System. 15.8.2 SPSS Package. 15.8.3 HLM Program. 15.8.4 MLwiN Program. 15.8.5 SYSTAT System. 16. Multiway Frequency Analysis. 16.1 General Purpose and Description. 16.2 Kinds of Research Questions. 16.2.1 Associations among Variables. 16.2.2 Effect on a Dependent Variable. 16.2.3 Parameter Estimates. 16.2.4 Importance of Effects. 16.2.5 Effect Size. 16.2.6 Specific Comparisons and Trend Analysis. 16.3 Limitations to Multiway Frequency Analysis. 16.3.1 Theoretical Issues. 16.3.2 Practical Issues. 188.8.131.52 Independence. 184.108.40.206 Ratio of Cases to Variables. 220.127.116.11 Adequacy of Expected Frequencies. 18.104.22.168 Absence of Outliers in the Solution. 16.4 Fundamental Equations for Multiway Frequency Analysis. 16.4.1 Screening for Effects. 22.214.171.124 Total Effect. 126.96.36.199 First-Order Effects. 188.8.131.52 Second-Order Effects. 184.108.40.206 Third-Order Effect. 16.4.2 Modeling. 16.4.3 Evaluation and Interpretation. 220.127.116.11 Residuals. 18.104.22.168 Parameter Estimates. 16.4.4 Computer Analyses of Small-Sample Example. 16.5 Some Important Issues. 16.5.1 Hierarchical and Nonhierarchical Models. 16.5.2 Statistical Criteria. 22.214.171.124 Tests of Models. 126.96.36.199 Tests of Individual Effects. 16.5.3 Strategies for Choosing a Model. 188.8.131.52 SPSS HILOGLINEAR (Hierarchical). 184.108.40.206 SPSS GENLOG (General Log-Linear). 220.127.116.11 SAS CATMOD and SPSS LOGLINEAR (General Log-Linear). 16.6 Complete Example of Multiway Frequency Analysis. 16.6.1 Evaluation of Assumptions: Adequacy of Expected Frequencies. 16.6.2 Hierarchical Log-Linear Analysis. 18.104.22.168 Preliminary Model Screening. 22.214.171.124 Stepwise Model Selection. 126.96.36.199 Adequacy of Fit. 188.8.131.52 Interpretation of the Selected Model. 16.7 Comparison of Programs. 16.7.1 SPSS Package. 16.7.2 SAS System. 16.7.3 SYSTAT System. Appendix A: A Skimpy Introduction to Matrix Algebra. A.1 The Trace of a Matrix. A.2 Addition or Subtraction of a Constant to a Matrix. A.3 Multiplication or Division of a Matrix By a Constant. A.4 Addition and Subtraction of Two Matrices. A.5 Multiplication, Transposes, and Square Roots of Matrices. A.6 Matrix "Division" (Inverses and Determinants). A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix. Appendix B: Research Designs for Complete Examples. B.1 Women's Health and Drug Study. B.2 Sexual Attraction Study. B.3 Learning Disabilities Data Bank. B.4 Reaction Time to Identify Figures. B.5 Clinical Trial for Primary Biliary Cirrhosis. Appendix C: Statistical Tables. C.1 Normal Curve Areas. C.2 Critical Values of the T Distribution for alpha =.05 and.-1, Two-Tailed Test. C.3 Critical Values of the F Distribution. C.4 Critical Values of Chi Square (CHI5). C.5 Critical Values for Squares Multiple Correlation (R5) in Forward Stepwise Select. C.6 Critical Values for Fmax (S5max/S5min) Distribution for alpha =.05 and.01.|
|責任：||Barbara G. Tabachnick ; Linda S. Fidell.|
After the Introduction Chapter, the second Chapter gives a guide to the multivariate techniques that are covered in this book and palces them in context with the more familiare univeriate and bivariate statistics where possible. Included in this chapter is a flow chart that organizes statistical techniques on the basis of the major research questions asked. Chapter three provides a brief review of univariate and bivariate statistical techniques for those who are interested. Chapter four deals with the assumptions an limitations of mulitvariate statistical methods. Assessment and violation of assumptions are discussed, along with alternatives for dealing with violations when they occur. This chapter is also meant to be referred to often, and the reader ist guided back to it frequently in Chapters five through sixteen an eighteen (online). Chapters five through sixteen and eighteen (online) cover specific multivariate techniques. They include descriptive, conceptual sections as well as a guided tour through a real-world data set for which the analysis is apporopriate. The tour includes an example of a Results section describing the outcome of the statistical analysis apporopriate for submissions to a professional journal. Each technique chapter includes a comparision of cumputer programs. Chapter seventeen is an attempt to integrate univariate, bivariate, and multivariate statistics through the multivariate general linear model. The common elements underlying all the techniques are emphasized, rather than the differences among them. This Chapter is ment to pull together the material in the remainder of the book with a conceptual rather than pragmatic emphasis.