Using Multivariate Statistics

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This text takes a practical approach to multivariate data analysis, with an introductionto 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 students with a timely and comprehensive introduction to today's most commonly encountered statistical and multivariate techniques, while assuming only a limited knowledge ofhigher-level mathematics. *A new chapter on survival analysis (Ch. 15) allows students to analyze data where the outcome is time until something happens. This is very popular in biomedical research. *A new chapter on time series analysis (Ch. 16) encourages students to learn to model patterns in data gathered over many trials and to test for the effectiveness on an intervention (either experimentally or naturally occurring). This is especially useful in the social sciences. *The data files for the complete examples are available in several formats at the website (www.abacon.com/tabachnick). Updated SAS and SPSS Workbooks for Windows are also available. *This edition upgrades all syntax and output to SAS release 7, SPSS release 10, and SYSTAT release 9, so students can concentrate on the research question and the meaning of the output rather than on getting the program to run. *The revised Chapter 4 on data screening contains new procedures for inputting missing values, and provides students with the most up-to-date procedures for both statistical and graphical methods of data screening. *Chapters on Multiple Regression (Ch. 5), Profile Analysis of Repeated Measures (Ch. 10), and Logistic Regression (Ch. 12) have been extensively revised. *Each technique chapter discusses tests for assumptions of analysis (and procedures for dealing with their violation), presents a small example hand-worked for the most basic analysis, describes varieties of analysis, discusses important issues (such as effect size), provides an example with a real data set from tests of assumptions to write-up of a results section, and compares features of relevant programs. *For each technique, an example with real data is provided, from assessment of assumptions to a Results section in APA format giving students a step-by-step algorithm for conducting an analysis and writing it up.

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1. Introduction. Multivariate Statistics: Why?The Domain of Multivariate Statistics: Numbers of IVs and DVs. Experimental and Nonexperimental Research. Computers and Multivariate Statistics. Why Not.Some Useful Definitions.Continuous, Discrete, and Dichotomous Data. Samples and Populations. Descriptive and Inferential Statistics. Orthogonality. Standard and Sequential Analyses.Combining Variables.Number and Nature of Variables to Include.Statistical Power.Data Appropriate for Multivariate Statistics.The Data Matrix. The Correlation Matrix. The Variance-Covariance Matrix. The Sum-of-Squares and Cross-Products Matrix. Residuals.Organization of the Book.2. A Guide to Statistical Techniques: Using the Book. Research Questions and Associated Techniques.Degree of Relationship among Variables. Significance of Group Differences. Prediction of Group Membership. Structure. Time Course of Events.A Decision Tree.Technique Chapters.Preliminary Check of the Data.3. Review of Univariate and Bivariate Statistics. Hypothesis Testing.One-Sample z Test as Prototype. Power. Extensions of the Model.Analysis of Variance.One-Way Between-Subjects ANOVA. Factorial Between-Subjects ANOVA. Within-Subjects ANOVA. Mixed Between-Within-Subjects ANOVA. Design Complexity. Specific Comparisons.Parameter Estimation.Strength of Association.Bivariate Statistics: Correlation and Regression.Correlation. Regression.Chi-Square Analysis.4. Cleaning Up Your Act: Screening Data Prior to Analysis. Important Issues in Data Screening.Accuracy of Data File. Honest Correlations. Missing Data. Outliers. Normality, Linearity, and Homoscedasticity. Common Data Transformations. Multicollinearity and Singularity. A Checklist and Some Practical Recommendations.Complete Examples of Data Screening.Screening Ungrouped Data. Screening Grouped Data.5. Multiple Regression. General Purpose and Description.Kinds of Research Questions.Degree of Relationship. Importance of IVs. Adding IVs. Changing IVs. Contingencies among IVs. Comparing Sets of IVs. Predicting DV Scores for Members of a New Sample. Parameter Estimates.Limitations to Regression Analyses.Theoretical Issues. Practical Issues.Fundamental Equations for Multiple Regression.General Linear Equations. Matrix Equations. Computer Analyses of Small Sample Example.Major Types of Multiple Regression.Standard Multiple Regression. Sequential Multiple Regression. Statistical (Stepwise) Regression. Choosing among Regression Strategies.Some Important Issues.Importance of IVs. Statistical Inference. Adjustment of R2. Suppressor Variables. Regression Approach to ANOVA. Centering When Interactions and Powers of IVs Are Included.Complete Examples of Regression Analysis.Evaluation of Assumptions. Standard Multiple Regression. Sequential Regression.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.6. Canonical Correlation. General Purpose and Description.Kinds of Research Questions.Number of Canonical Variate Pairs. Interpretation of Canonical Variates. Importance of Canonical Variates. Canonical Variate Scores.Limitations.Theoretical Limitations. Practical Issues.Fundamental Equations for Canonical Correlation.Eigenvalues and Eigenvectors. Matrix Equations. Proportions of Variance Extracted. Computer Analyses of Small Sample Example.Some Important Issues.Importance of Canonical Variates. Interpretation of Canonical Variates.Complete Example of Canonical Correlation.Evaluation of Assumptions. Canonical Correlation.Comparison of Programs.SAS System. SPSS Package. SYSTAT System.7. Multiway Frequency Analysis. General Purpose and Description.Kinds of Research Questions.Associations among Variables. Effect on a Dependent Variable. Parameter Estimates. Importance of Effects. Strength of Association. Specific Comparisons and Trend Analysis.Limitations to Multiway Frequency Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Multiway Frequency Analysis.Screening for Effects. Modeling. Evaluation and Interpretation. Computer Analyses of Small Sample Example.Some Important Issues.Hierarchical and Nonhierarchical Models. Statistical Criteria. Strategies for Choosing a Model.Complete Example of Multiway Frequency Analysis.Evaluation of Assumptions: Adequacy of Expected Frequencies. Hierarchical Loglinear Analysis.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.8. Analysis of Covariance. General Purpose and Description.Kinds of Research Questions.Main Effects of IVs. Interactions among IVs. Specific Comparisons and Trend Analysis. Effects of Covariates. Strength of Association. Parameter Estimates.Limitations to Analysis of Covariance.Theoretical Issues. Practical Issues.Fundamental Equations for Analysis of Covariance.Sums of Squares and Cross Products. Significance Test and Strength of Association. Computer Analyses of Small Sample Example.Some Important Issues.Test for Homogeneity of Regression. Design Complexity. Evaluation of Covariates. Choosing Covariates. Alternatives to ANCOVA.Complete Example of Analysis of Covariance.Evaluation of Assumptions. Analysis of Covariance.Comparison of Programs.SPSS Package. SYSTAT System. SAS System.9. Multivariate Analysis of Variance and Covariance. General Purpose and Description.Kinds of Research Questions.Main Effects of IVs. Interactions among IVs. Importance of DVs. Parameter Estimates. Specific Comparisons and Trend Analysis. Strength of Association. Effects of Covariates. Repeated-Measures Analysis of Variance.Limitations to Multivariate Analysis of Variance and Covariance.Theoretical Issues. Practical Issues.Fundamental Equations for Multivariate Analysis of Variance and Covariance.Multivariate Analysis of Variance. Computer Analyses of Small Sample Example. Multivariate Analysis of Covariance.Some Important Issues.Criteria for Statistical Inference. Assessing DVs. Specific Comparisons and Trend Analysis. Design Complexity. MANOVA vs. ANOVAs.Complete Examples of Multivariate Analysis of Variance and Covariance.Evaluation of Assumptions. Multivariate Analysis of Variance. Multivariate Analysis of Covariance.Comparison of Programs.SPSS Package. SYSTAT System. SAS System.10. Profile Analysis: The Multivariate Approach to Repeated Measures. General Purpose and Description.Kinds of Research Questions.Parallelism of Profiles. Overall Difference among Groups. Flatness of Profiles. Contrasts Following Profile Analysis. Parameter Estimates. Strength of Association.Limitations to Profile Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Profile Analysis.Differences in Levels. Parallelism. Flatness. Computer Analyses of Small Sample Example.Some Important Issues.Contrasts in Profile Analysis. Univariate vs. Multivariate Approach to Repeated Measures. Doubly Multivariate Designs. Classifying Profiles. Imputation of Missing Values.Complete Examples of Profile Analysis.Profile Analysis of Subscales of the WISC. Doubly Multivariate Analysis of Reaction Time.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.11. Discriminant Function Analysis. General Purpose and Description.Kinds of Research Questions.Significance of Prediction. Number of Significant Discriminant Functions. Dimensions of Discrimination. Classification Functions. Adequacy of Classification. Strength of Association. Importance of Predictor Variables. Significance of Prediction with Covariates. Estimation of Group Means.Limits to Discriminant Function Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Discriminant Function Analysis.Derivation and Test of Discriminant Functions. Classification. Computer Analyses of Small Sample Example.Types of Discriminant Function Analysis.Direct Discriminant Function Analysis. Sequential Discriminant Function Analysis. Stepwise (Statistical) Discriminant Function Analysis.Some Important Issues.Statistical Inference. Number of Discriminant Functions. Interpreting Discriminant Functions. Evaluating Predictor Variables. Design Complexity: Factorial Designs. Use of Classification Procedures.Complete Example of Discriminant Function Analysis.Evaluation of Assumptions. Direct Discriminant Function Analysis.Comparison of Programs.SPSS Package. SYSTAT System. SAS System.12. Logistic Regression. General Purpose and Description.Kinds of Research Questions.Prediction of Group Membership or Outcome. Importance of Predictors. Interactions among Predictors. Parameter Estimates. Classification of Cases. Significance of Prediction with Covariates. Strength of Association.Limitations to Logistic Regression Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Logistic Regression.Testing and Interpreting Coefficients. Goodness-of-Fit. Comparing Models. Interpretation and Analysis of Residuals. Computer Analyses of Small Sample Example.Types of Logistic Regression.Direct Logistic Regression. Sequential Logistic Regression. Stepwise (Statistical) Logistic Regression. Probit and Other Analyses.Some Important Issues.Statistical Inference. Number and Type of Outcome Categories. Strength of Association for a Model. Coding Outcome and Predictor Categories. Classification of Cases. Hierarchical and Nonhierarchical Analysis. Interpretation of Coefficients Using Odds. Logistic Regression for Matched Groups.Complete Examples of Logistic Regression.Evaluation of Limitations. Direct Logistic Regression with Two-Category Outcome. Sequential Logistic Regression with Three Categories of Outcome.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.13. Principal Components and Factor Analysis. General Purpose and Description.Kinds of Research Questions.Number of Factors. Nature of Factors. Importance of Solutions and Factors. Testing Theory in FA. Estimating Scores on Factors.Limitations.Theoretical Issues. Practical Issues.Fundamental Equations for Factor Analysis.Extraction. Orthogonal Rotation. Communalities, Variance, and Covariance. Factor Scores. Oblique Rotation. Computer Analyses of Small Sample Example.Major Types of Factor Analysis.Factor Extraction Techniques. Rotation. Some Practical Recommendations.Some Important Issues.Estimates of Communalities. Adequacy of Extraction and Number of Factors. Adequacy of Rotation and Simple Structure. Importance and Internal Consistency of Factors. Interpretation of Factors. Factor Scores. Comparisons among Solutions and Groups.Complete Example of FA.Evaluation of Limitations. Principal Factors Extraction with Varimax Rotation.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.14. Structural Equation Modeling by Jodie B. Ullman. 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. Mediation. 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. Survival/Failure Analysis. General Purpose and Description.Kinds of Research Questions.Proportions Surviving at Various Times. Group Differences in Survival. Survival Time with Covariates.Limitations to Survival Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Survival Analysis.Life Tables. Standard Error of Cumulative Proportion Surviving. Hazard and Density Functions. Plot of Life Tables. Test for Group Differences. Computer Analyses of Small Sample Example.Types of Survival Analysis.Actuarial and Product-Limit Life Tables and Survivor Functions. Prediction of Group Survival Times from Covariates.Some Important Issues.Proportionality of Hazards. Censored Data. Effect Size and Power. Statistical Criteria. Odds Ratios.Complete Example of Survival Analysis.Evaluation of Assumptions. Cox Regression Survival Analysis.Comparison of Programs.SAS System. SYSTAT System. SPSS Package.16. Time Series Analysis. General Purpose and Description.Kinds of Experimental Questions.Pattern of Autocorrelation. Seasonal Cycles and Trends. Forecasting. Effect of an Intervention. Comparing Time Series. Time Series with Covariates. Effect Size and Power.Assumptions of Time Series Analysis.Theoretical Issues. Practical Issues.Fundamental Equations for Time Series ARIMA Models.Identification of ARIMA (p, d, q) Models. Estimating Model Parameters. Diagnosing a Model. Computer Analysis of Small Sample Time Series Example.Types of Time Series Analysis.Models with Seasonal Components. Models with Interventions. Adding Continuous Variables.Some Important Issues.Patterns of ACFs and PACFs. Effect Size. Forecasting. Statistical Methods for Comparing Two Models.Complete Example of a Time Series Analysis.Evaluation of Assumptions. Baseline Model Identification. Baseline Model Diagnosis. Intervention Analysis.Comparison of Programs.SPSS Package. SAS System. SYSTAT System.17. An Overview of the General Linear Model. Linearity and the General Linear Model.Bivariate to Multivariate Statistics and Overview of TechniquesBivariate Form. Simple Multivariate Form. Full Multivariate Form.Alternative Research Strategies.Appendix A. A Skimpy Introduction to Matrix Algebra. The Trace of a Matrix.Addition or Subtraction of a Constant to a Matrix.Multiplication or Division of a Matrix by a Constant.Addition and Subtraction of Two Matrices.Multiplication, Transposes, and Square Roots of Matrices.Matrix "Division" (Inverses and Determinants).Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix.Appendix B. Research Designs for Complete Examples. Women's Health and Drug Study.Sexual Attraction Study.Learning Disabilities Data Bank.Reaction Time to Identify Figures.Clinical Trial for Primary Biliary Cirrhosis.Impact of Seat Belt Law.Appendix C. Statistical Tables. Normal Curve Areas.Critical Values of the t Distribution for a = .05 and .-1, Two-Tailed Test.Critical Values of the f Distribution.Critical Values of Chi Square (c2).Critical Values for Squares Multiple Correlation (R2) in Forward Stepwise Selection.Critical Values for Fmax (S2max/S2min) Distribution for a = .05 and .01.

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