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Introduction | |

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Multivariate Statistics: Why? | |

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The Domain of Multivariate Statistics: Numbers of IVs and DVs | |

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Experimental and Nonexperimental Research | |

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Computers and Multivariate Statistics | |

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Why Not | |

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Some Useful Definitions | |

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Continuous, Discrete, and Dichotomous Data | |

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Samples and Populations | |

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Descriptive and Inferential Statistics | |

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Orthogonality | |

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Standard and Sequential Analyses | |

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Combining Variables | |

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Number and Nature of Variables to Include | |

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Statistical Power | |

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Data Appropriate for Multivariate Statistics | |

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The Data Matrix | |

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The Correlation Matrix | |

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The Variance-Covariance Matrix | |

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The Sum-of-Squares and Cross-Products Matrix | |

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Residuals | |

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Organization of the Book | |

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A Guide to Statistical Techniques: Using the Book | |

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Research Questions and Associated Techniques | |

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Degree of Relationship among Variables | |

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Significance of Group Differences | |

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Prediction of Group Membership | |

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Structure | |

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Time Course of Events | |

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A Decision Tree | |

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Technique Chapters | |

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Preliminary Check of the Data | |

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Review of Univariate and Bivariate Statistics | |

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Hypothesis Testing | |

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One-Sample z Test as Prototype | |

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Power | |

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Extensions of the Model | |

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Analysis of Variance | |

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One-Way Between-Subjects ANOVA | |

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Factorial Between-Subjects ANOVA | |

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Within-Subjects ANOVA | |

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Mixed Between-Within-Subjects ANOVA | |

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Design Complexity | |

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Specific Comparisons | |

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Parameter Estimation | |

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Strength of Association | |

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Bivariate Statistics: Correlation and Regression | |

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Correlation | |

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Regression | |

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Chi-Square Analysis | |

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Cleaning Up Your Act: Screening Data Prior to Analysis | |

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Important Issues in Data Screening | |

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Accuracy of Data File | |

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Honest Correlations | |

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Missing Data | |

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Outliers | |

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Normality, Linearity, and Homoscedasticity | |

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Common Data Transformations | |

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Multicollinearity and Singularity | |

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A Checklist and Some Practical Recommendations | |

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Complete Examples of Data Screening | |

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Screening Ungrouped Data | |

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Screening Grouped Data | |

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Multiple Regression | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Degree of Relationship | |

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Importance of IVs | |

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Adding IVs | |

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Changing IVs | |

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Contingencies among IVs | |

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Comparing Sets of IVs | |

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Predicting DV Scores for Members of a New Sample | |

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Parameter Estimates | |

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Limitations to Regression Analyses | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Multiple Regression | |

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General Linear Equations | |

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Matrix Equations | |

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Computer Analyses of Small Sample Example | |

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Major Types of Multiple Regression | |

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Standard Multiple Regression | |

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Sequential Multiple Regression | |

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Statistical (Stepwise) Regression | |

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Choosing among Regression Strategies | |

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Some Important Issues | |

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Importance of IVs | |

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Statistical Inference | |

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Adjustment of R2 | |

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Suppressor Variables | |

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Regression Approach to ANOVA | |

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Centering When Interactions and Powers of IVs Are Included | |

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Complete Examples of Regression Analysis | |

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Evaluation of Assumptions | |

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Standard Multiple Regression | |

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Sequential Regression | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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Canonical Correlation | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Number of Canonical Variate Pairs | |

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Interpretation of Canonical Variates | |

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Importance of Canonical Variates | |

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Canonical Variate Scores | |

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Limitations | |

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Theoretical Limitations | |

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Practical Issues | |

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Fundamental Equations for Canonical Correlation | |

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Eigenvalues and Eigenvectors | |

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Matrix Equations | |

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Proportions of Variance Extracted | |

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Computer Analyses of Small Sample Example | |

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Some Important Issues | |

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Importance of Canonical Variates | |

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Interpretation of Canonical Variates | |

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Complete Example of Canonical Correlation | |

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Evaluation of Assumptions | |

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Canonical Correlation | |

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Comparison of Programs | |

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SAS System | |

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SPSS Package | |

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SYSTAT System | |

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Multiway Frequency Analysis | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Associations among Variables | |

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Effect on a Dependent Variable | |

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Parameter Estimates | |

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Importance of Effects | |

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Strength of Association | |

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Specific Comparisons and Trend Analysis | |

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Limitations to Multiway Frequency Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Multiway Frequency Analysis | |

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Screening for Effects | |

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Modeling | |

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Evaluation and Interpretation | |

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Computer Analyses of Small Sample Example | |

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Some Important Issues | |

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Hierarchical and Nonhierarchical Models | |

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Statistical Criteria | |

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Strategies for Choosing a Model | |

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Complete Example of Multiway Frequency Analysis | |

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Evaluation of Assumptions: Adequacy of Expected Frequencies | |

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Hierarchical Loglinear Analysis | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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Analysis of Covariance | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Main Effects of IVs | |

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Interactions among IVs | |

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Specific Comparisons and Trend Analysis | |

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Effects of Covariates | |

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Strength of Association | |

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Parameter Estimates | |

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Limitations to Analysis of Covariance | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Analysis of Covariance | |

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Sums of Squares and Cross Products | |

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Significance Test and Strength of Association | |

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Computer Analyses of Small Sample Example | |

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Some Important Issues | |

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Test for Homogeneity of Regression | |

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Design Complexity | |

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Evaluation of Covariates | |

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Choosing Covariates | |

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Alternatives to ANCOVA | |

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Complete Example of Analysis of Covariance | |

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Evaluation of Assumptions | |

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Analysis of Covariance | |

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Comparison of Programs | |

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SPSS Package | |

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SYSTAT System | |

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SAS System | |

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Multivariate Analysis of Variance and Covariance | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Main Effects of IVs | |

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Interactions among IVs | |

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Importance of DVs | |

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Parameter Estimates | |

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Specific Comparisons and Trend Analysis | |

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Strength of Association | |

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Effects of Covariates | |

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Repeated-Measures Analysis of Variance | |

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Limitations to Multivariate Analysis of Variance and Covariance | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Multivariate Analysis of Variance and Covariance | |

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Multivariate Analysis of Variance | |

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Computer Analyses of Small Sample Example | |

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Multivariate Analysis of Covariance | |

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Some Important Issues | |

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Criteria for Statistical Inference | |

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Assessing DVs | |

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Specific Comparisons and Trend Analysis | |

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Design Complexity | |

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MANOVA vs | |

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ANOVAs | |

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Complete Examples of Multivariate Analysis of Variance and Covariance | |

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Evaluation of Assumptions | |

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Multivariate Analysis of Variance | |

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Multivariate Analysis of Covariance | |

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Comparison of Programs | |

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SPSS Package | |

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SYSTAT System | |

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SAS System | |

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Profile Analysis: The Multivariate Approach to Repeated Measures | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Parallelism of Profiles | |

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Overall Difference among Groups | |

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Flatness of Profiles | |

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Contrasts Following Profile Analysis | |

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Parameter Estimates | |

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Strength of Association | |

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Limitations to Profile Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Profile Analysis | |

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Differences in Levels | |

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Parallelism | |

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Flatness | |

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Computer Analyses of Small Sample Example | |

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Some Important Issues | |

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Contrasts in Profile Analysis | |

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Univariate vs | |

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Multivariate Approach to Repeated Measures | |

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Doubly Multivariate Designs | |

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Classifying Profiles | |

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Imputation of Missing Values | |

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Complete Examples of Profile Analysis | |

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Profile Analysis of Subscales of the WISC | |

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Doubly Multivariate Analysis of Reaction Time | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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Discriminant Function Analysis | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Significance of Prediction | |

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Number of Significant Discriminant Functions | |

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Dimensions of Discrimination | |

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Classification Functions | |

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Adequacy of Classification | |

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Strength of Association | |

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Importance of Predictor Variables | |

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Significance of Prediction with Covariates | |

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Estimation of Group Means | |

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Limits to Discriminant Function Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Discriminant Function Analysis | |

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Derivation and Test of Discriminant Functions | |

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Classification | |

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Computer Analyses of Small Sample Example | |

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Types of Discriminant Function Analysis | |

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Direct Discriminant Function Analysis | |

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Sequential Discriminant Function Analysis | |

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Stepwise (Statistical) Discriminant Function Analysis | |

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Some Important Issues | |

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Statistical Inference | |

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Number of Discriminant Functions | |

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Interpreting Discriminant Functions | |

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Evaluating Predictor Variables | |

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Design Complexity: Factorial Designs | |

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Use of Classification Procedures | |

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Complete Example of Discriminant Function Analysis | |

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Evaluation of Assumptions | |

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Direct Discriminant Function Analysis | |

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Comparison of Programs | |

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SPSS Package | |

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SYSTAT System | |

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SAS System | |

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Logistic Regression | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Prediction of Group Membership or Outcome | |

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Importance of Predictors | |

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Interactions among Predictors | |

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Parameter Estimates | |

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Classification of Cases | |

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Significance of Prediction with Covariates | |

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Strength of Association | |

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Limitations to Logistic Regression Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Logistic Regression | |

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Testing and Interpreting Coefficients | |

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Goodness-of-Fit | |

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Comparing Models | |

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Interpretation and Analysis of Residuals | |

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Computer Analyses of Small Sample Example | |

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Types of Logistic Regression | |

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Direct Logistic Regression | |

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Sequential Logistic Regression | |

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Stepwise (Statistical) Logistic Regression | |

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Probit and Other Analyses | |

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Some Important Issues | |

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Statistical Inference | |

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Number and Type of Outcome Categories | |

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Strength of Association for a Model | |

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Coding Outcome and Predictor Categories | |

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Classification of Cases | |

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Hierarchical and Nonhierarchical Analysis | |

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Interpretation of Coefficients Using Odds | |

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Logistic Regression for Matched Groups | |

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Complete Examples of Logistic Regression | |

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Evaluation of Limitations | |

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Direct Logistic Regression with Two-Category Outcome | |

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Sequential Logistic Regression with Three Categories of Outcome | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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Principal Components and Factor Analysis | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Number of Factors | |

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Nature of Factors | |

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Importance of Solutions and Factors | |

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Testing Theory in FA | |

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Estimating Scores on Factors | |

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Limitations | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Factor Analysis | |

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Extraction | |

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Orthogonal Rotation | |

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Communalities, Variance, and Covariance | |

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Factor Scores | |

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Oblique Rotation | |

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Computer Analyses of Small Sample Example | |

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Major Types of Factor Analysis | |

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Factor Extraction Techniques | |

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Rotation | |

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Some Practical Recommendations | |

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Some Important Issues | |

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Estimates of Communalities | |

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Adequacy of Extraction and Number of Factors | |

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Adequacy of Rotation and Simple Structure | |

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Importance and Internal Consistency of Factors | |

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Interpretation of Factors | |

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Factor Scores | |

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Comparisons among Solutions and Groups | |

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Complete Example of FA | |

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Evaluation of Limitations | |

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Principal Factors Extraction with Varimax Rotation | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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Structural Equation Modeling by Jodie B | |

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Ullman | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Adequacy of the Model | |

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Testing Theory | |

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Amount of Variance in the Variables Accounted for by the Factors | |

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Reliability of the Indicators | |

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Parameter Estimates | |

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Mediation | |

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Group Differences | |

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Longitudinal Differences | |

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Multilevel Modeling | |

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Limitations to Structural Equation Modeling | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Structural Equations Modeling | |

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Covariance Algebra | |

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Model Hypotheses | |

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Model Specification | |

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Model Estimation | |

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Model Evaluation | |

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Computer Analysis of Small Sample Example | |

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Some Important Issues | |

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Model Identification | |

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Estimation Techniques | |

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Assessing the Fit of the Model | |

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Model Modification | |

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Reliability and Proportion of Variance | |

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Discrete and Ordinal Data | |

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Multiple Group Models | |

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Mean and Covariance Structure Models | |

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Complete Examples of Structural Equation Modeling Analysis | |

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Model Specification for CFA | |

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Evaluation of Assumptions for CFA | |

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Model Modification | |

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SEM Model Specification | |

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SEM Model Estimation and Preliminary Evaluation | |

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Model Modification | |

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Comparison of Programs | |

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EQS | |

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LISREL | |

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SAS System | |

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AMOS | |

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Survival/Failure Analysis | |

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General Purpose and Description | |

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Kinds of Research Questions | |

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Proportions Surviving at Various Times | |

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Group Differences in Survival | |

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Survival Time with Covariates | |

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Limitations to Survival Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Survival Analysis | |

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Life Tables | |

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Standard Error of Cumulative Proportion Surviving | |

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Hazard and Density Functions | |

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Plot of Life Tables | |

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Test for Group Differences | |

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Computer Analyses of Small Sample Example | |

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Types of Survival Analysis | |

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Actuarial and Product-Limit Life Tables and Survivor Functions | |

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Prediction of Group Survival Times from Covariates | |

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Some Important Issues | |

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Proportionality of Hazards | |

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Censored Data | |

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Effect Size and Power | |

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Statistical Criteria | |

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Odds Ratios | |

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Complete Example of Survival Analysis | |

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Evaluation of Assumptions | |

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Cox Regression Survival Analysis | |

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Comparison of Programs | |

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SAS System | |

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SYSTAT System | |

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SPSS Package | |

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Time Series Analysis | |

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General Purpose and Description | |

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Kinds of Experimental Questions | |

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Pattern of Autocorrelation | |

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Seasonal Cycles and Trends | |

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Forecasting | |

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Effect of an Intervention | |

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Comparing Time Series | |

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Time Series with Covariates | |

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Effect Size and Power | |

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Assumptions of Time Series Analysis | |

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Theoretical Issues | |

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Practical Issues | |

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Fundamental Equations for Time Series ARIMA Models | |

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Identification of ARIMA (p, d, q) Models | |

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Estimating Model Parameters | |

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Diagnosing a Model | |

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Computer Analysis of Small Sample Time Series Example | |

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Types of Time Series Analysis | |

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Models with Seasonal Components | |

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Models with Interventions | |

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Adding Continuous Variables | |

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Some Important Issues | |

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Patterns of ACFs and PACFs | |

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Effect Size | |

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Forecasting | |

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Statistical Methods for Comparing Two Models | |

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Complete Example of a Time Series Analysis | |

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Evaluation of Assumptions | |

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Baseline Model Identification | |

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Baseline Model Diagnosis | |

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Intervention Analysis | |

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Comparison of Programs | |

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SPSS Package | |

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SAS System | |

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SYSTAT System | |

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An Overview of the General Linear Model | |

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Linearity and the General Linear Model | |

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Bivariate to Multivariate Statistics and Overview of Techniques | |

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Bivariate Form | |

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Simple Multivariate Form | |

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Full Multivariate Form | |

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Alternative Research Strategies | |

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A Skimpy Introduction to Matrix Algebra | |

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The Trace of a Matrix | |

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Addition or Subtraction of a Constant to a Matrix | |

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Multiplication or Division of a Matrix by a Constant | |

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Addition and Subtraction of Two Matrices | |

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Multiplication, Transposes, and Square Roots of Matrices | |

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Matrix Division (Inverses and Determinants) | |

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Eigenvalues and Eigenvectors: Procedures for Consolidating Variance from a Matrix | |

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Research Designs for Complete Examples | |

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Women's Health and Drug Study | |

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Sexual Attraction Study | |

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Learning Disabilities Data Bank | |

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Reaction Time to Identify Figures | |

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Clinical Trial for Primary Biliary Cirrhosis | |

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Impact of Seat Belt Law | |

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Statistical Tables | |

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Normal Curve Areas | |

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Critical Values of the t Distribution for a = .05 and .-1, Two-Tailed Test | |

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Critical Values of the f Distribution | |

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Critical Values of Chi Square (c2) | |

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Critical Values for Squares Multiple Correlation (R2) in Forward Stepwise Selection | |

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Critical Values for Fmax (S2max/S2min) Distribution for a = .05 and .01 | |