A primer of multivariate statistics

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A primer of multivariate statistics / [by] Richard J. Harris

資料種別:: 図書
出版情報:: New York : Academic Press, c1975
形態:: xiv, 332 p. ; 24 cm
著者名:: Harris, Richard J. <DA02845243>
ISBN:: 9780123272508 [0123272505]
書誌ID:: BA0768966X

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注記:

Bibliography: p. 317-322

主題:

Multivariate analysis

言語:

英語

目次情報:

The Forest before the Trees / 1：

Why Statistics? / 1.0：

Statistics as a Form of Social Control / 1.01：

Objections to Null Hypothesis Significance Testing / 1.02：

Should Significance Tests be Banned? / 1.03：

Math Modeling's the Ultimate Answer / 1.04：

Some Recent Developments in Univariate Statistics / 1.05：

Why Multivariate Statistics? / 1.1：

Bonferroni Adjustment: An Alternative to Multivariate Statistics / 1.1.1：

Why Isn't Bonferroni Adjustment Enough? / 1.1.2：

A Heuristic Survey of Statistical Techniques / 1.2：

Student's t test / 1.2.1：

One-Way Analysis of Variance / 1.2.2：

Hotelling's T[superscript 2] / 1.2.3：

One-Way Multivariate Analysis of Variance / 1.2.4：

Higher Order Analysis of Variance / 1.2.5：

Higher Order Manova / 1.2.6：

Pearson r and Bivariate Regression / 1.2.7：

Multiple Correlation and Regression / 1.2.8：

Path Analysis / 1.2.9：

Canonical Correlation / 1.2.10：

Analysis of Covariance / 1.2.11：

Principal Component Analysis / 1.2.12：

Factor Analysis / 1.2.13：

Structural Equation Modeling / 1.2.14：

Learning to Use Multivariate Statistics / 1.3：

A Taxonomy of Linear Combinatons / 1.3.1：

Why the Rest of the Book? / 1.3.2：

Quiz 1 See How Much You Know after Reading Just One Chapter!

Sample Answers to Quiz 1

Multiple Regression: Predicting One Variable from Many / 2：

Data Set 1

The Model / 2.1：

Choosing Weights / 2.2：

Least Squares Criterion / 2.2.1：

Maximum Correlation Criterion / 2.2.2：

The Utility of Matrix Algebra / 2.2.3：

Independence of Irrelevant Parameters / 2.2.4：

Relating the Sample Equation to the Population Equation / 2.3：

R[subscript x] versus S[subscript x] versus x'x as the Basis for MRA / 2.3.1：

Specific Comparisons / 2.3.2：

Illustrating Significance Tests / 2.3.3：

Stepwise Multiple Regression Analysis / 2.3.4：

Computer Programs for Multiple Regression / 2.4：

Computer Logic and Organization / 2.4.1：

Sage Advice on Use of Computer Programs / 2.4.2：

Computerized Multiple Regression Analysis / 2.4.3：

Some General Properties of Covariance Matrices / 2.5：

Measuring the Importance of the Contribution of a Single Variable / 2.6：

Anova via MRA / 2.7：

Alternatives to the Least-Squares Criterion / 2.8：

Path analytic Terminology / 2.9：

Preconditions for Path Analysis / 2.9.2：

Estimating and Testing Path coefficients / 2.9.3：

Decomposition of Correlations into Components / 2.9.4：

Overall Test of Goodness of fit / 2.9.5：

Examples / 2.9.6：

Some Path-Analysis References / 2.9.7：

Demonstration Problem

Answers

Some Real Data and a Quiz Thereon

Path Analysis Problem

Answers to Path Analysis Problem

Hotelling's T[superscript 2]: Tests on One or Two Mean Vectors / 3：

Single-Sample t and T[superscript 2] / 3.1：

Linearly Related Outcome Variables / 3.2：

Two-Sample t and T[superscript 2] / 3.3：

Profile Analysis / 3.4：

Discriminant Analysis / 3.5：

Relationship between T[superscript 2] and MRA / 3.6：

Assumptions Underlying T[superscript 2] / 3.7：

The Assumption of Equal Covariance Matrices / 3.7.1：

Known Covariance Matrix / 3.7.2：

The Assumption of Multivariate Normality / 3.7.3：

Analyzing Repeated-Measures Designs via T[superscript 2] / 3.8：

Single-Symbol Expressions for Simple Cases / 3.9：

Computerized T[superscript 2] / 3.10：

Single-Sample and Two-Sample T[superscript 2] / 3.10.1：

Within-Subjects Anova / 3.10.2：

Demonstration Problems

Multivariate Analysis of Variance: Differences Among Several Groups on Several Measures / 4：

One-Way (Univariate) Analysis of Variance / 4.1：

The Overall Test / 4.1.1：

Multiple Profile Analysis / 4.1.2：

Multiple Discriminant Analysis / 4.4：

Greatest Characteristic Roots versus Multiple-Root Tests in Manova / 4.5：

"Protected" Univariate Tests / 4.5.1：

Simulataneous Test Procedures and Union Intersection / 4.5.2：

Invalidity of Partitioned-U Tests of Individual Roots / 4.5.3：

Simplified Coefficients as a Solution to the Robustness Problem / 4.5.4：

Finite-Intersection Tests / 4.5.5：

Simple Cases of Manova / 4.6：

Higher Order Anova: Interactions / 4.7：

Within-Subject Univariate Anova Versus Manova / 4.8：

Computerized Manova / 4.10：

Generic Setup for SPSS MANOVA / 4.10.1：

Supplementary Computations / 4.10.2：

Pointing and Clicking to a Manova on SPSS PC / 4.10.3：

Generic Setup for SAS PROC GLM / 4.10.4：

Canonical Correlation: Relationships Between Two Sets of Variables / 5：

Formulae for Computing Canonical Rs / 5.1：

Heuristic Justification of Canonical Formulae / 5.1.1：

Simple Cases of Canonical Correlations / 5.1.2：

Example of a Canonical Analysis / 5.1.3：

Relationships to Other Statistical Techniques / 5.2：

Likelihood-Ratio Tests of Relationships between Sets of Variables / 5.3：

Generalization and Specialization of Canonical Analysis / 5.4：

Testing the Independence of m Sets of Variables / 5.4.1：

Repeated-Battery Canona / 5.4.2：

Rotation of Canonical Variates / 5.4.3：

The Redundancy Coefficient / 5.4.4：

What's Missing from Canonical Analysis? / 5.4.5：

Computerized Canonical Correlation / 5.5：

Matrix-Manipulation Systems / 5.5.1：

SAS PROC CANCORR / 5.5.2：

Canona via SPSS MANOVA / 5.5.3.：

SPSS Canona From Correlation Matrix: Be Careful / 5.5.4：

Demonstration Problems and Some Real Data Employing Canonical Correlation

Principal Component Analysis: Relationships Within a Single Set of Variables / 6：

Definition of Principal Components / 6.1：

Terminology and Notation in PCA and FA / 6.1.1：

Scalar Formulae for Simple Cases of PCA / 6.1.2：

Computerized PCA / 6.1.3：

Additional Unique Properties (AUPs) of PCs / 6.1.4：

Interpretation of Principal Components / 6.2：

Uses of Principal Components / 6.3：

Uncorrelated Contributions / 6.3.1：

Computational Convenience / 6.3.2：

Principal Component Analysis as a Means of Handling Linear Dependence / 6.3.3：

Examples of PCA / 6.3.4：

Quantifying Goodness of Interpretation of Components / 6.3.5：

Significance Tests for Principal Components / 6.4：

Sampling Properties of Covariance-Based PCs / 6.4.1：

Sampling Properties of Correlation-Based PCs / 6.4.2：

Rotation of Principal Components / 6.5：

Basic Formulae for Rotation / 6.5.1：

Objective Criteria for Rotation / 6.5.2：

Examples of Rotated PCs / 6.5.3：

Individual Scores on Rotated PCs / 6.5.4：

Uncorrelated-Components Versus Orthogonal-Profiles Rotation / 6.5.5：

Factor Analysis: The Search for Structure / 7：

Communalities / 7.1：

Theoretical Solution / 7.2.1：

Empirical Approximations / 7.2.2：

Iterative Procedure / 7.2.3：

Is the Squared Multiple Correlation the True Communality? / 7.2.4：

Factor Analysis Procedures Requiring Communality Estimates / 7.3：

Principal Factor Analysis / 7.3.1：

Triangular (Choleski) Decomposition / 7.3.2：

Centroid Analysis / 7.3.3：

Methods Requiring Estimate of Number of Factors / 7.4：

Other Approaches to Factor Analysis / 7.5：

Factor Loadings versus Factor Scores / 7.6：

Factor Score Indeterminacy / 7.6.1：

Relative Validities of Loadings-Derived versus Scoring-Coefficient-Derived Factor Interpretations / 7.6.2：

Regression-Based Interpretation of Factors is Still a Hard Sell / 7.6.3：

Relative Merits of Principal Component Analysis versus Factor Analysis / 7.7：

Similarity of Factor Scoring Coefficients / 7.7.1：

Bias in Estimates of Factor Loadings / 7.7.2：

Computerized Exploratory Factor Analysis / 7.8：

Confirmatory Factor Analysis / 7.9：

Sas Proc Calis / 7.9.1：

The Forest Revisited / 8：

Scales of Measurement and Multivariate Statistics / 8.1：

Effects of Violations of Distributional Assumptions in Multivariate Analysis / 8.2：

Nonlinear Relationships in Multivariate Statistics / 8.3：

The Multivariate General Linear Hypothesis / 8.4：

General Approach and Examples / 8.5：

SEM Is Not a General Model for Multivariate Statistics / 8.5.2：

Other User-Friendly SEM Programs / 8.5.3：

Where to Go from Here / 8.6：

Summing Up / 8.7：

Finding Maxima and Minima of Polynomials / Digression 1：

Derivatives and Slopes / D1.1：

Optimization Subject to Constraints / D1.2：

Matrix Algebra / Digression 2：

Basic Notation / D2.1：

Linear Combinations of Matrices / D2.2：

Multiplication of Matrices / D2.3：

Permissible Manipulations / D2.4：

Inverses / D2.5：

Determinants / D2.6：

Some Handy Formulae for Inverses and Determinants in Simple Cases / D2.7：

Rank / D2.8：

Matrix Calculus / D2.9：

Partitioned Matrices / D2.10：

Characteristic Roots and Vectors / D2.11：

Solution of Homogeneous Systems of Equations / D2.12：

Solution of Cubic Equations / Digression 3：

Statistical Tables / Appendix A：

(Why omitted from this edition) / A.1 - A.4：

Greatest Characteristic Root Distribution / A.5：

Computer Programs Available from the Author / Appendix B：

cvinter: p values and Critical Values for Univariate Statistics / B.1：

gcrinter: Critical Values for the Greatest Characteristic Root (g.c.r.) Distribution / B.2：

Derivations / Appendix C：

Per-Experiment and Experimentwise Error Rates for Bonferroni-Adjusted Tests / Derivation 1.1：

Scalar Formulae for MRA with One, Two, and Three Predictors / Derivation 2.1：

Coefficients That Minimize Error Also Maximize Correlation / Derivation 2.2：

Maximizing r via Matrix Algebra / Derivation 2.3：

Variances of b[subscript j]s and of Linear Combinations Thereof / Derivation 2.4：

Drop in R[superscript 2] = b[superscript 2][subscript j](1 - [characters not reproducible]) / Derivation 2.6：

MRA on Group-Membership Variables Yields Same F As Anova / Derivation 2.7：

Unweighted Means and Least-Squares Anova Are Identical in the 2[superscript n] Design / Derivation 2.8：

T[superscript 2] and Associated Discriminant Function / Derivation 3.1：

Single-Sample T[superscript 2]

Two-Sample T[superscript 2]

Two-Sample t Versus Pearson r With Group-Membership Variables / Derivation 3.2：

Single-Sample t Test versus "Raw-Score" r[subscript xy]

T[superscript 2] Versus MRA

Maximizing F(a) in Manova / Derivation 4.1：

Canonical Correlation and Canonical Variates / Derivation 5.1：

Canonical Correlation as "Mutual Regression Analysis" / Derivation 5.2：

Relationship between Canonical Analysis and Manova / Derivation 5.3：

Principal Components / Derivation 6.1：

PC Coefficients Define Both Components in Terms of Xs and Xs in Terms of PCs / Derivation 6.2：

What Does Rotation of Loadings Do to Coefficients? / Derivation 6.3：

Near Equivalence of PCA and Equal-Communalities PFA / Derivation 7.1：

References

Index

The Forest before the Trees / 1：

Why Statistics? / 1.0：

Statistics as a Form of Social Control / 1.01：

Objections to Null Hypothesis Significance Testing / 1.02：

Should Significance Tests be Banned? / 1.03：

Math Modeling's the Ultimate Answer / 1.04：

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