Beschreibung
It has been evident from many years of research work in the geohydrologic sciences that a summary of relevant past work, present work, and needed future work in multivariate statistics with geohydrologic applications is not only desirable, but is necessary. This book is intended to serve a broad scientific audience, but more specifi cally is geared toward scientists doing studies in geohydrology and related geo sciences.lts objective is to address both introductory and advanced concepts and applications of the multivariate procedures in use today. Some of the procedures are classical in scope but others are on the forefront of statistical science and have received limited use in geohydrology or related sciences. The past three decades have seen a significant jump in the application of new research methodologies that focus on analyzing large databases. With more general applications being developed by statisticians in various disciplines, multivariate quantitative procedures are evolving for better scientific applica tion at a rapid rate and now provide for quick and informative analyses of large datasets. The procedures include a family of statistical research methods that are alternatively called "multivariate analysis" or "multivariate statistical methods".
Autorenporträt
InhaltsangabeI Introduction to General Statistical and Multivariate Concepts.- 1 General Concepts.- 1.1 Concepts.- 1.2 Definitions.- 1.3 Introduction to Statistical Concepts.- 1.3.1 Meaning of Statistics.- 1.3.2 Probability and Randomness.- 1.4 Meaning of Multivariate Analysis.- 1.5 Univariate to Multivariate Mathematical Generalizations.- 1.6 Nature of References.- 1.7 Related Texts and Publications.- 1.8 Processing Data.- 1.9 Summary.- 1.10 Supplemental Reading.- 2 Introduction to Multivariate Statistical Procedures.- 2.1 Concept.- 2.2 Definitions.- 2.3 Purpose and Rationale.- 2.4 Development of Multivariate Quantitative Procedures.- 2.5 Selection of Methods.- 2.6 Scales of Measurement.- 2.7 Testing for Normality.- 2.7.1 Coefficient of Skewness.- 2.7.2 Coefficient of Kurtosis.- 2.7.3 Significance Tests - Normality.- 2.8 Normal Distribution.- 2.9 Central Limit Theorem.- 2.10 Significance Tests.- 2.10.1 Chi-Square Goodness of Fit and Probability Plats.- 2.10.2 Significance Tests-Homogeneity of Variances.- 2.11 Division of Procedures: Variable-Directed or Individual Directed Tests.- 2.12 Sampling Design in Multivariate Procedures.- 2.13 Sample Survey Design.- 2.14 Standardization.- 2.15 The Statistical Model.- 2.16 Random Variables.- 2.17 Description of Multivariate Quantitative Procedures.- 2.18 General Significance Testing for Multivariate Data.- 2.19 Summary.- 2.20 Supplemental Reading.- II Variable-Directed Procedures Based on Normal Distribution Assumptions.- 3 Correlation.- 3.1 Concept.- 3.2 Definitions.- 3.3 Objective of Procedures.- 3.4 Problems.- 3.5 Significance Tests for Correlations.- 3.6 Interpretation.- 3.7 Numerical Example on Cave Lithology.- 3.8 Numerical Example on Carbonate-Rock Geohydrology.- 3.9 Numerical Example on Fluvial Sediment Geochemistry.- 3.10 Numerical Example - Discussion.- 3.11 Summary.- 3.12 Supplemental Reading.- 4 Factor Analysis.- 4.1 Concept.- 4.2 Matrices.- 4.3 Definitions.- 4.4 Contrasts Between Factor and Principal Components Analyses.- 4.5 Significance Tests - Factor Analysis Decision Tests.- 4.5.1 Significance Tests - Barlett's Test of Sphericity.- 4.5.2 Generalizations About Correlations and Factor Analysis.- 4.6 Determining Significance of Output.- 4.6.1 Significance Tests - Factor Loadings.- 4.6.2 Significance Tests - Amount of Explained Variation.- 4.7 Extraction Techniques for Factors.- 4.8 Other Significance Tests - Comparisons of Solutions and Datasets.- 4.9 Factor Analysis Procedure.- 4.10 Numerical Example on Water Chemistry.- 4.11 Numerical Example on Sediment Geochemistry.- 4.12 Numerical Example on Drainage Basin Properties.- 4.13 Numerical Example on Detrital Sediment Characteristics.- 4.14 Summary.- 4.15 Supplemental Reading.- 5 Canonical Correlation.- 5.1 Concept.- 5.2 Definitions.- 5.3 Overview of Method.- 5.4 Significance Tests-Importance of Wilks' Lambda (?).- 5.5 Significance Tests - Bartlett's Test Using Chi-Square Variable.- 5.6 Canonical Correlation Procedure.- 5.7 Numerical Example on Sediment and Soil Pollution.- 5.8 Summary.- 5.9 Supplemental Reading.- 6 Multiple Regression.- 6.1 Concept.- 6.2 Definitions.- 6.3 Overview of Methods.- 6.4 Multiple Regression Procedure.- 6.5 Stepwise Multiple Regression.- 6.6 Significance Tests - Addressing Multicollinearity.- 6.7 Multiple Regression Applications.- 6.8 Numerical Example on Water Yield.- 6.9 Numerical Example on Streamflows.- 6.10 Numerical Example on Geomorphic Variables.- 6.11 Numerical Example on Sampling Sites.- 6.12 Multivariate Multiple Regression.- 6.13 Nonlinear Regression.- 6.14 Multivariate Models with Qualitative (Dummy) Variables.- 6.14.1 Multivariate Models with One Qualitative Variable.- 6.14.2 Multivariate Models with Multiple Qualitative Variables.- 6.15 Summary.- 6.16 Supplemental Reading.- 7 Multivariate Analysis of Variance.- 7.1 Concept.- 7.2 Definitions.- 7.3 Overview of Analysis of Variance.- 7.3.1 Procedure.- 7.3.2 Repeated Measures Design in Analysis of Variance.- 7.3.3 Two-Way Multivariate Analysis of V
