Numerical Petrology - 1st Edition - ISBN: 9780444420985, 9781483289748

Numerical Petrology, Volume 8

1st Edition

Statistical Interpretation of Geochemical Data

Authors: R.W. Le Maitre
eBook ISBN: 9781483289748
Imprint: Elsevier Science
Published Date: 1st July 1982
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Table of Contents

Chapter 1. The Nature of Petrological Data

1.1 Introduction

1.2 Sources of Error in Chemical Analyses

1.2.1 Random Sampling Procedures

1.2.2 Homogeneity of Rock Powders

1.2.3 Precision versus Accuracy

1.3 Frequency distributions and probability

1.3.1 The Normal Distribution

1.3.2 The Lognormal Distribution

1.3.3 The Binomial Distribution

1.3.4 The Poisson Distribution

1.3.5 Transformation of Variables

1.3.6 Some Observed Petrological Frequency Distributions

Chapter 2. Estimating and Testing Population Parameters

2.1 Introduction

2.2 Estimation of Population Mean μ, and Standard Deviation σ

2.3 Standard Deviation of the Sample Mean

2.4 Principles of Hypothesis Testing

2.5 Confidence Limits for Population Mean when σ Known

2.6 Sample Size

2.7 Confidence Limits for Population Mean when σ Unknown

2.8 Testing for a Difference Between Two Means

2.9 Variance Ratio Test and F Distribution

2.10 Goodness-of-Fit or Chi-Square Test

Chapter 3. Analysis of Variance - Testing Differences Among Several Means

3.1 Introduction

3.2 One-Way Classification

3.3 Two-Way Classification with Single Observations

3.4 Two-way Classification with Multiple Observations

3.5 Homogeneity of Variances

Chapter 4. Linear Relationships Between Two Variables

4.1 Introduction

4.2 The Correlation Coefficient

4.2.1 Testing the Correlation Coefficient for Significance

4.2.2 Confidence Limits for the Population Correlation Coefficient

4.2.3 The Problem of Closure

4.3 Linear Regression Analysis

4.3.1 Testing the Significance of a Regression

4.3.2 Confidence Limits for the Regression Coefficient and Intercept

4.3.3 Confidence Limits for the Location of the Regression Line

4.3.4 Confidence Limits for an Individual y Value

4.4 Functional and Structural Relationships

4.4.1 Significance Tests

Chapter 5. The Geometry of Petrological Data Space

5.1 Introduction

5.2 Distance Between Two Points

5.3 Definition of Directions in Space

5.4 Equation of a Line and the Addition-Subtraction Problem

5.5 Transformation of Coordinates

5.6 Equation of a Hyperplane

5.7 Some Limitations on the Use of Ratios

Chapter 6. Multiple Linear Regression and Petrological Mixing Models

6.1 Introduction

6.2 Multiple Linear Regression

6.2.1 Testing the Significance of the Regression

6.2.2 Confidence Limits for the Regression Coefficients

6.2.3 Confidence Limits for the Location of the Regression Surface

6.2.4 Confidence Limits for an Individual Value of y

6.3 Petrological Mixing Models

6.3.1 The Simple Mixing Model

6.3.2 The Constrained Simple Mixing Model

6.3.3 The Geometric Interpretation of Simple Models

6.3.4 The Generalized Mixing Model

6.3.5 Solutions Using Linear Programming

6.3.6 Weighted Mixing Models

6.3.7 Problem of Errors Associated with Petrological Mixing Models

Chapter 7. Principal Components Analysis

7.1 Introduction

7.2 Geometric Interpretation

7.3 Scaling the Variables

7.4 Basic Mathematics

7.5 Problems with Constructing Variation Diagrams

7.6 Use as a "Surface-Fitting" Procedure

7.7 Significance Tests

Chapter 8. Factor Analysis

8.1 Introduction

8.2 R-Mode Factor Analysis

8.2.1 Simplified Version Commonly Used in Geology

8.2.2 Rotation of Factors

8.3 Q-Mode Factor Analysis

8.4 Extended Q-Mode Factor Analysis

8.4.1 Graphical Representation and Rotation of Factors

8.4.2 Factor-Variance Diagrams

Chapter 9. Multiple Discriminant Analysis

9.1 Introduction

9.2 Geometric Interpretation

9.3 Basic Mathematics

9.3.1 The Problem of Singular Matrices

9.4 Testing the Significance of the Discrimination

9.4.1 An overall Test for Differences Between Group Means

9.4.2 Testing Successive Discriminant Functions

9.5 The Logic of Assignment Rules

9.5.1 For Two Group Discriminant Analysis

9.5.2 For Three or more group Discriminant Analysis

9.5.3 Use in Estimating Amount of Misclassification

9.6 Comparison with Principal Components Analysis

9.7 Application to Metamorphic Phase Diagrams

Chapter 10. Cluster Analysis and Classification

10.1 Introduction

10.2 Cluster Analysis

10.2.1 The Choice of Similarity Measure

10.2.2 The Choice of Linkage Method

10.3 Classification Procedure

10.3.1 Application to More than One Group

10.3.2 Using Prior Probabilities

10.3.3 Reducing the Dimensionality of the Problem

10.3.4 The Problem of Singular Matrices

Chapter 11. Propagation of Errors

11.1 Introduction

11.2 Counting X-Rays and Other Radiations

11.2.1 Single Counts

11.2.2 Testing Count Stability

11.2.3 Optimizing Peak and Background Counting Times

11.2.4 Measuring Concentration in an Unknown

11.2.5 Optimizing Unknown and Standard Counting Times

11.2.6 Lower Limit of Detection

11.3 Mineral Recalculations

11.3.1 Based on a Fixed Number of Oxygens

11.3.2 Partitioning Iron Between FeO and Fe203

11.3.3 Weighted Sums of Oxides

11.3.4 Weighted Cation Ratios

11.3.5 Weighted Oxide Ratios

11.4 Normative Calculations

11.4.1 Limitations on Use

Chapter 12. Petrological Data Management

12.1 Introduction

12.2 Petrological Databases

12.2.1 Some Source Databases

12.2.2 Some Reference Databases

12.2.3 Starting a Database

12.3 Data Processing Packages

12.3.1 The CLAIR Data Processing System

12.3.2 The KEYBAM Package

12.4 Conclusions



Author Index

Subject Index


Developments in Petrology, Volume 8: Numerical Petrology: Statistical Interpretation of Geochemical Data presents the methods that are likely to be useful to the average petrologist. This book deals with the problems of closed data and singular matrices in multiple discriminant analysis and classification procedure.

Organized into 12 chapters, this volume begins with an overview of the petrological data that can be quantified, including both discrete and continuous variables. This text then examines the methods of testing for differences between the means of two populations. Other chapters consider the three methods of evaluating linear trends within such bivatiate plots, namely, the use of the correlation coefficient, linear regression analysis, and either structural or functional relationships. This book discusses as well the propagation of errors in mineral and normative recalculations. The final chapter deals with the use of computers to manage the tremendous amount of information that is available.

This book is a valuable resource for petrologists, geochemists, and geologists.


© Elsevier Science 1982
Elsevier Science
eBook ISBN:


@qu:...destined to become a necessary part of the education of any modern petrologist, and an essential buy for any graduate-level student or professional geologist engaged in chemical aspects of petrology. @source: Episodes

About the Authors

R.W. Le Maitre Author