Ratio Correlation: A Manual for Students of Petrology and Geochemistry

by Felix Chayes

University of Chicago Press, 1971
Cloth: 978-0-226-10218-4 | Paper: 978-0-226-10220-7
Library of Congress Classification QE431.5.C47
Dewey Decimal Classification 552.001519537

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TABLE OF CONTENTS

Contents

Preface

1.
Ratios, Relatedness, and Correlation in Petrography

1.
Ratios in Petrography

2.
Petrographic Relation and Numerical Correlation

3.
Notation

4.
Approximation Technique

2.
The Simple Ratio Correlations

1.
Null Correlation of a Ratio with Its Numerator

2.
Other Forms of Simple Ratio Correlation

3.
Some Sampling Experiments in Ratio Correlation

4.
Simple Ratios Formed from Proportions

5.
Correlation of a Ratio with Its Numerator When Numerator and Denominator are Correlated

3.
The Part-Whole and Common-Element Correlations

1.
The Part-Whole Correlation

2.
The Common-Element Correlation

3.
Correlation between the Whole and the Ratio of a Part to the Whole

4.
Correlation between the Whole and the Ratio of a Part to the Whole When Both Are Proportions

5.
Correlation between Two Ratios When the Denominator of Each Is the Sum of Its Numerator and a Common Term

4.
Correlations between Proportions: The Closed Array

1.
The Closure Effect

2.
Null Correlation between Ratios Whose Numerators Are Common Elements in Their Common Denominator

3.
The Sign of the Closure Correlation

4.
Closure Correlation When Variances and Means are Homogeneous in X

5.
Closure Correlation When Variances are Proportional to Means in X

6.
The Ternary Closed Array

5.
Assigning Values to the Parameters of the Hypothetical Open Array

1.
Relations between the Means and Variances of X and Y

2.
An Alternative Method for Computing the Variances of X

6.
Testing the Significance of an Observed Correlation between Proportions

1.
Calculating the Closure Correlation

2.
The Fisher z Transformation

3.
Closure Correlation in Reference Material G-2

4.
Two Major Limitations of the Test

5.
The Interpretation of Negative Elements in σ

6.
A Further Note on the Ternary Array

7.
The Effect of Ratio Formation on Regression

1.
The Analytical Relation between Regression and Correlation Coefficients

2.
Null Regression Coefficients for the Simple Ratios

3.
Null Regression Coefficients between Ratios Whose Numerators Are Common Elements in the Sum Which Is Their Common Denominator

4.
Testing the Regression Coefficient

5.
Alternative Forms of Regression Analysis

8.
The Remaining-Space Transformation and the Niggli Variation Diagram

1.
Rationale of the Remaining-Space Transformation

2.
The Remaining-Space Transformation

3.
The Niggli-Number Transformation

4.
Null Correlations for the Remaining-Space and Niggli-Number Correlations

9.
Harker and Related Variation Diagrams

1.
Factors Controlling the Sign of σi² in Harker and Similar Arrays

2.
Negative Elements in σ Computed from some Harker Arrays

3.
The Elimination of Negative Elements in σ

4.
Modifying Sample Variables by Linear Combination

5.
Some Linear Transformations Applicable to the Harker Array

6.
Testing the Significance of Correlations between Transformed Harker Variables

References

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