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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

TOC

  • 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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