The G Factor: The Science of Mental Ability

By Arthur R. Jensen | Go to book overview

Appendix A
Spearman's "Law of Diminishing Returns"

Spearman ( 1927, pp. 217-21) compared the disattenuated correlation matrices (based on 12 diverse cognitive tests) of 78 "normal" children and 22 "defective" children. He found that the mean r of the matrix for the normal children was +.466; for the retarded children the mean r was +.782. Deary and Pagliari ( 1991) performed principal components analyses of Spearman's correlation matrix for the normal children and the correlation matrix for the defective children. The average loadings on the first principal component (PCI) of each matrix were +.325 and +.899, respectively. Yet the PC1 was clearly the same factor in both the normal and retarded groups, as indicated by a congruence coefficient of +.988. Spearman also noted in other data sets that tests' intercorrelations (and average g loadings) were larger for younger children than for older children. These findings suggested that the higher the level of g, the less is the amount of g variance in any particular mental test.

Spearman rather grandiosely likened this phenomenon to the "law of diminishing returns," as it applies in physics and in economics. That is, the higher a person's level of g, the less important it becomes in the variety of abilities the person possesses. High-g persons have more diversified abilities, with more of the total variance in their abilities existing in non-g factors (i.e., the various group factors and specificity). Others have explained this phenomenon in terms of what has become known as the differentiation theory, that higher g level (and the increase in mental abilities from childhood to early maturity) is accompanied by an increasing differentiation of general ability and the development of special abilities independent of g. (In the elderly, the reverse occurs for novel tests and tasks; there is dedifferentiation of abilities variance and a consequent increase in various tests' g loadings.) One might say that in the course of mental development g (or fluid ability, Gf) becomes increasingly invested in specialized skills, in which proficiency becomes partly automatized through practice. The automatized aspects of the special skills lose their g loading, and the non-g part

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The G Factor: The Science of Mental Ability
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface ix
  • Acknowledgments xiii
  • Chapter 2 - The Discovery of G 18
  • Notes 39
  • Chapter 3 - The Trouble with "Intelligence" 45
  • Notes 68
  • Chapter 4 - Models and Characteristics of G 95
  • Chapter 5 - Challenges to G 105
  • Notes 133
  • Chapter 6 - Biological Correlates of G 137
  • Notes 165
  • Chapter 7 - The Heritability of G 169
  • Notes 197
  • Chapter 8 - Information Processing and G 203
  • Notes 261
  • Chapter 9 - The Practical Validity of G 270
  • Notes 301
  • Chapter 10 - Construct, Vehicles, and Measurements 306
  • Notes 344
  • Chapter 11 - Population Differences in G 350
  • Notes 402
  • Chapter 12 - Population Differences in G: Causal Hypotheses 418
  • Notes 516
  • Chapter 13 - Sex Differences in G 531
  • Notes 542
  • Chapter 14 - The G Nexus 544
  • Notes 579
  • Appendix A - Spearman's "Law of Diminishing Returns" 585
  • Appendix B - Method of Correlated Vectors 589
  • Appendix C - Multivariate Analyses of a Nexus 593
  • References 597
  • Name Index 635
  • Subject Index 643
  • About the Author 649
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