Challenging the 'Law of diminishing returns'

[Abstract]: 'The Law of Diminishing Returns' (Spearman, 1927) states that the size of the average correlation between cognitive tasks tends to be relatively small in high ability groups and relatively high in low ability groups. Studies supporting this finding have tended to contrast very low ability subjects (IQ < 78) with subjects from higher ability ranges and to use tests that have poor discriminatory power among the higher ability levels. In the first study described in this paper, tasks that provide good discrimination among the higher ability levels were used. A sample of High ability (N = 25) and of Low ability (N = 20) 15-years old boys completed four single tests, two with low and two with high g saturations, and two competing tasks formed from these single tests. The results indicated that, contrary to the predictions of the Law of Diminishing Returns, the amount of common variance was greater in the High ability group. It is suggested that the Law of Diminishing Returns does not take into account the factor of task difficulty and that there are situations where the exact reverse of this law holds. A second study again compared correlations obtained with extreme groups (N=28 & N=29), this time on measures of Perceptual Speed, which are easy for all ability levels. Results indicated that correlations among the Perceptual Speed measures were the same for both groups. In neither of these studies was there any support for the Law, which seems to be dependent on the very high correlations obtained from samples at the extreme lower end of the ability continuum

Competing tasks as an index of intelligence

[Abstract]: Most studies involving competing (or dual) tasks have been concerned with the investigation of models of attention and have stressed the importance of task characteristics in determining competing-task performance. The relatively few studies which have looked at indi¬vidual differences in competing-task performance suggest that measures of this performance could reflect operations which are central to cognitive functioning. This paper examines two key questions which stem from this research: is there a separate ability involved in competing-task performance? Is competing-task performance more indicative of general intellectual functioning? A battery composed of both single and competing tasks was presented to 91 Ss. Two sets of scores, primary and `secondary', were obtained from the competing tasks. The results indicate that `single' and `primary' scores are basically measuring the same thing but that secondary' scores measure what is perhaps a time-sharing factor. There is also some evidence that primary and secondary scores are more indicative of the general factor, as measured by this battery, than their single counterparts

The space of ideals in the minimal tensor product of C∗C^*-algebras

For $C^*$-algebras $A_1, A_2$ the map $(I_1,I_2)\to ker(q_{I_1}\otimes q_{I_2})$ from $Id^{\prime}(A_1)\times Id^{\prime}(A_2)$ into $Id^{\prime}(A_1\otimes_{\mathrm{min}} A_2) is a homeomorphism onto its image which is dense in the range. Here, for a$C^*$-algebra$A$, the space of all proper closed two sided ideals endowed with an adequate topology is denoted$Id^{\prime}(A)$and$q_I$is the quotient map of$A$onto$A/I$. New proofs of the equivalence of the property (F) of Tomiyama for$A_1\otimes_{\mathrm{min}} A_2$ with certain other properties are presented.Comment: 9 pages, minor mistakes were correcte