An Evaluation of Spearman's Hypothesis by Manipulating g Saturation

Spearman's Hypothesis holds that the magnitude of mean White–Black differences on cognitive tests covaries with the extent to which a test is saturated with g. This paper evaluates Spearman's Hypothesis by manipulating the g saturation of cognitive composites. Using a sample of 16,384 people from the General Aptitude Test Battery database, we show that one can decrease mean racial differences in a g test by altering the g saturation of the measure. Consistent with Spearman's Hypothesis, the g saturation of a test is positively and strongly related to the magnitude of White–Black mean racial differences in test scores. We demonstrate that the reduction in mean racial differences accomplished by reducing the g saturation in a measure is obtained at the cost of lower validity and increased prediction errors. We recommend that g tests varying in mean racial differences be examined to determine if the Spearman's Hypothesis is a viable explanation for the results.     

Contributions to the mathematical theory of human relations. IV

An attempt is made to define and treat analytically the concept of individual freedom in a society. Two possible definitions are briefly discussed. One takes as a measure of freedom the ratio (w ₀ –w)w ₀, wherew ₀ is the maximum amount of work that a person can physically perform per unit time andw is the amount of work which he has actually to perform per unit time in a given society. The other definition takes as a measure of freedom that fraction of an individual's time during which he can indulge in any activity of his own choice without interfering with other individuals. Expressions are derived by way of illustration, giving the individual freedom in terms of other parameters which characterize the social structure.     

Assessing sensitivity in a multidimensional space: some problems and a definition of a general d'

This article provides a formal definition for a sensivity measure,d′ _g , between two multivariate stimuli. In recent attempts to assess perceptual representations using qualitative tests on response probabilities, the concept of ad′ between two multidimensional stimuli has played a central role. For example, Kadlec and Townsend (1992a, 1992b) proposed several tests based on multidimensional signal detection theory that allow conclusions concerning the perceptual and/or decisional interactions of stimulus dimensions. One proposition, referred to as thediagonal d′test, relies on specific stimulus subsets of a feature-complete factorial identification task to infer perceptual separability. Also, Ashby and Townsend (1986), in a similar manner, attempted to relate perceptual independence to dimensional orthogonality in Tanner’s (1956) model, which also involvesd′ between two multivariate signals. An analysis of the proposedd′ _g reveals shortcomings in the diagonald′ test and also demonstrates that the assumptions behind equating perceptual independence to dimensional orthogonality are too weak. Thisd′ _g can be related to a common measure of statistical distance, Mahalanobis distance, in the special case of equal covariance matrices.     

A statistical test for means of samples from skew populations

This paper presents a test for determining significance of differences between means of samples which are drawn from positively skewed populations, more specifically, those having a Pearson Type III distribution function. The quantity 2npx _g /x _p (wherep equals the mean squared divided by the variance andn is the number of cases in the sample), which distributes itself as Chi Square for 2np degrees of freedom, may be referred to the tables of Chi Square for testing hypotheses about the value of the true mean. For two independent samples, the larger mean divided by the smaller mean, which distributes itself asF for 2n ₁ p ₁ and 2n ₂ p ₂ degrees of freedom, may be referred to theF distribution tables for testing significance of difference between means. The test assumes that the range of possible scores is from zero to infinity. When a lower theoretical score limit (c) exists which is not zero, the quantity (Mean —c) should be used instead of the mean in all calculations.     

Investigations of the optical spectra and EPR g-factors for the tetragonal Ce3+ centers in YPO4 and LuPO4 crystals

The optical spectral band positions and EPR g-factors (g_‖ , g _⊥) for the tetragonal Ce³⁺ centers in YPO₄ and LuPO₄ crystals with the zircon-structure are calculated using a complete diagonalization (of the energy matrix) method (CDM) related to 4f¹ ions in tetragonal symmetry. In this method, the Zeeman interaction term are added to the Hamiltonian in the conventional CDM and so no perturbation calculations are required to obtain the g factors. The crystal-field parameters used in the calculations are obtained from the superposition model in which the local lattice relaxation related to the bonding lengths is considered. The calculated results are in reasonable agreement with the experimental values. It is found that the four observed optical bands for both the systems can be attributed to Ce³⁺ ions in a tetragonal crystal field.     

Ability EI as an intelligence? Associations of the MSCEIT with performance on emotion processing and social tasks and with cognitive ability

Associations among the MSCEIT, a broad-bandwidth measure of ability emotional intelligence (EI), self-report EI, social perception ability, psychometric intelligence and performance on inspection time (IT) tasks, which assessed the speed of processing of emotional and non-emotional information were investigated in two student samples (N=99, 199). The main findings were that MSCEIT scores were unrelated to fluid ability or speed of non-emotional information processing as assessed by IT, but evidence for associations of MSCEIT scores with crystallised ability was found. Positive associations were found between MSCEIT scores, self-report EI and some emotion/social task scores. The results suggest that EI as assessed by the MSCEIT has some properties of an intelligence and is more closely related to crystallised than to fluid ability. The relatively small MSCEIT/g _c correlations suggest that the MSCEIT is not a pure ability measure, although restriction of range in the samples used may also be relevant. More work, and the development of new measures, is required to determine whether performance EI has a fluid component.     

Cognitive,behavioral and psychological functioning in children with metopic synostosis: a meta-analysis examining the impact of surgical status

Neurodevelopmental delays are known to occur in children with metopic synostosis, but it is presently unclear whether the cognitive, behavioral and psychological outcomes of children with metopic synostosis differ to those of their healthy peers. This meta-analysis consolidated data from 17 studies (published prior to August 2017) that examined the cognitive, behavioral and psychological outcomes of children (n = 666; aged ≤19 yrs) with metopic synostosis. Hedges’g (g_w) effect sizes compared the outcomes of samples with metopic synostosis (unoperated, operated) to healthy controls or normative data and, where available, the prevalence of problems/disorders was calculated. Children with unoperated metopic synostosis performed significantly worse than their healthy peers on measures of: general cognition (g_w = ?.38), motor functioning, (g_w = ?.81), and verbal (g_w = ?.82) and visuospatial (g_w = ?.92) abilities. Children with operated metopic synostosis performed significantly worse on measures of motor functioning (g_w = ?.45), visuospatial skills (g_w = ?.32), attention (g_w = ?.50), executive functioning (g_w = ?.36), arithmetic ability (g_w = ?.37), and behavior (g_w = ?.34). Cognitive, behavioral, and psychological problems were prevalent, but variable. Overall, the cognitive, behavioral, and psychological outcomes of children with metopic synostosis are generally worse than their healthy peers, regardless of surgical status. However, research is sparse, samples small, controls are rarely recruited, and the severity of metopic synostosis often not stated. Nevertheless, the findings suggest that children with metopic synostosis are likely to experience a variety of negative outcomes and should therefore receive ongoing monitoring and support.     

Generalizations of the partial,part and bipartial canonical correlation analysis

Theg ₁- andg ₂-bipartial canonical correlation analyses are developed as generalizations of the partial, part, and bipartial canonical correlation analysis. Illustrative examples are provided.     

Group differences and first principal-component loadings in the Hawaii family study of cognition: a test of the generality of ‘Spearman's hypothesis’

The generality of Spearman's hypothesis that varying differences between whites and blacks on various tests of mental ability are correlated with their g-loadings was tested by analyzing group data from the Hawaii Family Study of Cognition. Data from the three largest ethnic groups tested in the Hawaii Study (Americans of Japanese, Chinese or European ancestry; total N = 5333) were subjected to a principal-component analysis and the first principal component was used as a measure of g. Ethnic group and generation (parent-offspring) differences on 15 tests of specific cognitive abilities were then correlated with their first principal-component loadings. In general, correlations between ethnic group differences and g-loadings are smaller than those recently reported for white-black differences by Jensen (1983); however, those between generation differences and g-loadings are larger. Ethnic group differences on first principal-component scores in the Hawaii Study are less than parent-offspring differences; thus, the correlation between group differences on tests of mental ability and their g-loadings may be a function of the magnitude of the group difference for general mental ability. Because a group difference on g requires group differences on tests which load on g, an observed group difference in general mental ability may necessarily result in a correlation between group differences on individual tests and their g-loadings.     

Effect of network connectivity on thermal properties of As30Te70– x Tl x glasses

Alternating differential scanning calorimetry (ADSC) studies were undertaken to investigate the effect of Tl addition on the thermal properties of As₃₀Te_{70– x} Tl _x (6?≤?x?≤?22 at%) glasses. These include parameters such as glass-transition temperature (T _g), changes in specific heat capacity (ΔC _p) and relaxation enthalpy (ΔH ^NR) at the glass transition. It was found that T _g of the glasses decreased with the addition of Tl, which is in contrast to the dependence of T _g in As–Te glasses on the addition of Al and In. The change in heat capacity ΔC _p through the glass transition was also found to decrease with increasing Tl content. The addition of Tl to the As–Te matrix may lead to a breaking of As–Te chains and the formation of Tl⁺Te^?AsTe_2/2 dipoles. There was no significant dependence of the change of relaxation enthalpy, through the glass transition, with composition.     

A comment on Birnbaum's three-parameter logistic model in the latent trait theory

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞,θ _g ). It is suggested that we should useθ _g as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group. The work described in this paper was partially done while the author was at University of New Brunswick, Canada, in 1968–1970, supported by NRC Grant APA-345 from National Research Council of Canada.     

Identifying the Source of Misfit in Item Response Theory Models

When an item response theory model fails to fit adequately, the items for which the model provides a good fit and those for which it does not must be determined. To this end, we compare the performance of several fit statistics for item pairs with known asymptotic distributions under maximum likelihood estimation of the item parameters: (a) a mean and variance adjustment to bivariate Pearson's X², (b) a bivariate subtable analog to Reiser's (1996) overall goodness-of-fit test, (c) a z statistic for the bivariate residual cross product, and (d) Maydeu-Olivares and Joe's (2006) M₂ statistic applied to bivariate subtables. The unadjusted Pearson's X² with heuristically determined degrees of freedom is also included in the comparison. For binary and ordinal data, our simulation results suggest that the z statistic has the best Type I error and power behavior among all the statistics under investigation when the observed information matrix is used in its computation. However, if one has to use the cross-product information, the mean and variance adjusted X² is recommended. We illustrate the use of pairwise fit statistics in 2 real-data examples and discuss possible extensions of the current research in various directions.     

Comparing subtest profiles of g loadings and correlations with RT measures

It is argued that if a response time (RT) measure correlates with psychometric test (PT) scores because it shares variance in common with general intelligence, g, then the profile of g loadings for a set of PTs would be predictable from the profile of correlations between the RT measure and the PT scores. On the other hand, if an RT correlates with PTs through variance not shared with g, the g loadings of the PTs should be unrelated to the correlations between RT and PTs. The profiles of g loadings and correlations with RT were compared for a set of 6 RT measures and 8 PT scores from Smith and Stanley (1983). To demonstrate statistical significance, standard errors of the statistics were generated by Efron's bootstrap technique (Efron, 1979). It was clearly shown that the profile of the PT's g loadings could be well predicted from the RT-PT correlations for four of the RT measures. It can be concluded that RT tasks do measure general intelligence. Analysis of the errors in prediction suggested that the RTs may correlate more with fluid than crystallized intelligence.     

Determination of glass-forming ability of Ge1− x Sn x Se2.5 (0 ≤ x ≤ 0.5) alloys using differential scanning calorimetry

The glass-forming ability of Ge_{1? x} Sn _x Se_2.5 (0 ≤ x ≤ 0.5) alloys was studied using differential scanning calorimetry. Samples were scanned at different heating rates under non-isothermal conditions. Various simple quantitative methods were employed to assess the stability of the glassy materials in the above-mentioned system. All of these methods are based on characteristic temperatures, such as the glass-transition temperature, T _g, the onset-of-crystallization temperature, T _c, and the peak crystallization temperature, T _p. A crystallization rate factor, K, has also been used as a measure of the thermal stability of the glasses. It was found that Ge_0.7Sn_0.3Se_2.5 was the least stable among all the samples.     

Monotonic measures of agreement for ranked data

The τ_b and y statistics are interpreted as rank-monotonic coefficients of partial agreement. Using a method of transposition employed by Pearson's r_i intraclass correlation coefficient, the τ_bi and y_i intraclass coefficients of total monotonic agreement are created. Transpositional measures of agreement like τ_bi and τ_i measure the combined effects of cell and marginal disagreement which make them particularly suitable for reliability studies. The coefficients are also made applicable to K > 2 sets of ranks.     

Examining interrelationships between the Cigarette Purchase Task and delay discounting among pregnant women

Two common behavioral economic simulation tasks used to study cigarette smoking are the Cigarette Purchase Task, a measure of cigarette demand, and delay discounting, a measure of the subjective value of rewards as a function of delays to delivery. Few studies have evaluated whether combining these tasks enhances understanding of smoking beyond either alone. The current study represents an initial evaluation of the intersection between cigarette demand indices and delay discounting among pregnant smokers by examining associations between these measures and whether a woman makes antepartum quit attempts before entering prenatal care (a reliable predictor of eventual quitting). Participants were 159 pregnant women enrolled in a smoking‐cessation trial. Low O _max and shallow discounting were each associated with antepartum quit attempts. Participants were next categorized into four subgroups (low O _max, shallow discounting; low O _max, steep discounting; high O _max, shallow discounting; high O _max, steep discounting) using median splits. Those with shallow discounting and low O _max were more likely to have made quit attempts than each of the other three subgroups. That is, steep discounting appears to undermine the association of low O _max and efforts to quit smoking during pregnancy while high O _max overshadows any protective influence associated with shallow discounting.     

THE DEVELOPMENT OF KNOWLEDGE CONCERNING WRITTEN ARITHMETIC: A CROSS-CULTURAL STUDY

This study is concerned with the manner in which Western mathematics is assimilated by children raised in traditional African cultures. It was predicted that after an initial period of difficulty in learning school arithmetic, African children (Baoulé and Dioula from the Ivory Coast) acquire basic concepts, develop invented strategies, and make errors similar to those of American children. Further, it was predicted that Dioula children, since they are members of a commercial culture, perform at a somewhat higher level than the Baoulé, members of a farming culture which does not seem to stress computational activity. To investigate these hypotheses, American, Baoulé, and Dioula children at two age levels were given a variety of arithmetic problems involving basic skills (e.g., reading numbers), number knowledge (e.g., place value), and calculational abilities (e.g., written computation). The results showed that, in general, older African and American children (fifth- and sixth-graders) were quite similar in all respects. The only large and significant differences occurred in the case of younger children (second- and third-graders). At this level American children generally performed at a higher level than Africans, as predicted, and Dioula occasionally at a higher level than Baoulé, also as predicted. At the same time, qualitative aspects of African and American children's performance were similar: for example, both groups made the same types and proportions of errors in written calculations. The results generally support the hypotheses and can be explained in terms of both educational and cognitive factors.     

Jensen Effects and African/Coloured/Indian/White differences on Raven's Standard Progressive Matrices in South Africa

A test is made to determine whether various ethnic group differences on tests of cognitive performance in South Africa are like the Black/White differences in the United States in being positively associated with a tests' g loadings, where g is the general factor of intelligence. A non-parametric re-analysis is made of data from 1056 White, 1063 Indian, 778 mixed-race “Coloured,” and 1093 Black 14 year olds on the Raven's Standard Progressive Matrices Test in South Africa, given without time limits by Owen (1992) [Personality and Individual Differences, 13, 149]. The new analyses showed that the more highly correlated an item was with g, the more it predicted the White/Indian/Coloured/African differences on the test (Spearman's rhos from 0.35 to 0.85; all Ps<0.01). The effects remained regardless of which group g was extracted from. Understanding group differences around the world requires new research on the nature and nurture of g.     

The evaluation of linear forms

This presentation deals with the evaluation and transformation of linear forms. Especial emphasis is given to implicit methods in which it is not necessary to find the explicit values,x _i . The relation of the Aitken triple product matrixCA ^–1 B to the result of a linear transformation of linear forms is noted, and the numerical computation of this triple product matrix is indicated with the use of the simple Abbreviated Doolittle solution. Application is also made to the evaluation ofA ^–1 and ofA ^–1 C.     

Unusual room-temperature compressive plasticity in nanocrystal-toughened bulk copper-zirconium glass

Cast Cu₅₀Zr₅₀ alloy rods with a diameter of 1?mm have been found to consist of a glassy phase containing fine crystalline particles with a size of about 5?nm. They have a glass transition temperature T _g of 675?K, and a large supercooled-liquid region extending 57?K above T _g. The rods exhibit a high yield strength of 1860?MPa and a Young's modulus of 104?GPa. Because they contain a dispersion of embedded nanocrystals, the as-cast bulk metallic glass rods can sustain a compressive plastic strain at room temperature of more than 50%, an exceptional value which is explicable by compensation of any shear softening by nanocrystal coalescence and pinning of shear bands.