Lack of asymmetry of g: investigating the relationships between the subtests of an high level mental ability test

Xavier Jouve — Fri, 18 Feb 2011 15:18:50 +0000

I’m working on a paper about an investigation of the internal structure of the C-10. To those unfamiliar with the C-10, this psychometric questionnaire is a liberally timed test that consists in three subtests, verbal analogies (ANA), numerical sequences (SEQ) and word similarities (SIM), each one prepared with 20 items (for examples of items that make up the C-10, see Table 1). It aims at assessing cognitive ability in gifted individuals, most likely in adults and in older adolescents for whom traditional scales may be of too restrictive ceiling. Problems were written so that they were expected to be sufficiently discriminative in such individuals.

Participants. The sample of participants consisted in 102 individuals aged 12 to 85 (M = 36.17, SD = 13.10). Of these, 10 (10.2%) were females, 83 (84.7%) were males. The majority of these participants attended university (73.4%); among them, 13 (13.3%) have completed a doctorate, 13 others a masters, and 7 (7.1%) indicated to have studied until completion of a bachelor degree. The remaining 39 (39.8%) did not mentioned a precise college level. Even though the C-10 was only available in English, participants were not all English natives. The cohort gathered 27 (27.5%) English, 12 Germans (12.2%), and small groups of Frenchs, Greeks, Indians, Italians, Portuguese’s and Spanish’s – each of these groups of examinees accounted for not more than 6% of the total sample.

People who spent time taking the C-10 were for the most part, members of clubs for intellectually gifted individuals, such as Cerebrals and Mensa, which the respective cut-off for applying is the percentile rank of 99.7 and 98 on a supervised intelligence test. These levels roughly correspond to 141 and 130 of a deviation-IQ using a mean of 100 and 15 points per standard deviation. As an indication, 20 participants took the JCCES, both tests appeared highly correlated (r_corr = .84), and their average CEI was 142.43 (SD = 11.95).

Procedure. The C-10 was proposed as a contest on the Cerebrals Society website during a six months period. Participation was free, and all visitors were welcomed to send their answers. Instructions given to the participants were straightforward to simply answer as best as they can with permission to use references for the verbal analogies and calculators for the number series if needed. The questionnaire was available in Portable Document Format (PDF) for being easily printed along with an electronic form to submit the answers.

Results of interest.The three subtests of the C-10 were each observed to relate highly to a general ability factor (g(β)), or in order words to the first unrotated axis of a principal components factor analysis, with loadings ranging from .88 to .92. This factor accounted for 80.5% of the total trace. Reasoning (RG) and verbal (V) factors were also found but did not show high statistical significance (the required eigenvalue to extract them was a little less than.34).

Furthermore, items of the test appeared to be scaled according to a Guttman’s effect when represented all together into a Euclidian space. This indicates the existence of a continuum from the easiest to the hardest item, no matter the differences in the tasks involved.

Discussion. These findings suggest a significant appearance of a general latent trait among items of the C-10. In a general population representative cohort, this would not have been surprising, but considering the difficulty of the items and the singularity of the sample, relatively to the level of intelligence; the lack of asymmetry of g (Evans, 2000) is an interesting fact to note. Is this asymmetry a phenomenon linked to g as suggested by previous authors, or is it an artifact because of the lack of appropriate ceiling in traditional intelligence tests?

I’ve uploaded the draft of this paper. I apologize for the grammatical and spelling mistakes.

Two-dimensional scaling for the items of the C-10

Xavier Jouve — Tue, 07 Sep 2010 17:47:38 +0000

I’ve performed a quick multidimensional scaling analysis for the items of the C-10. The study is based on very few subjects (N=42) and has to be taken carefully.

The C-10 is prepared with 20 verbal analogies, 20 numerical sequences and 20 word similarities. With such a difference in items along with the small sample size, a Guttman effect (1955) wasn’t expected to be shown. However, as can be seen in Figure 1, a horse-shoe shape appeared even if the inadequacies are not perfect for a two-dimensional solution (STRESS=.30, RSQ=.66) -which is quite logical-.

Of course, it would be too early to draw conclusions out of these preliminary results, but one can make the assumption that even if the items apply different cognitive abilities, they are sufficiently g-loaded for a continuum from the easiest to the hardest one to be shown in a two-dimensional Euclidean space.

References.
Guttman, L (1955). A generalized simplex for factor analysis. Psychometrika, 20, pp 173-192.

Cerebrals Contest 2010

Xavier Jouve — Mon, 14 Jun 2010 16:48:13 +0000

I’ve uploaded the questionnaire for the new Cerebrals Contest.

LINK OUTDATED.

2-Parameters Logistic Model Item Characteristic Curves for the Cerebrals Contest 2009

Xavier Jouve — Wed, 31 Mar 2010 12:42:00 +0000

I’ve finally found the time today to report the characteristic curves for the Cerebrals Contest 2009 using the 2-Parameters Logistic Model.

Which Word? questions number 2, 4 and 7 didn’t show an appropriate response function.

Download here (pdf)

Cogn-IQ » Contest

Lack of asymmetry of g: investigating the relationships between the subtests of an high level mental ability test

Two-dimensional scaling for the items of the C-10

Cerebrals Contest 2010

2-Parameters Logistic Model Item Characteristic Curves for the Cerebrals Contest 2009