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Principal Components Factor analysis for the JCTI and SAT relationship

A principal components factor analysis has been performed with the data collected from 85 out of 119 persons, takers of the Jouve-Cerebrals Test of Induction (JCTI), whom reported previously obtained Scholastic Assessment Test-Recentered (SAT-I) scores. Individuals with perfect scores on the Mathematical and/or the Verbal part of the SAT-I were discarded in order to avoid ceiling effects. The SAT-I is often described as an objective, standardized, three-hour test that measures verbal and mathematical reasoning abilities that students develop over time, both in and out of school. Many US colleges and universities use the SAT for admission purposes because it is purported to predict successful performance in college. The recentered SAT, used between 1995 and 2005, was divided into two sections, (i) a verbal part with emphasis on critical reading in which vocabulary was tested in the context of reading passages and in analogy and sentence-completion questions and (ii) a mathematical part with emphasis on data interpretation and applied math questions in which calculators were permitted but not required.

Long-time evidence exists to suggest that the SAT is closely related to g. Prepared originally to be an IQ test for the US Army (Lemann, 1999) and despite of its revisions over the years, the SAT is still highly correlated with intelligence tests. Frey and Detterman (2003) reported a correlation of .72 between the SAT-I and the Advanced Progressive Matrices (APM) by Raven (1998). Additionally, these authors indicated that the pre-recentered SAT correlated from .56 to .82 with intelligence measures, with most correlations being higher than .70 in magnitude. Likewise, a study conducted by Raz, Willerman, Ingmundson, and Hanlon (1983) resulted in a correlation between the SAT and the Culture Fair Intelligence Test (Cattell, Krug, & Barton, 1973) of .81.

Factor analysis is a common method of examining the patterns of relationships among a set of variables and is a commonly recommended analytical approach in order to evaluate the presence and structure of any latent constructs among a set of items, or tests (Cronbach, 1990; Kamphaus, 2001). For exploring the presence of a general latent trait among the JCTI and the two subscales of the SAT-I, the method of principal factor was chosen. Although the method known as principal components might have been justified on the basis of the high reliability of scores from these tests, this method begins with the assumption of perfect reliability, with a guessed communality of 1 for each variable. The principal factor method does not make such assumption beginning with r2 (the squared correlation of all the other subtest scores with the one being considered) in the diagonal and then estimating the communality of each variable through an iterative process until h2 (the maximal communality estimate) is reached. That estimate is then placed into the diagonal of the matrix for the final factor extraction. In such analyses the first unrotated factor to be extracted is commonly interpreted as g. However, the nature of this first axis relatively represents the nature of each variable which served in the analysis. The correlations of each test with this factor, in other words, the factor loadings, are indicators of the degree to which each subtest is a measure of ability as a whole as opposed to more specific components of ability.

Results

In this study, a first unrotated factor was extracted with an eigenvalue of 2 and accounted for 70% of the variance of scores. As shown in Table 1, the highest loading was observed for the Mathematical SAT-I which correlated at .94 with this first axis. The reasoning index of the JCTI was also very highly saturated, with a factor loading of .88, and the Verbal subscale of the SAT-I shown a significantly lower loading at .67. Even though the scholastic assessment requires knowledge, these two parts of the SAT-I are indeed called reasoning tests and this latent trait is a probable representation of general reasoning. This factor is noted as gθ or general ability for a reasonable but singular representation.

References.

  Cattell, R. B., Krug, S. E., & Barton, K. (1973). Technical Supplement for the Culture Fair Intelligence Tests, Scales 2 and 3. Champaign, IL: Institute for Personality and Ability Testing.
  Cronbach, L. J. (1990). Essentials of psychological testing (5th ed.). Boston, MA: Addison-Wesley.
  Frey, M. C., & Detterman, D. K. (2003). Scholastic Assessment or g? The Relationship Between the Scholastic Assessment Test and General Cognitive Ability. Psychological Science, 15 (6), 373-378.
  Kamphaus, R. W. (2001). Clinical assessment of child and adolescent intelligence (2nd ed.). Needham Heights, MA: Allyn & Bacon.
  Lemann, N. (1999). The big test: The secret history of the American meritocracy. New York City, NY: Farrar, Straus, & Giroux.
  Raz, N., Willerman, L., Ingmundson, P., & Hanlon, M. (1983). Aptitude-related differences in auditory recognition masking. Intelligence, 7 (2), 71-90.
  Raven, J., Raven, J. C., & Court, J. H. (1998). Raven Manual: Sec. 4. Advanced Progressive Matrices (1998 ed.). Oxford: Oxford Psychologists Press.

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

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.

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