Spearman's Two-Factor Theory, Spearman found the measure of intelligence tended to correlate to different degrees with each other. He then put together a theory of general intelligence that postulated the existence of general intelligence.

This theory has become known as a two-factor theory of intelligence with g representing the portion of the variance that all intelligence tests have in common and the remaining portions of the variance are accounted for other components (s), or error components (e).

These tests show a high positive correlation with other intelligence tests were thought to be highly saturated with g, whereas tests with low or moderate correlations with other intelligence tests were viewed as possible (Cohen, Sturman&Swerdlik, 2013).

Cattell-Horn two factor theory and the Cattell-Horn and Carroll's CHC model are similar in some respects, among them the designation in broad abilities. One difference between these two models involves the existence of general intellectual (g) factor. For Carroll the g factor is the third stratum factor.

By contrast, g has no place in the Cattell-Horn model. Another difference between the two models questions whether or not abilities labeled quantitative knowledge and reading writing ability should be considered a distinct (Cohen et al., 2013).

The McGrew Flanagan CHC model makes no provision for the general intellectual ability factor (g). The model was the product of efforts designed to improve the practice of psychological assessment in education by identifying tests from different types that could be use to offered comprehensive assessment of abilities. According the McGrew and Flanagan g was not employed in their CHC model because it lacked the utility in psycho educational evaluations.

Excluding (g) did not mean that the model did not allow separating general human ability or did not exist they felt it did not have relevance to the assessment or interpretation (Cohen et al., 2013).
Wechsler Intelligence Scale for Children, fourth and fifth editions.

The WISC-IV was published in 2003, this test represents the result of a five year research program which involved several research stages. The fourth edition is said to be noticeable "warming" to the CHC model of intelligence, this believed (g) to be very much alive and well in the instruments designed to measure intelligence.

Kaufman Assessment Battery for Children, second edition.

The K-ABC focuses on information processing and its distinction between sequential and simultaneous processing (Cohen et al., 2013). This is designed to measure the processing and cognitive abilities of children and adolescents ages ranging from 3 - 18.

The intelligence theory that this follows is the Luria's Information Processing Approach. It is grouped into categories that require sequential processing and simultaneous processing of information (Intellectual Assessment, 2009).
Stanford-Binet Intelligence Scales, fifth edition.

The Stanford-Binet Intelligence Scales fifth edition was designed for administration to assess those from 2 to 85. The test yields a number of scores including IQ. Content related evidence of validity for the SB5 was found in many ways. It is said that the SB5 and Wechsler tests were to supposed to tap (g) (Cohen et al., 2013).This test relies on the Cattell-Horn and Carroll's CHC Model and is designed to access intelligence and cognitive abilities (Intellectual Assessment, 2009).

Woodcock-Johnson Tests of Cognitive Abilities, third or fourth editions.

The WJIII is a psycho educational test package which contained two tests, 1) Tests of Achievement and Tests of Cognitive Abilities. The WJ-III holds a measure of general intellectual ability (g) as well as measures of cognitive abilities, achievement, and oral language (Cohen et al., 2013).

The Woodcock-Johnson is used for ages 2 - 90. The intelligence theories that this relies on are Cattell-Horn and Carroll's CHC Model (Intellectual Assessment, 2009).

I believe that the theory of intelligence I find would most affiliate with the context of my professional goals would be the Woodcock Johnson Tests of Cognitive Abilities due to the ability of measuring cognitive ability and oral language. Working in the education field this test will allow for an understanding of where a student is on the academic level. This will give the instructors the opportunity to plan for intervention on an academic level.

Reference

Cohen, R.J., Swerdlik, M.E., &Sturman, E.D. (2013). Psychological testing and assessment (8thed.). Dubuque: McGraw-Hill Education. (2009). Intellectual Assessment Theories and Tests. [Power point slides]