by DAN CALLOWAY
Published 9 September 2010
WEAVERVILLE, NC - A variable construct that would be difficult to measure directly is intelligence. However, using the concept of factor analysis as outlined in Vogt (2007) and as discussed in Darlington (2010), one might be able to learn more about the degree of intelligence, say, in humans, if we used a set of multiple indicators such as math, verbal, and spatial skills. These three indicators are much easier to measure using standard tests that could be developed to evaluate those skill levels. The math indicator could be a simple 50-question test using multiple-choice responses of a, b, or c, where the most correct response to any question would be a unique math solution represented by the answers corresponding to either a, b, or c. The scale that could be employed might be a categorical numerical-valued range scale where scores from 0 – 33 correspond to poor math abilities (assigned a value of 0), scores of 34 – 66 correspond to intermediate math abilities (assigned a value of 1), and scores ranging between 67 – 100 represent advanced math abilities (assigned a score of 2). Similarly, the indicator of verbal skills could be based on a 50-question multiple-choice test with responses of a, b, or c that correspond to unique answers to verbally-related questions, such as use of tense, case, spelling, and grammar. The scale that would be employed here would be identical to the scale created to evaluate the math skills; that is, 0 – 33 corresponding to poor verbal skills (assigned a value of 0), 34 – 66 corresponding to intermediate verbal skills (assigned a value of 1), and achieving a score in the range of 67 – 100 would correspond to advanced verbal skills (assigned a value of 2). And, finally, the indicator of spatial skills might be a little more difficult to measure, but could be reasonably measured using the 50-question multiple-choice test method wherein responses of a, b, or c would represent the unique response sought as an answer to the question. However, in this test, the use of 3-dimensional diagrams would be required to represent the spatial relationships among the various factors identified within each question, and the solutions representing the most correct response. Here again, a categorical numerical-valued range scale of 0 – 33 (assigned a value of 0), 34 – 66 (assigned a value of 1), and 67 – 100 (assigned a value of 2) could be developed to represent poor, intermediate, and advanced spatial skills of the individual being tested. The overall measure of intelligence would be determined by the equation:
I = 2 (M + V) + S ,
where M, V, and S correspond to the numerical values assigned to the three indicators of math, verbal, and spatial skills, respectively, determined from the overall scores in each indicator being measured and compiled from the three tests given to the subject; and I represents the measure of intelligence of the subject ranging from 0 to 10, where 0 would represent a score of 0 in all three categories of skills being tested and 10 would represent a maximum score of 2 in each category within the skills being evaluated. As connoted in the equation above, less emphasis is placed on the math and verbal skills than is the spatial skills in determining overall measure of intelligence of the individual being tested.
The role of factor analysis in the above example is to find patterns in the correlations among the variables. These patterns are used to cluster the variables into groups, referred to as factors. These factors can then be treated as new composite variables (Vogt, 2007). The development of a correlation matrix would be necessary among the factors identified within the three indicators of math, verbal, and spatial skills, noted earlier in order to determine which were highly correlated and which were not, thus determining whether the factor would be included or excluded, respectively, from the matrix being considered.
References:
Darlington, R. B. (2010). Factor Analysis. Retrieved from http://www.psych.cornell.edu/Darlington/factor.htm.
Vogt, W. P. (2007). Quantitative Research Methods for Professionals (Custom., p. 334). Boston, MA: Allyn & Bacon.
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