Gf=g revisted: Maybe not

Does Gf=g?

The possibility that Gf is isomorphic with general intelligence (g - if you believe g exists) has been discussed/debated in many research articles during the past few decades.  Kvist and Gustafsson (2008) recently took a new approach to investigating the viability of the Gf=g hypothesis [The reference and the journal abstract are included at the bottom of this post.]  These researchers use Cattell's investment theory to test the hypothesis. They argue, as per an extension of Catell's Investment hypothesis, that in populations with homogeneous learning experiences the Gf=g relationship would hold, while in more heterogenous populations the relationship between Gf and g would not approach unity.  As noted in their abstract and article, their research confirmed their hypothesis. 

They then attempt to explalin the lack of the Gf=g relation in other studies as per population/sample differences (viz., the failure to find this relation is possibly due to samples that are heterogeneous with regard to differential opportunities to develop knowledge and skills).  They attempt to explain Carroll's (2003) failure to find Gf=g in an analysis of the WJ-R norm data.  According to Kvist and Gustafsoon:

•  "in the study by Carroll (2003) previously referred to, which failed to find the perfect relation between Gf and g, the matrices analyzed were pooled across the ages from kindergarten to adulthood, and this may have caused a population heterogeneity which prevented the perfect relation to appear.  These data could be reanalyzed with the data organized into homogeneous age groups to test this hypothesis." (p. 433).

As coauthor of the more current Woodcock-Johnson III (where the broad CHC constructs [Gf, Gc, Glr, etc.] have even better construct validity than the WJ-R), I thought I'd take a peak at the Gf-->g loadings in the age-differentiated analyses reported in the WJ III Technical Manual (McGrew & Woodcock, 2001).  Below are the Gf loadings on g (by five age-differentiated groups), as well as other broad factor loadings that were of similar magnitude or higher in each respective group (click here for more complete summary tables).

• 6 to 8 years --   Gf (.96), Ga (.98)
• 9 to 13 years -- Gf (.89), Gsm (.91)
• 14-19 years  --  Gf (.92), .Gc (.90)
• 20-39 years --   Gf (.92), Ga (.96), Glr (.95)
• 40 and above -- Gf (.94), Ga (.97)

What to conclude? First, if I can find the time, I could re-run these models and constrain the Gf-->g loading to 1.0 and do a chi-square difference test (alas...so much data...so little time).  However, it is my experience that latent factor loadings in the high .80's and low .90's typically fail this test.  More importantly, notice the fact that other broad CHC abilities show latent factor g loadings equal to (and sometimes a bit higher) than Gf.  The above results, which follow Kvist and Gustafsson's recommendation to analyze the data by different age levels (and not pool into a single grand wide-age span sample), in my judgement, failsto support their hypotheses for the failure to find the Gf=g relation.  So....the Kvist and Gustafsson findings need to be tempered with the possible alternative hypothesis that studies may or may not replicate the Gf=g relation due to study differences in the type and breadth of markers used to operationalize ability constructs (that are then modeled to load on g).


Kvist, A. & Gustafsson, J-E. (2008) The relation between fluid intelligence and the general factor as a function of cultural background: A test of Cattell's Investment theory.  Intelligence, 36, 422-436 (click to view)

• Abstract:  According to Cattell's [Cattell, R.B. (1987). Intelligence: Its structure, growth and action. New York: North-Holland.]Investment theory individual differences in acquisition of knowledge and skills are partly the result of investment of FluidIntelligence (Gf) in learning situations demanding insights in complex relations. If this theory holds true Gf will be a factor of General Intelligence (g) because it is involved in all domains of learning. The purpose of the current study was to test the Investment theory, through investigating the effects on the relation between Gf and g of differential learning opportunities for different subsets of a population. A second-order model was fitted with confirmatory factor analysis to a battery of 17 tests hypothesized to measure four broad cognitive abilities The model was estimated for three groups with different learning opportunities (N=2358 Swedes, N=620 European immigrants, N=591 non-European immigrants), as well as for the total group. For this group the g–Gf relationship was .83, while it was close to unity within each of the three subgroups. These results support the Investment theory.
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