Following up with the previous analyses, I looked at the relationship between the variance components and g-loadings in La Buda et al. (1987), a study which was based on a sample from the Colorado Reading Project. This study provided variance component estimates computed with LISREL and a subtest correlation matrix. To extract g-loadings, I used:

MATRIX DATA VARIABLES=INF SIM VOC COMP PA PC BD OA ARI DS CODE

/contents=corr

/N=200.

BEGIN DATA.

1

0.43 1

0.52 .47 1

0.47 0.46 0.51 1

0.27 0.15 0.23 0.16 1

0.22 0.23 0.24 0.24 0.13 1

0.19 0.09 0.03 0.06 0.17 0.28 1

0.18 0.18 0.13 0.19 0.14 0.22 0.44 1

0.33 0.27 0.19 0.26 0.13 0.09 0.29 0.24 1

0.09 0.19 0.21 0.12 0.03 0.10 0.22 0.16 0.39 1

0.05 0.00 0.11 0.05 0.06 -.01 0.17 0.22 0.23 0.18 1

END DATA.

EXECUTE.

FACTOR MATRIX=IN(COR=*)

/MISSING LISTWISE

/PRINT UNIVARIATE INITIAL CORRELATION SIG DET KMO EXTRACTION

/PLOT EIGEN

/CRITERIA MINEIGEN(1) ITERATE(25)

/EXTRACTION PC

/ROTATION NOROTATE

/METHOD=CORRELATION.

In the MCV literature there is some disagreement as to which g-loadings should be used. Some argue that only sample g-loadings should be used, while other maintain that it is preferable to use g-loadings derived from numerous samples. Given this situation, I correlated the variance components with the (a) g-loadings derived from the correlation matrices for the sample, (b) the sample g-loadings corrected for attenuation using the standardization reliabilities presented in Kan (2011), (c) the corrected g-loadings based on the average g loadings across numerous Wechsler’s editions, and (d) the corrected g-loadings based on the WISC-R standardization — the WISC-R being the test given in this study. Results below:

Generally, in this sample, there was no non trivial positive correlation between g and c^2. Interestingly, the correlations varied considerably depending on which g-loadings were adopted. This situation introduces the question: Which g-loadings should be used when conducting such an analysis — the loadings based on the specific sample with corrections based on the standardization sample, the loadings with corrections based on the standardizations sample, or the loadings based on the averages across editions? As usual, I don’t even know how to begin to think about this.

The g-loading and reliabilities reported in Kan (2011) are as below:

**References**

Kan, K. J. (2012). The nature of nurture: the role of gene-environment interplay in the development of intelligence.

LaBuda, M. C., DeFries, J. C., & Fulker, D. W. (1987). Genetic and environmental covariance structures among WISC-R subtests: A twin study. Intelligence, 11(3), 233-244.

I’m in a hurry, and I’ll reply to other comments later, notably on the SQRT(reliability) formula. But here, as for your question : which g-loadings should you use? Simple. Recall what Nijenhuis said in Score gains on g-loaded tests: No g.

Because our sample was not large and quite specific, estimates of g loadedness were taken from Lynn, Allik, and Irwing’s (2004) item analysis of RSPM in Estonia using a large (N=2735), nationally representative sample.So, do not hesitate if you think the sample is quite specific, not representative, or too small, and all.