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You are correct that the WISC-V indices were derived from only their first two subtests. In addition, the GAI/FSIQ do not include all of the subtests that contribute to the primary indices, and the FSIQ further does not include all of the CPI (WMI/PSI) subtests. (The GAI expressly does not include any of them, of course.) GAI has the two primary verbal subtests, the two primary fluid reasoning subtests, and the first visual spatial subtest (block design). The FSIQ adds one subtest each from WMI (digit span) and PSI (coding).
Which, you'll notice, means that the FSIQ is not the average of the GAI and the CPI, consisting as it does of 5/7 GAI subtests, and 2/7 CPI subtests. (If you've been looking at documents pertaining to the WISC-IV, I can see how this detail may have slipped by, since it changed on the test revision.) In fact, the GAI/FSIQ are not even evenly constituted from the three indices considered more reasoning-focused, since VS only has one subtest contributing.
If you feel like digging through this () intercorrelation tables by age for the indices and subtests begin on page 48. You'll see that generally, the FSIQ has the best intercorrelation numbers with the GAI, followed by the VCI/FRI. (For obvious reasons). The VSI and CPI come after that.
I have a feeling I've missed one of your questions somewhere along the way, so please ask again if not satisfied!
...pronounced like the long vowel and first letter of the alphabet...